\listfiles
\documentclass[12pt]{report}


\usepackage[all]{nowidow}
%\usepackage[none]{hyphenat}
\usepackage[intoc]{nomencl}
\textwidth=6in \oddsidemargin=1in \topmargin=1in
\textheight=9in  % 9in must include page numbers
\textfloatsep = 0.4in \addtocontents{toc}{\vspace{0.2in} \hfill Page\endgraf} 
\addtocontents{lof}{\vspace{0.2in} Figure\hfill Page\endgraf} 
\addtocontents{lot}{\vspace{0.2in} Table \hfill Page\endgraf}

\newcommand\upstrut{\rule{0pt}{14pt}}
\newcommand\downstrut{\rule[-6pt]{0pt}{6pt}}
\newcommand\mystrut{\upstrut\downstrut}

%\usepackage{comment}
\usepackage{pdflscape}
\usepackage{longtable}
\usepackage{gensymb}
\usepackage{lscape}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{multirow}
\usepackage{dcolumn}
\usepackage{caption}
\usepackage{setspace}
\usepackage{titlesec}
\usepackage{color}
\usepackage[left=1in,right=1in,top=1in,bottom=1in]{geometry} 
\usepackage[table]{xcolor}
\usepackage{amsfonts}
\usepackage{amsmath}
\usepackage{amsbsy,bm}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage{setspace}
\usepackage{rotating}
\usepackage{float}
\usepackage{stmaryrd}
\usepackage{multirow}
\usepackage{color}
\usepackage{soul}
\usepackage{caption}
\usepackage{eepic}
\usepackage{colortbl}
%\usepackage[authoryear]{natbib}
\usepackage {multirow}
\usepackage{setspace}
\usepackage{indentfirst}
\usepackage{titlesec}
\usepackage{subfig}
\usepackage[mathscr]{euscript}
\usepackage[titletoc,title]{appendix}
\usepackage[titletoc]{appendix}
%\usepackage[tocgraduated]{tocstyle}
\usepackage{tocbasic}

\usepackage{textcomp}
\usepackage{array}
\usepackage{listings}
\usepackage{setspace}
\usepackage{mathptmx}
\usepackage{colortbl}
\usepackage{graphicx}
\usepackage{amssymb, amsmath}
\usepackage{subfig}
\usepackage{epsfig}
\usepackage{times}
\usepackage{float}
\usepackage{rotating}
\usepackage{makeidx}
\usepackage{url}
\usepackage{multirow}
\usepackage{booktabs}
\usepackage[subfigure, titles]{tocloft}  
\usepackage{acronym}
\usepackage{datetime}
\usepackage{algorithm}
\usepackage{algorithmic}
\usepackage{geometry}

\renewcommand{\nomname}{LIST OF ABBREVIATIONS}
\makenomenclature
\graphicspath{{images/}}
\DeclareGraphicsExtensions{.pdf,.jpeg,.png,.PNG, .eps, .tiff}

\urlstyle{same}

\usepackage{makecell}
\usepackage{titletoc}
\usepackage{appendix}
\usepackage[nottoc]{tocbibind}
\setcounter{secnumdepth}{7}
\setcounter{tocdepth}{7} 


%new chapter/section and subsection commands
\newcommand{\hsuchapter}[1]{\chapter*{#1} \addcontentsline{toc}{chapter}{#1}} 
\newcommand{\hsusection}[1]{\section*{#1} \addcontentsline{toc}{section}{#1}} 
\newcommand{\hsusubsection}[1]{\subsection*{#1} \addcontentsline{toc}{subsection}{#1}} 

%%%%%%%Configure Table of Contents%%%%%%%%%%%%
\renewcommand{\contentsname}{TABLE OF CONTENTS}
%\renewcommand{\cftchapafterpnum}{\vskip5em}
%\renewcommand{\cftsubsecafterpnum}{\vskip25em}
\renewcommand{\cftchapfont}{\normalfont}
\renewcommand{\cftchappagefont}{\normalfont}
\renewcommand{\cftchapleader}{\cftdotfill{\cftdotsep}}

%%%%%%%Configure List of Figures%%%%%%%%%%%%
\renewcommand{\listfigurename}{LIST OF FIGURES}
\setlength{\cftfigindent}{0 em}
\setlength{\cftbeforefigskip}{0.2in}

%%%%%%%Configure List of Tables%%%%%%%%%%%%
\renewcommand{\listtablename}{LIST OF TABLES}
\setlength{\cfttabindent}{0 em}
\setlength{\cftbeforetabskip}{0.2in} 

%%%%%%%Configure Bibliography%%%%%%%%%%%%
\renewcommand{\bibname}{ \texorpdfstring{{REFERENCES\vspace{10mm}}}{REFERENCES}   }

%%%%%%%Configure Chapter Headings%%%%%%%%%%%%
\makeatletter
\def\@makechapterhead#1{%
	%  \vspace*{50\p@}%
	{\parindent \z@ \centering
		\normalfont
		\ifnum \c@secnumdepth >\m@ne
		\if@mainmatter
		\@chapapp\space \thechapter
		\par\nobreak
		\vskip 20\p@
		\fi
		\fi
		\interlinepenalty\@M
		#1\par\nobreak
		\vskip 40\p@
}}
\def\@schapter#1{\if@twocolumn
	\@topnewpage[\@makeschapterhead{#1}]%
	\else
	\@makeschapterhead{#1}%
	\@afterheading
	\fi}
\def\@makeschapterhead#1{%
	% \vspace*{-10\p@}%
	{\parindent \z@ \centering
		\normalfont
		\interlinepenalty\@M
		#1\par\nobreak
		\vskip 10\p@
}}


%%%%%%%Configure Section Headings%%%%%%%%%%%%
\renewcommand\section{\@startsection {section}{1}{\z@}%
	{-3.5ex \@plus -1ex \@minus .2ex}%
	{2.3ex \@plus.2ex}%
	{\centering\normalfont}}

%%%%%%%Configure Sub-Section Headings%%%%%%%%%%%%
\renewcommand\subsection{\@startsection {subsection}{2}{\z@}%
	{-3.5ex \@plus -1ex \@minus -.2ex}%
	{2.3ex \@plus.2ex}%
	{\noindent \normalfont  }}

%%%%%%%Configure Table of Contents Heading%%%%%%%%%%%%
\renewcommand{\@cftmaketoctitle}{
	\chapter*{\contentsname}
	\addcontentsline{toc}{chapter}{TABLE OF CONTENTS}}

%%%%%%%Configure List of Figures Heading%%%%%%%%%%%%
\renewcommand{\@cftmakeloftitle}{
	\chapter*{\listfigurename}
	%\addtocontents{lof}{Figure \hfill Page}
	\addcontentsline{toc}{chapter}{LIST OF FIGURES} }

%%%%%%%Configure List of Tables Heading%%%%%%%%%%%%
\renewcommand{\@cftmakelottitle}{
	\chapter*{\listtablename}
	\addcontentsline{toc}{chapter}{LIST OF TABLES}  }

\makeatother

\setcounter{section}{-1}     

% Define new commands here
\newcommand{\etal}{\emph{et al.}}
\newcommand{\leftsup}[2]{{\vphantom{#2}}^{#1}{#2}}
\newcommand{\leftsub}[2]{{\vphantom{#2}}_{#1}{#2}}
\newcommand{\leftsupsub}[3]{{\vphantom{#3}}^{#1}_{#2}{#3}}

\DeclareMathOperator*{\assembly}{\textbf{\Large A} }

\definecolor{lightblue}{rgb}{.90,.95,1} 
\newcommand{\hllb}[1]{
	\sethlcolor{lightblue}
	\hl{#1}
	\sethlcolor{yellow}
}

\newcommand{\hlc}[2][yellow]{{\sethlcolor{#1}\hl{#2}} }

% Define floats here
\floatstyle{plain}
\newfloat{Box}{h}{lob}
\newcommand{\boxedtext}[3]{
	\begin{Box} \caption{\small{#1}}
		\hspace{1.cm}
		\fbox{\begin{minipage}[c]{0.85\linewidth} 
				
				\small{#2}
				
		\end{minipage}}
		
		\label{#3}
	\end{Box}
}

\begin{document} 
	
	%\pagestyle{myheadings} \markright{\today}
	
	\pagenumbering{alph}
	
	\begin{titlepage}
		\thispagestyle{empty}\enlargethispage{\the\footskip}%
		\begin{center}
			{\setstretch{1.66} {New insights into ancient life: the Ediacara biota through the windows of taphonomy and fluid mechanics}\par }%
			\vskip.4in
			By
			\vskip .3in
			{Brandt M. Gibson}
			\vskip .3in
			
			\begin{doublespace}
				Dissertation\\
				Submitted to the Faculty of the \\
				Graduate School of Vanderbilt University \\
				in partial fulfillment of the requirements \\
				for the degree of \\ [.1in]
			\end{doublespace}
			
			\MakeUppercase{Doctorate of Philosophy} \\[.1in]
			in \\[.1in]
			{Earth and Environmental Science} \\[.25in]
			July 2020 \\[.25in]
			Nashville, Tennessee
			\vskip .5in
		\end{center}
		%%Uncomment for Signatures%%%
		\vfill
		Approved: \hskip 3.13 in Date:\\[1.2em]
		\rule{3.75in}{.5pt} \hskip 0.1in \rule{2.25in}{.5pt} \\[.01in]
		Simon A.F. Darroch, Ph.D.\\[.14in]
		\rule{3.75in}{.5pt} \hskip 0.1in \rule{2.25in}{.5pt}  \\[.01in]
		David J. Furbish, Ph.D.\\[.14in]
		\rule{3.75in}{.5pt} \hskip 0.1in \rule{2.25in}{.5pt}  \\[.01in]
		Mar\'{i}a Luisa S.P. Jorge, Ph.D.\\[.14in]
		\rule{3.75in}{.5pt} \hskip 0.1in \rule{2.25in}{.5pt}  \\[.01in]
		Marc Laflamme, Ph.D.\\[.14in]
		\rule{3.75in}{.5pt} \hskip 0.1in \rule{2.25in}{.5pt}  \\[.01in]
		James D. Schiffbauer, Ph.D.\\[.14in]
		\\[.14in]
		%%%%%%%%%%%%%%
		%%%%%%Uncomment  for Approved Names%%%%%%
%		\begin{center}
%			\begin{doublespace}
%				Approved:\\
%				Simon A.F. Darroch, Ph.D.\\
%				David J. Furbish, Ph.D.\\
%				Maria Luisa Jorge, Ph.D.\\
%				Marc Laflammme, Ph.D.\\
%				James D. Schiffbauer, Ph.D.
%			\end{doublespace}
%		\end{center}
	\end{titlepage} 
	
	\doublespacing 
	
	
	\pagenumbering{roman} \setcounter{page}{2}
	
	\chapter*{\vspace*{0.5\textheight} }%To my dogs and wife, for their midnight barks and snores...}
	\addcontentsline{toc}{chapter}{DEDICATION}
	\vspace{7mm}
	
	\chapter*{ACKNOWLEDGMENTS} 
	\addcontentsline{toc}{chapter}{ACKNOWLEDGMENTS}
	\vspace{7mm}
	I am indebted to a great number of individuals without whom this dissertation would not have been realized. While some of these individuals likely know the impacts their counseling had on this work, others may not recognize the importance of our brief meetings and informal discussions. During the journey of this dissertation, I learned much from not only Earth \& Environmental Science's faculty but from my fellow graduate students as well. 
	
	Importantly, I would like to thank my committee members, Mar\'ia Luisa S.P. Jorge,  David J. Furbish, Marc Laflamme, James D. Schiffbauer, and Simon A.F. Darroch. Your continuous entertainment of Ediacaran discussions, advice on optimizing methods for each experiment, and just fun discussions of really old waffles were pivotal for keeping these projects moving forward. Not only could I have not asked for a more supportive and intellectually engaging committee, I could never have imagined a better group of people to keep science and discovery both entertaining and rewarding. Malu, I always came away from our discussions with new ideas and unique perspectives that would have remained absent without you. David, almost none of this would be possible without your support, guidance, and friendship. More than an introduction to fluids, you showed me entire new ways of thinking. Marc, you seemed available at any time and were a wealth of information and guidance. Jim, I appreciated being called dingus. And, Simon, you opened a door to an undergraduate student who would have never known this world without your interception. Since that chance encounter, you have introduced me to an abundance of knowledge and gifted me many new experiences. All of these have influenced each of these chapters. You are an exceptional mentor, an inspirational scientist, and a true friend.
	
	Apart from my committee, there are several individuals who helped make this dissertation possible. I am indebted to Imran A. Rahman for sharing with me your extensive knowledge from combining the fields of fluid modeling and paleontology, and I am further indebted to you for setting the standard as a collaborator. I continue to strive to emulate your constructive behavior to maintain myself as a productive member of any collaboration. Next, I would like to acknowledge my family, Kesley J. Gibson, Edie B. Gibson, Michael A. Gibson, and my wife, Amber S. Gibson. The emotional support that you provided was exceptional, and I am eternally grateful. Thank you for always being there.
	
	\begin{flushleft}
		\singlespacing
		\tableofcontents
		
		\listoftables
		\newpage
		\listoffigures
		\newpage
		
		\addtocontents{toc}{%
			\protect\contentsline{chapter}{\normalsize \textnormal{Chapter} \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill \hfill }{}{}}
	\end{flushleft}
	
	\normalsize
	\doublespacing
	\pagenumbering{arabic}
	\setcounter{page}{1}
	%\sloppypar
	
%---------------------------------------------------------------------------------------------------------------%
%------------------------------------------------SECTION------------------------------------------------%
%---------------------------------------------------------------------------------------------------------------%
\chapter{Introduction}\label{section1intro}
\vspace{-7mm}
The Neoproterozoic Ediacara biota ($\sim571-539$ Ma) is an enigmatic group of soft-bodied multicellular organisms that represents the first radiation of complex, eukaryotic macroscopic life (Xiao \& Laflamme, 2009; Liu \textit{et al.}, 2015; Darroch \textit{et al.}, 2018a). These organisms first appear in late Ediacaran sediments ($\sim571-566$ Ma) preserved around Mistaken Point, Newfoundland (Liu \textit{et al.}, 2015; Pu \textit{et al.}, 2016), become more diverse and widespread in younger and shallower-water sediments ($\sim558-550$ Ma) from South Australia and the White Sea area of Russia (Martin \textit{et al.}, 2000; Droser \textit{et al.}, 2019), and persist right up until the Cambrian boundary $\sim539$ Ma in both Namibia (Grotzinger \textit{et al.}, 1995; Narbonne \textit{et al.}, 1997; Darroch \textit{et al.}, 2015; Linnemann \textit{et al.}, 2019) and the southwestern USA (Smith \textit{et al.}, 2016; 2017). Following  $\sim30$ million years as the dominant components of benthic ecosystems, the Ediacara biota disappear at the base of the Cambrian in what some have suggested represents the first mass extinction of complex life (Amthor \textit{et al.}, 2003; Laflamme \textit{et al.}, 2013; Darroch \textit{et al.}, 2015; 2018\textit{a,b}; Muscente \textit{et al.}, 2018; Zhang \textit{et al.}, 2018; although see Hoyal-Cuthill \& Han, 2018 for an opposing view).

While some Ediacara biota likely represent metazoans (Fedonkin \textit{et al.}, 2007; Gold \textit{et al.}, 2015; Dunn \textit{et al.}, 2017; Bobrovskiy, \textit{et al.}, 2018), many members do not appear to share synapomorphies with extant metazoan clades (Budd \& Jensen, 2000; Xiao \& Laflamme, 2009; Darroch \textit{et al.}, 2018\textit{a}), and are characterized by bizarre body plans that hamper our ability to understand their relationships to extant, eukaryotic groups. This uncertainty is further complicated a unique mode of preservation that has been suggested to be largely absent from the Phanerozoic (MacGabhann \textit{et al.}, 2019), for example whereby their soft tissues can be preserved as three-dimensional casts and molds frequently in association with iron sulfide minerals. While the Ediacara biota are often suggested to have `exceptional preservation,' much is still unknown about how this preservational process works including to what extent this pathway faithfully preserves the architecture of these organisms. The uncertainties surrounding them further extends beyond their preservation,  into their individual paleoecologies and phylogenetic placements. Their bizarre morphologies and unique preservation shields these fossils from definitive understanding of what they were doing and how they were living. Understanding this paleoecological information is pivotal for understanding the Earth's earliest complex ecosystems (Darroch \textit{et al.}, 2018\textit{a}) and discerning where these organisms fit on a tree of life, including their potential as the origin of animal dominated biosphere.

In this dissertation, I present three new contributions to understanding the taphonomy and paleobiology of the Ediacaran organisms. Each of these contributions is a standalone manuscript formatted for specific journals at which they have been submitted or published. In Chapter 1 I build on the  pyritic `death mask' hypothesis (Gehling, 1999) to constrain Ediacaran soft-bodied preservation. Understanding this preservational pathway likely has broad implications for discerning what these enigmatic organisms were, provides information pertinent for placing them on a tree of life, and informs our understanding of their paleoecologies by elucidating what features may or may not have been preserved (Gibson \textit{et al.}, 2018). I show that while bioavailable iron is necessary to precipitate iron sulfides (as predicted in Gehling, 1999), it is not a sufficient constraint alone. The formation of iron sulfide veneers is mutually dependent on reactive sulfur compounds and available organic material for nucleation and growth. Furthermore, these results suggest that death mask style preservation may not rely solely on pyrite formation, and instead might exploit alternative iron sulfide polymorphs such as marcasite. These actualistic taphonomic results represent the first laboratory-generated iron sulfide veneers replicating tissue character, particularly under death mask conditions. They also demonstrate that this preservational pathway is versatile and capable of occurring in a range of environments. 

In Chapter 2 I build on previous Ediacaran fluids modeling studies to discern possible feeding modes for the engimatic Ediacaran \textit{Ernietta}. Using computational fluid dynamics (CFD), I show that individual \textit{Ernietta} were likely gravity suspension feeders relying on their body shape to cycle nutrient rich water for feeding. In addition, I conduct the first multi-individual Ediacaran CFD experiments to demonstrate that these organisms likely aggregated to aid in feeding, similar to what is observed in modern invertebrate hummocks. Importantly, these results provide one of the oldest examples of facilitation in the fossil record, and demonstrate a cryptic ecological complexity not currently known from this time (Gibson \textit{et al.}, 2019). 

Lastly, in Chapter 3 I review the current literature of Ediacaran fluid physics experiments to demonstrate the fidelity of these techniques. I introduce a more sophisticated CFD approach than what is currently used in paleontological CFD experiments, and I outline future directions of Ediacaran fluid physics analyses. The case study presented represents the first analysis of its kind used in paleontology, and demonstrates the fidelity of well tailored approaches. 

The chapters presented here demonstrate that previous interpretations of Ediacaran ecosystems as being relatively simple (see e.g. `the Garden of Ediacara'; McMenamin, 1986) are antiquated and instead document increasingly complex ecological interactions and geochemical processes occurred during the latest Neoproterozoic. Three dimensional soft-bodied preservation of Ediacaran organisms occurs due to a complex interaction of porewater and sediment chemistry that can occur under a range of paleoenvironments. Social cooperation within populations of benthic taxa date back to at least the youngest Ediacara biota, establishing common Phanerozoic behaviors existed in the Precambrian. Ultimately these results and the implementation of more sophisticated fluid experiments outlined within chapter 3 helps to move forward our understanding of Earth's earliest, complex eukaryotes, and presents new directions for future Ediacara paleobiology studies using fluid physics approaches. 

\begin{thebibliography}{100}
	\bibitem{Bobrovskiy2018} Bobrovskiy, Ilya, Janet M. Hope, Andrey Ivantsov, Benjamin J. Nettersheim, Christian Hallmann, and Jochen J. Brocks. 2018. Ancient steroids establish the Ediacaran fossil \textit{Dickinsonia} as one of th earliest animals. \emph{Science} \textbf{361}, 1246-1249.
	\bibitem{Bobrovskiy2019} Bobrovskiy, Ilya, Anna Krasnova, Andrey Ivantsov, Ekaterina Luzhnaya (Serezhnikova), and Jochen J. Brocks. 2019. Simple sediment rheology explains the Ediacara biota preservation. \emph{Nature Ecology \& Evolution} \textbf{3}, 582-598.
	\bibitem{Darroch2017} Darroch, Simon A.F., Imran A. Rahman, Brandt Gibson, Rachel A. Racicot, and Marc Laflamme. 2017. Inference of facultative mobility in the enigmatic Ediacaran organism \textit{Parvancorina}. \emph{Biology Letters} \textbf{13}, 20170033.
	\bibitem{Darroch2015} Darroch, Simon A.F., Erik A. Sperling, Thomas H. Boag, Rachel A. Racicot, Sara J. Mason, Alex S. Morgan, Sarah Tweedt, Paul Myrow, David T. Johnston, Douglas H. Erwin, and Marc Laflamme. 2015. Biotic replacement and mass extinction of the Ediacara biota. \emph{Proceedings Royal Society B} \textbf{282}, 20151003.
	\bibitem{Darroch2018} Darroch, Simon A.F., Marc Laflamme, and Peter J. Wagner. 2018a. High ecological complexity in benthic Ediacaran communities. \emph{Nature Ecology \& Evolution} \textbf{2} 1541-1547.
	\bibitem{Darroch2018b} Darroch, Simon A.F., Emily F. Smith, Marc Laflamme, and Douglas H. Erwin. 2018b. Ediacaran extinction and Cambrian explosion. \emph{Trends in Ecology \& Evolution} \textbf{33}, 653-663.
	\bibitem{Dunn2018} Dunn, Frances S., Alexander G. Liu, and Philip C.J. Donoghue. 2018. Ediacaran developmental biology. \emph{Biological Reviews} \textbf{93} 914-932.
	\bibitem{Erwin2011} Erwin, Douglas H., Marc Laflamme, Sarah M. Tweedt, Erik A. Sperling, Davide Pisani, and Kevin J. Peterson. 2011. The Cambrian conundrum: early divergence and later ecological success in the early history of animals. \emph{Science} \textbf{334} 1091-1097.
	\bibitem{Fedonkin1997} Fedonkin, Mkihail A., and Benjamin M. Waggoner. 1997. The Late Precambrian fossil \textit{Kimberella} is a mollusc-like bilaterian organism. \emph{Nature} \textbf{388}, 868-871.
	\bibitem{Gehling1999} Gehling, James G. 1999. Microbial mats in terminal Proterozoic siliciclastics: Ediacaran death masks. \emph{Palaios} \textbf{14}, 40-57.
	\bibitem{Gibson2018} Gibson, Brandt M., James D. Schiffbauer, and Simon A.F. Darroch. 2018. Ediacaran-style decay experiments using mollusks and sea anemones. \emph{Palaios} \textbf{33}, 185-203.
	\bibitem{Gibson2019} Gibson, Brandt M., Imran A. Rahman, Katie M. Maloney, Rachel A. Racicot, Helke Mocke, Marc Laflamme, and Simon A.F. Darroch. 2019. Gregarious suspension feeding in a modular Ediacaran organism. \emph{Science Advances} \textbf{5}, eaaw0260.
	\bibitem{Glaessner1984} Glaessner, Martin F. 1984. \emph{The Dawn of Animal Life. A Biohistorical Study.} Cambridge University Press, Cambridge.
	\bibitem{McMenamin1986} McMenamin, Mark A.S. 1986. The garden of Ediacara. \emph{PALAIOS} \textbf{1}, 178-182.
	\bibitem{Rahman2015a} Rahman, I.A., Darroch, S.A.F., Racicot, R.A., \& Laflamme, M. (2015). Suspension feeding in the enigmatic Ediacaran organism \textit{Tribrachidium} demonstrates complexity of Neoproterozoic ecosystems. \emph{Science Advances} \textbf{1}, e1500800.
	\bibitem{Schiffbauer2020} Schiffbauer, James D., Tara Selly, Sara M. Jacquet, Rachel A. Merz, Lyle L. Nelson, Michael A. Strange, Yaoping Cai, and Emily F. Smith. 2020. Discovery of bilaterian-type through-guts in cloudinomorphs from the terminal Ediacaran Period. \emph{Nature Communications} \textbf{11}, 205(2020).
	\bibitem{Schopf1998} Schopf, K.M., \& Baumiller, T.K. (1998). A biomechanical approach to the Ediacaran hypotheses: how to weed the Garden of Ediacara. \emph{Lethaia} \textbf{31}, 89-97.
	\bibitem{Seilacher1989} Seilacher, Adolf. 1989. Vendozoa: organismal construction in the Proterozoic biosphere. \emph{Lethaia} \textbf{22}, 229-239.
	\bibitem{Seilacher1992} Seilacher, Adolf. 1992. Vendobionta and Psammocorallia: lost constructions of Precambrian evolution. \emph{Journal of the Geological Society} \textbf{149}, 607-613.
	\bibitem{Singer2012} Singer, Amy, Roy Plotnick,and Marc Laflamme. 2012. Experimental fluid mechanics of an Ediacaran frond. \emph{Paleontologia Electronica} \textbf{15}, 19A.
	\bibitem{Tarhan2016} Tarhan, Lydia G., Ashleigh v.S. Hood, Mary L. Droser, James G. Gehling, and Derek E.G. Briggs. 2016. Exceptional preservation of soft-bodied Ediacara Biota promoted by silica-rich oceans. \emph{Geology} \textbf{44}, 951-954.
	\bibitem{Xiao2009} Xiao, Shuhai, and Marc Laflamme. 2009. On the eve of animal radiation: phylogeny, ecology and evolution of the Ediacara biota. \emph{Trends in Ecology \& Evolution} \textbf{24}, 31-40.
	
\end{thebibliography}

\clearpage

%---------------------------------------------------------------------------------------------------------------%
%------------------------------------------------SECTION------------------------------------------------%
%---------------------------------------------------------------------------------------------------------------%
\chapter{The role of iron in the formation of Ediacaran `death masks'}\label{Chapter2title}
\vspace{-7mm}
\section{Abstract}\label{Section2abstract}
The Ediacara biota is an enigmatic and latest Neoproterozoic group of soft-bodied fossils, which are suggested to have been preserved as unusual pyritic microbial ``death masks." The specific conditions necessary for this style preservation still require exploration, including the role of bioavailable iron of preservational fidelity. We perform decay experiments on sea anemones (\textit{Condylactis gigantea}) and sea slugs (\textit{Elysia crispata}) under a range of iron-supplemented environments to characterize its role in the exceptional preservation of Ediacaran organisms. These results represent the first experimentally produced Fe--S veneers as predicted by the pyritic death mask model, and through geochemical analyses demonstrate Fe alone is an insufficient requirement for death mask style preservation to occur. Ultimately, these results demonstrate Ediacaran preservation need not be a ``perfect storm" of paleoenvironmental porewater and sediment chemistry, but instead can occur under a range of conditions.

\section{Introduction}\label{Section2introduction}
The Ediacara biota is an enigmatic group of soft-bodied fossils known from latest Neoproterozoic ($\sim$571--539 Ma) sediments worldwide. Despite recent advances in determining where several Ediacaran groups fit on the eukaryotic tree of life (Gold et al., 2015; Hoekzema et al., 2017; Dunn et al., 2018; Bobrovskiy et al., 2018; Schiffbauer et al., 2020), the vast majority possess uncertain relationships to extant animals (Xiao and Laflamme, 2009; Darroch et al., 2018). Understanding what the Ediacara biota represent and their relationships, if any, to extant animal phyla are keys to understanding both the early evolution of Metazoa and the origins of the modern marine biosphere (Darroch et al., 2018). One aspect that complicates our understanding of these fossils is their unusual mode of preservation.

Ediacaran soft tissues are commonly preserved as three-dimensional casts and molds in siliciclastic sediments (Gehling, 1999; Narbonne, 2005; Callow and Brasier, 2009), or alternatively as two-dimensional compressions (Zhu et al., 2008; Cai et al., 2010; Anderson et al., 2011). While compression-type preservation is well-known from numerous deposits throughout the Phanerozoic (Muscente et al., 2017), the once-dominant three-dimensional mode of preservation is largely absent outside of the Ediacaran (Gehling, 1999; Hagadorn and Bottjer, 1997; Jensen et al., 1998; although see MacGabhann et al., 2019 and Tarhan et al., 2016). This has led many authors to suggest that the cast and mold Ediacaran taphonomic pathway is controlled, to some degree, by aspects of the Neoproterozoic paleoenvironment, for example the composition of seawater (Tarhan et al., 2016) or the near-ubiquitous presence of seafloor microbial mats (Seilacher and Pflueger, 1994; Seilacher, 1999; Noffke et al., 2002; Noffke, 2010). Despite over 70 years of work, there is still uncertainty surrounding the pathway of Ediacaran fossil preservation; multiple models have been proposed, and the ubiquity of each can be questioned based on differences between fossil deposits. Nonetheless, although recent models based on early silica cementation (Tarhan et al., 2016) and sediment rheology (Bobrovskiy et al., 2019) have gained momentum, the leading hypothesis for over the past two decades has been the microbial `death mask' model (Gehling, 1999; Gehling et al., 2005; Droser et al., 2006).

The death mask model posits that soft-bodied Ediacaran organisms living in association with the microbial seafloor substrate were frequently buried by sediment during obrution events (such as during storms). After burial, microbial mats recolonized the overlying sediment-water interface, preventing the re-diffusion of oxygenated water down into pore spaces surrounding the carcass; the onset of decay subsequently creates anoxic conditions, which in turn reduces the rate of decay. Contemporaneously, sulfate-reducing bacteria (SRBs) reduce seawater sulfate (SO$_4^{2-}$) to hydrogen sulfide (H$_2$S), which then reacts with ferrous iron (Fe$^{2+}$) in pore water to form iron monosulfides (FeS), followed by pyrite (FeS$_2$). Lastly, carcass tissues and organics within surrounding sediments act as a nucleation sites for pyrite formation, which molds the external surfaces of the organisms.

This model has received a wealth of both field and experimental support. In South Australia, iron oxides and oxyhydroxides between bedding planes and fossil material are indicators of weathered pyrite (Wade, 1968; Tarhan et al., 2015; Liu, 2016; Liu et al., 2019). In Newfoundland, pyrite and iron oxides are found inside clay layers surrounding fossils (Laflamme et al., 2011; Liu, 2016), and pyritized microbial filaments have been reported from Ediacaran fossil surfaces in the White Sea area of Russia (Steiner and Reitner, 2001). Rudimentary `death masks' have also been experimentally produced in the laboratory. Darroch et al. (2012) decayed ecdysozoan larvae on freshwater microbial mats under simulated Ediacaran-style burial conditions, and demonstrated the precipitation of sedimentary iron sulfides around decaying carcasses. Newman et al. (2019) performed an experimental decay study on scallop muscles, demonstrating the precipitation of iron-bearing phases within tissues resembling greigite and hematite. Lastly, in Ediacaran-style experimental decay of sea anemones and mollusks, Gibson et al. (2018) were able to demonstrate the precipitation of iron sulfide minerals in association with decaying organisms, noting a morphological change from framboidal to blocky pyrite with increasing starting concentrations of reduced iron. While previous studies have assessed the influence of iron saturation levels on pyrite crystal shapes (Murowchick and Barnes, 1987), few studies have done so at low temperature under decay conditions. Gibson et al. (2018) moreover suggested that the relatively fine grain-size of framboidal pyrite may be optimal for preserving fine anatomical detail (and thus responsible for high-fidelity preservation of soft-bodied Ediacaran fossils), while the growth of blocky pyrite would likely overprint finer-scale features, creating poorly-preserved fossils with little recognizable anatomy.

This combination of field and experimental evidence provides strong support for microbial `death masks' in many (if not all) instances of Ediacaran fossil preservation, and hints at an overriding control exerted by initial sedimentary iron concentrations on the processes and quality of fossilization. Here, we address the following specific questions: 1) what is the minimal initial concentration of reduced iron in sediments required to form Fe--S associations or a microbial death mask? 2) How does the initial concentration of sedimentary iron affect the length and fidelity of the taphonomic window for death mask preservation? 3) To what extent does the initial concentration of sedimentary iron affect the crystal habit/morphology of iron sulfides forming around carcasses? And, 4) what effect does the crystal habit of iron sulfides have on the quality of fossil preservation? Addressing these questions is key not only understanding the formation of death masks and the extent to which they preserve the architecture of Ediacaran organisms, but also tests for the presence of facies- and paleoenvironmental-based biases in Ediacaran fossil preservation that may be influencing our understanding of benthic ecosystems and eukaryotic evolution in the latest Precambrian.

In this study, we conduct a series of decay experiments on two groups of soft-bodied marine invertebrates in which we vary the initial concentrations of sedimentary iron. We quantify the extent of iron sulfide development on tissues and surrounding sediment, identify the crystal habit of iron sulfides, and examine the relationship between initial iron concentration, extent of death mask formation, and rates/patterns of organismal decay.

\section{Methods}\label{Section2methods}
As model organisms, we decayed actinian cnidarians (\textit{Condylactis gigantea} -- the Caribbean sea anemone) and shell-less gastropods (\textit{Elysia crispata} -- the lettuce sea slug). We chose these organisms because of their similarities to previously studied Ediacaran decay analogues (McMahon et al., 2017; Gibson et al., 2018), and to incorporate both diploblastic and triploblastic organisms (i.e. two and three dermal grades). Decay specimens were purchased from online retailers (Saltwaterfish.com; KPAquatics.com) and were typically $\sim1-6$ cm in length. All organisms were euthanized using magnesium chloride hexahydrate (MgCl$_2*6$H$_2$O) following the protocols outlined in Gibson et al. (2018). Replicates were decayed individually in separate 300 mL plastic rectangular decay vessels with lids. Microbial mats and sediment were collected on the western, soundside of Dauphin Island, AL, from an estuarine tidal flat with abundant mats comprised of cyanobacteria and sulfur-reducing bacteria (based on a typical purple to green-color vertical gradient). Eolian blown medium to fine-grained (\textcolor{red}{Figure ESM 1}) subangular quartz dune sand was also collected from approximately the same location. Before sediment was used, it was dry sieved through a 1 mm mesh to remove larger organics (e.g. terrestrial plant material) that may have been present. Reduced ferrous iron (II) powder was then hand-mixed with the sieved sand to specified iron concentrations via vigorous shaking (Table \ref{tab:decay1}). Concentrations were chosen to represent a broad range of possible sediments. A thin layer of iron-mixed sediment was then placed in the bottom of each vessel. Microbial mat was placed on top of the iron-mixed sand, and decay replicates were then placed (Figure \ref{fig:decay1}) on top of the mat. We then placed two layers of plastic film along the edges of the vessel to allow for easy separation later. By limiting the plastic film to the edges, free exchanges of decay fluids and anions/cations between the mat and overlying sediment were permitted. Additional sediment of the same iron concentration was then placed overtop the mat and decay specimens, and the entire vessel was inundated with Instant Ocean Artificial Seawater (specific gravity = 1.02). Lastly, the vessels were sealed with lids and placed in a Heracell VIOS i160 tri-gas incubator to ensure consistent environmental conditions.

\begin{table}[h!]
	\centering
	\caption{Concentrations and removal periods for experiments. Each date-concentration combination consisted of three replicates per species.}
	\label{tab:decay1}
	\begin{tabular}{lllll}
		Concentration & 7-days & 14-days & 28-days &  \\
		\hline\hline
		0.00\%        &        &         &         &  \\
		0.01\%        &        &         &         &  \\
		0.05\%        &        &         &         &  \\
		0.10\%        &        &         &         &  \\
		0.50\%        &        &         &         &  \\
		1.00\%        &        &         &         &  \\
		5.00\%        &        &         &         & 
	\end{tabular}
\end{table}

Three replicates per iron concentration per species ($n = 3$) were removed from the incubator at timesteps of 7, 14, and 28 days ($n = 42$ organisms per timestep; $N = 108$). Vessels were immediately frozen to $−81\degree$ C for storage until completion of the experiment to allow for analyzing specimens in a solid form (see e.g. Darroch et al., 2012). After freezing, individual experiments were separated along the seam created by the two-layered plastic film. Remains were photographed and scored for decay state following the decay stages outlined by Gibson et al. (2018). As shown in Figure 1, sediment samples were then collected from each experiment from the intersection of tissue and sediment. For a subset of experiments, we collected additional mineralized tissue samples to assess pyrite formation. Sediment (and mineralized tissue) samples were affixed onto carbon disc adhesive-prepared aluminum stubs, with additional effort made to ensure nearly complete coverage of the carbon disc. No conductive sputter-coating was applied.

\begin{figure}[h!]
	\includegraphics[width=\textwidth]{Figure1.jpg}
	\centering
	\caption{Model of individual replicate experimental setup. A) Lid cover sealing has exchange. B) Mixed-species, sulfate reducing microbial mat. C) Decay replicate. D) Sand with supplemental iron. E) Double layered plastic film with circle removed around organism. Red dot indicates location of sediment retrieval per replicate.}
	\label{fig:decay1}
\end{figure}

All geochemical analyses were conducted at the University of Missouri X-ray Microanalysis Core Facility (Mizzo$\mu$X). Tissues and sediment were analyzed using scanning electron microscopy and energy dispersive x-ray spectroscopy (SEM-EDS). These analyses were conducted on a Zeiss Sigma 500 VP SEM with dual, co-planar Bruker XFlash 6$|$30 silicon drift EDS detectors (30 mm$^2$ active window). All data were collected under identical operating conditions: low chamber vacuum (40 Pa); 20 keV beam accelerating voltage; high current mode (40 nA probe current); and sample working distance of 8.5 mm. Two different aperture settings were used: a 60 $\mu$m aperture was used during electron imaging, and a 120 $\mu$m aperture was used for X-ray spectroscopy to improve signal. For imaging we used two detectors: a high definition five-segment backscattered electron detector (HDBSD; with all radial segments and the angular arm segment positively biased) for compositional imaging; and a cascade current detector (C2D; 30\% bias applied) for topographic imaging (measuring the resulting current from an ionization cascade through the 99.999\% N2 chamber gas). Images are a concurrent signal-mix from both detectors (75:25 [HDBSD:C2D]). Elemental mapping was conducted on each sample by using both co-planar EDS systems simultaneously to reduce shadow effects between affixed grains. Elemental mapping was conducted with a live time of 360 seconds, and at the described operating conditions yielded $>$ 250 kilocounts per second (kcps) combined between the two detectors. We collected area spectra and elemental maps for $\sim$ 4.5 X 3.4 mm regions of interest (ROIs) on the prepared stubs. We specifically focused ROIs on dense sediment cover, which were typically located at the center of the stub unless it lacked adequate sediment coverage over the carbon tape. In such cases, the field of view was repositioned to the nearest area with dense sediment cover (aiming for $\sim$ 80\% coverage when possible). Full regional spectra were assessed from the elemental maps, and ZAF corrected and quantified using the Bruker Esprit 2 software package, with compositional results reported in normalized weight percentage. In all cases, a large proportion of the carbon signal resulted from the mounting adhesive. Cooccurrences of elements were visually assessed with maps compared side by side, or using the enhanced mixing function in the Bruker Esprit software.

\section{Results}\label{Section2Results}
We first describe the decay patterns for individual species based on iron concentration and decay length. Then, we present geochemical data, again separated by species. Lastly, we document pyrite veneers that developed in some experiments.

\subsection{Sea anemone decay} 
Decay patterns and rates varied based on tissue type, and were more rapid at higher iron concentrations. A comprehensive description of these patterns is presented in \textcolor{red}{ESM  2}. Anterior (tentacles) and pharynx tissues decayed most rapidly, while muscle and dermal tissues typically persisted the longest -- broadly following the patterns described by Gibson et al. (2018), whereby the thinnest tissues are the most labile and thickest most recalcitrant. Figure \ref{fig:decay2} shows the first and last occurrences of decay stages of broad scale anatomical features separated by amount of additional iron.

\begin{figure}[h!]
	\includegraphics[width=\textwidth]{Figure2-01.jpg}
	\centering
	\caption{Pattern and temporal range of Fe-supplemented death mask style decay assessed from generalized characters of \textit{Condylactis gigantea}. Colors indicate first and last occurrences of decay stages outlined in Gibson et al. (2018). Green indicates 0--25\% loss; Yellow indicates 25--50\% loss; Orange indicates 50--75\% loss; and white indicates 75--100\% loss.}
	\label{fig:decay2}
\end{figure}

\subsection{Sea slug decay}
Similar to the sea anemones, the decay rates and patterns for sea slugs varied among iron treatment groups. In contrast to the anemones, sea slug replicates for all iron groups saw entire tissue features lost by the second time step (14 days). Figure \ref{fig:decay3} shows the first and last occurrences of decay stages of broad-scale anatomical features separated by amount of additional iron. 

\begin{figure}[h!]
	\includegraphics[width=\textwidth]{Figure3-01.jpg}
	\centering
	\caption{Pattern and temporal range of Fe-supplemented death mask style decay assessed from generalized characters of \textit{Elysia crispata}. Colors indicate first and last occurrences of decay stages outlined in Gibson et al. (2018). Green indicates 0--25\% loss; Yellow indicates 25--50\% loss; Orange indicates 50--75\% loss; and white indicates 75--100\% loss.}
	\label{fig:decay3}
\end{figure}

\subsection{Geochemical characterization (sea anemones)}
Iron concentrations from elemental analyses increased, as expected, with increasing initial sedimentary iron (\textcolor{red}{Figure ESM3}). \textcolor{red}{Figures ESM 4--6} shows EDS data recovered from the sediment stubs. Organic sulfur was present in all replicates regardless of iron concentration or removal date. Not all sediment samples exhibit spatial association between Fe--S, particularly sediment samples form replicates removed early (e.g. 7 days) or that had low concentrations of initial iron. With increasing additions of iron and decay intervals, more spatial iron-sulfur (Fe--S) cooccurrences were present. Fe--S overlap was consistently observed in association with carbon (typically the microbial mat or carcass tissue adhered to sediment grains), and was rarely found on sediment grains without the presence of carbon. Within Fe--S associations in the EDS maps, there are few recognizable framboid and/or blocky (e.g. cubic, hexagonal) morphologies. Because precipitates lacked recognizable crystal structure (or general amorphous nature), we distinguish the Fe--S morphologies as ``spherical" and ``globular" as observed in Figure \ref{fig:decay4}. At lower iron concentrations, Fe--S precipitates were smaller and spherical in nature. Above 1.00\% iron, precipitates transitioned to more globular forms that were less distinctly developed (i.e. more amorphous). While Fe--S cooccurrences were more common later in the decay window, trends were more ambiguous between iron concentrations. For all replicates below 0.1\% at all sampling intervals, there was little spatial association between iron and sulfur. Most cooccurrences start with day 14, with the highest appearing on the samples removed on day 28. Figure \ref{fig:decay4} shows mixed-signal overlays where Fe--S is present in direct association with organic C, most often forming along tabular microbial mat material.
\begin{figure}[h!]
	\includegraphics[width=0.8\textwidth]{Figure4-01.jpg}
	\centering
	\caption{Energy Dispersive Spectroscopy maps of sea anemone decay sediment. Percentages represent iron concentration within the decay sediment. Scale bars represent 400 $\mu$m total.}
	\label{fig:decay4}
\end{figure}

\subsection{Geochemical characterization (sea slugs)}
Similar to sea anemones, iron concentrations from elemental analyses increased, as expected, with increasing initial sedimentary iron (\textcolor{red}{Figure ESM7}). \textcolor{red}{Figures ESM8--10} show EDS maps for sea slugs. Organic sulfur was also present throughout samples regardless of supplemental iron concentration or decay length. Associations between Fe--S were also observed within sediment samples removed from sea slug replicates. Similar to the sea anemones, Fe--S spatial overlap typically increased with increasing decay length and with increased initial abundance of iron, and Fe--S morphologies were typically either spherical or globular in nature. Also mimicking the anemones, Fe--S cooccurrences were precipitating on organics as observed in the Fe--S$+$carbon EDS maps (Figure \ref{fig:decay5}). Mineral growth was found on microbial mat or organics that had adhered to sediment grains, and precipitates were rarely found on grains lacking carbon.

\begin{figure}[h!]
	\includegraphics[width=0.5\textwidth]{Figure5-01.jpg}
	\centering
	\caption{Energy Dispersive Spectroscopy maps of lettuce sea slug decay sediment. Percentages represent iron concentration within the decay sediment.}
	\label{fig:decay5}
\end{figure}

\subsection{Fe--S veneers}
Several replicates developed visible macroscopic Fe--S veneers molding the surface of the carcass tissues (Figure \ref{fig:decay6}) or regions of microbial mat. These thin veneers formed almost exclusively along organic surfaces with some isolated clumps forming further out from the sediment-tissue interface (e.g. Figure \ref{fig:decay6}). Veneers did not form in all replicates (only $n=6$), instead forming almost exclusively in replicates with 1.0--5.0\% supplemental iron that were allowed to decay for 28 days. Fe--S coated the upper surface of the microbial mat with isolated aggregations of sulfur coating both the Fe--S veneer and regions lacking Fe--S. At a macroscale, veneers did not exhibit the rusty colors observed in the Gibson et al. (2018) experiments. Instead, our veneers were a mixture of golden to white [olden (e.g. almost silver) in color (see Figure \ref{fig:decay6}). 

\begin{figure}[h!]
	\includegraphics[width=1\textwidth]{Figure6-01.jpg}
	\centering
	\caption{Comparison of sea anemone decay tissues. 1) Pre-euthanization sea anemone. a) tentacles, b) body column, c) foot. 2) Pyritized tissue after 28 days in 1.00\% Fe sediment. d) probable microbial mat, e) veneer along anemone foot tissue, f) isolated veneer along microbial mat surface. 3) Energy Dispersive Spectroscopy map of veneer from a sea anemone after 28 days in 5.00\% Fe sediment. Scale 200 $\mu$m.}
	\label{fig:decay6}
\end{figure}

\section{Discussion}\label{Section2Discussion}
Iron sulfide veneers formed in sea anemone replicates encompassed in 1.00--5.00\% iron along the intersection of carcass tissue, microbial mats, and the overlying sediment (Figures \ref{fig:decay5}--\ref{fig:decay6}). While previous decay studies have successfully developed Fe--S associations (Darroch et al., 2012; Newman et al., 2019) and precipitated pyrite in various forms (Brock et al., 2006; Grimes et al., 2001; Gibson et al., 2018), this represents the first study to experimentally replicate entire Fe--S veneers along sediment-carcass interfaces -- broadly mimicking Ediacaran-type fossils. Here, we discuss the formation of associated iron, sulfides, and mineral veneers as they relate to the following questions: 1) what is the minimal initial concentration of reduced iron in sediments required to form Fe--S associations and a microbial death mask? 2) How does the initial concentration of sedimentary iron affect the length and fidelity of the taphonomic window for death mask preservation? 3) To what extent does the initial concentration of sedimentary iron affect the crystal habit/morphology of iron sulfides forming around carcasses? And, 4) what effect does the crystal habit of iron sulfides have on the quality of fossil preservation?

\subsection{What is the minimal initial concentration of reduced iron in sediments required to form Fe--S associations and a microbial death mask?}
While minor Fe--S spatial associations were observed in replicates decayed 0.05\% iron-mixed sediment, Fe--S associations were not consistently noticeable until 0.50\% initial iron, and macroscopic Fe--S veneers did not appear in experiments with less than 1.00\% initial iron. Replicates from both decay organisms demonstrate that increasing supplemental iron and decay length led to increased Fe--S precipitation, and these data demonstrate a strong spatial association between Fe--S and carbon (\textcolor{red}{Figures ESM4--6,8--10}), with Fe--S associations forming almost exclusively on microbial mats or carcass tissues (Figures \ref{fig:decay4}--\ref{fig:decay5}). Carcasses decayed in iron concentrations of $<1.00$\% overwhelmingly formed iron sulfide precipitates associated with organic material, though much less spatial overlap was observed between iron and sulfur. Replicates decayed in sand with $\ge1.00$\% supplemental iron developed Fe--S associations preferentially on organics but also developed growth along grains that appear to lack organics (compare panels in Figure \ref{fig:decay4}). This is likely due to a lack of available organic nucleation sites while porewater is both saturated with iron and sulfate. Interestingly, replicates decayed in sand with $\le$ 0.1\% supplemental iron did not develop consistent overlap between iron and sulfur, indicating that there is likely a lower limit on Fe--S precipitation for sediments at or above 1\% iron. In fact, Fe--S was almost exclusively found on organic surfaces (Figures \ref{fig:decay4}--\ref{fig:decay5}; Figures ESM 4--6,8--10) regardless of decay species, suggesting that while iron may be a limiting reagent, carbon/organic surfaces as nucleation and precipitation sites for Fe--S are also a possible control -- a result in agreement with some organic-walled Ediacaran fossils (Schiffbauer et al., 2020).

\subsection{How does the initial concentration of sedimentary iron affect the length and fidelity of the taphonomic window for death mask preservation?}
For both sea anemones and sea slugs, the slowest loss of original decay characters occurred in intermediate iron environments (0.05--0.50\%) with the highest initial iron concentrations (1.00--5.00\%) yielding less original organic material often starting with day 14. Interestingly, the veneers masking the original tissue characters preferentially develop in the highest initial iron concentration replicates. This suggests that intermediate iron concentration environments are conducive to slowing decay, while higher concentrations are more conducive to coating and masking the original carcass tissues. While original tissue was more likely to be present in the intermediate concentrations, the rapid mineralization in the highest concentrations is necessary to coat and replace decaying organics to thus preserve them as fossils. All of this mineralization occurred between days 14--28, suggesting that the presence of intermediate porewater iron concentrations may help to inhibit decay through the mineralization process and continue to form fossils on timescales longer than 4 weeks.

Our results suggest there is a disparity between Fe--S precipitation and preservation potential between the sea anemones and sea slugs. Replicates from both decay organisms developed Fe--S precipitates, but greater preservation occurred in sea anemone replicates likely due to large tissue volumes. Sea anemone tentacles (anterior region) were, however, the least likely to be preserved regardless of iron abundance, and replicates that did retain these tissues were typically found in lower iron concentration groups. This suggests that tentacle-type tissues/characters are least likely to be preserved regardless of the decay environment's ability to produce pyrite, which supports the conclusion reached by Gibson et al. (2018) that the most labile tissues (specifically tentacles) will rarely be preserved under Ediacaran death mask style preservation. This is further supported by a possible preservation bias against cnidarian-grade tissues decayed in anoxic environments (Hancy and Antcliffe, 2020). Also similar to previous results (Gibson et al., 2018), by day 28, sea slug replicates' tissue preservation was largely constrained to the outer dermal tissue regardless of iron concentration. This suggests that outer tissue taphonomic mineralization acts as a barrier to any preservational influence of iron on internal features (Gibson et al., 2018; Newman et al., 2019). In our experiments this is explained in that iron adsorption of ferrous iron to external carcass tissues slows decay by inhibiting enzymatic hydrolysis of the outer tissues by creating nucleation sites for pyrite. This explains why internal features are often lost but external morphology may be retained, and is further supported by previous work outlining a similar pathway from a theoretical basis (Petrovich, 2001).

\subsection{To what extent does the initial concentration of sedimentary iron affect the crystal habit/morphology of iron sulfides forming around carcasses, and what effect does the crystal habit of iron sulfides have on the quality of fossil preservation?}
Fe--S precipitates encasing soft-tissues have been suggested as helping to preserve Ediacaran fossils in coarse-grained siliciclastic sediments. This model has been supported both by direct evidence (i.e., the presence of pyrite framboids on tissues -- see e.g., Liu et al., 2016; 2019), or an association between fossils and the weathering products of iron sulfides (Gehling, 1999; Mapstone and McIlroy, 2006). While pyrite has been experimentally precipitated in the laboratory as quickly as 4 hours at high temperatures (100$\degree$ C; Luther, 1991), most pyrite experimentally produced at room temperature has precipitated on time scales of months to years (Wang and Morse, 1996; Morse and Wang, 1997; Ohfuji and Rickard, 2005). On organic tissues, this timescale occurs as quickly as 10 days (Grimes et al., 2008). Our Fe--S associations are consistently observed after 14 days of decay and become more visibly apparent after 28 days of decay. While we do not observe the blocky pyrite noted in Gibson et al. (2018), the presence of both framboidal and globular FeS morphologies suggests that pyrite death mask style preservation is less dependent on the specific mineral morphologies. Instead, our results suggest that a consistent coating of Fe--S phases on the outside of decay carcasses is more important for preservation potential than any single mineral morphology. This also provides an explanation for why external molds of soft-bodied organisms are often preserved, while ``guts" and other internal features are lost (Gibson et al., 2018; Newman et al., 2019).

In addition to addressing our initial questions, the results of experiments provide additional insights into the nature of Fe--S veneers (i.e., `death masks') on decaying organisms, the role of organic matter in providing nucleation sites for sulfide minerals, and the overall taphonomic pathway involved in `death mask'-style preservation.

\subsection{Fe--S Veneers}
Iron sulfide veneers formed on multiple replicates over a range of iron concentrations. These veneers coat single layers of organic matter thereby replicating the surface topography of the tissue of the organism, with thicker tissues (e.g. muscle, pharynx) having either flattened or been lost to decay. Veneers did not form on sea slug carcasses, though discrete aggregates of iron sulfides were present within the surrounding sand. This likely reflects an easier ability to precipitate pyrite on carcass material rather than just the microbial mat, counter to what is observed in the fossil record. Veneers that did form along the carcass-sediment interface did not perfectly replicate their original tissue morphology, but instead often developed into textured surfaces that made the tissues look deformed (Figure \ref{fig:decay6}). Sea anemones decayed in sand with the highest concentrations of iron developed Fe--S macroscopically visible veneers by 28 days, broadly conforming to predictions from the original death mask hypothesis (Gehling, 1999). Veneers under these conditions form between 2--4 weeks, and likely continue to develop past that suggesting that Ediacaran veneers form relatively quickly. Our veneers and isolated Fe--S aggregates from the matrix surrounding carcasses of both sea anemone and sea slug replicates exhibit spherical and globular shapes instead of the anticipated framboidal or blocky (hexahedron and cubic) morphologies. Likely this is because our Fe--S were not entire sheets of pyrite, but instead probably include marcasite and/or greigite as also indicated by the visible coloration of the veneer. While both are compositionally similar to pyrite (both FeS$_2$ and Fe$_3$S$_4$, respectively), acidic conditions can cause competition among mineral formation (Hilton et al., 1986), particularly between pyrite and marcasite (Murowchick, 1992). While marcasite has not been directly observed in Ediacaran fossils or modern marine sediments (Goldhaber, 2003), our results suggest it is successfully playing the role of pyrite in the original death mask hypothesis, whereby it is crucially coating and thus preserving external surfaces. Furthermore, marcasite converts to pyrite over time (Murowchick, 1992), and amorphous greigite has previously been suggested to play a role in Ediacaran preservation, particularly in mixed-redox environmental conditions (Newman et al., 2019).

\subsection{Role of organic nucleation sites}
Our results show a proclivity for Fe--S concentration along organic surfaces with little nucleation isolated within the sediment. Spatial cooccurrences in our replicates were typically constrained to carcass surfaces as compared to developing veneers along microbial mat surfaces. This broadly agrees with Newman et al.'s (2019) results that Fe--S enriches within carcass tissues, and that microbial mats may not necessarily be required for three-dimensional death mask style preservation. Two differences arise between their results and ours. First, our iron sulfates form along the surface of tissues instead of solely within the tissues. While we have not tested it, we hypothesize that iron sulfides may concentrate in different locations based on tissue type, such as coating along thinner tissues and penetrating into more developed muscle tissue. To this end, it is accepted that nucleation rates strongly depend on the physiochemical properties of interfaces, where for example different underlying histologies or chemical terminations may promote nucleation and deposition (e.g. see discussion of pyrite nucleation in Schiffbauer et al., 2014). Second, they note the presence of sulfate reducing heterotrophic bacteria are more important than capping microbial mats for creating anoxic conditions. Our results do not disagree with this assessment, though our experimental design also did not permit additional assessment of this phenomenon.

\subsection{An expansion of the `death mask'-style taphonomic pathway}
Our experiments provide insight into the types of mechanisms and timescales we might anticipate during `death mask'-style preservation. Our decay systems had an abundance of iron, organics, and sulfur, which led to a pathway whereby Fe--S could freely form over organics unimpeded. Likely, one of these conditions would be limited in Ediacaran seafloor environments. Similar to what is outlined in Schiffbauer et al. (2020) and Figure \ref{fig:decay7}, if sulfur were limited we would anticipate that our veneers would have been limited, and tissues would have been lost entirely. If porewater iron were limited, we should anticipate that some preservation might occur, but this would be limited with the rest of the organics eventually being decayed entirely. If organics were limited in an environment with abundant porewater iron and available sulfur, we would anticipate the carcass being entirely removed through decay with Fe--S phases replacing the volume of decayed material.

\begin{figure}[h!]
	\includegraphics[width=0.5\textwidth]{Figure7-01.jpg}
	\centering
	\caption{Alternative pathways for Ediacaran death mask preservation based on microenvironment conditions. Top: seawater sulfate limited in the presence of sufficient porewater iron and carcass organics yields Fe--S veneers along the carcass sediment surface and some inter-sediment grain pyrite framboids. Middle: limited porewater iron yields few sediment pyrite framboids (\textbf{F}) and causes limited veneer growth with the carcass ultimately completely decaying. Bottom: limited carcass organics in the presence of sufficient porewater iron and seawater sulfate yields the development of sediment pyrite framboids and significant replacement of carcass tissue with iron sulfides. A pyrite morphology gradient exists between the veneer/exterior (F: framboidal) and inner tissues (\textbf{B}: blocky).}
	\label{fig:decay7}
\end{figure}

Our results also demonstrate that the death mask model is not constrained to pyrite alone, and could feasibly be explained with other iron sulfide polymorphs. While pyrite framboids have been described from Ediacaran fossils (Liu, 2016), marcasite or greigite could mutually explain the presence of iron oxides and oxyhydroxides found in association with Ediacaran fossils (Tarhan et al., 2015; Liu, 2016; Liu et al., 2019). In such cases, we would anticipate that the local decay environment would have turned acidic to permit the formation of this iron sulfide polymorph. Previous work has suggested that microbial mats benefit but are not necessarily required for Ediacaran preservation (Newman et al., 2019), demonstrating that this preservational pathway is pliable and thus able to occur under a larger variety of environmental conditions. Our results similarly demonstrate how this taphonomic pathway may not be as rigid as previously thought. Ultimately, these results, in light additional recently published studies, emphasize that the novel fossilization of these organisms does not necessitate so much a ``perfect storm" of pore water microenvironmental and microbial substrate conditions, but instead can be explained in a greater variety of paleoenvironments. While Ediacaran preservation environments may not be consistent among fossil deposits, the underlying paleoenvironmental heterogeneity in porewater and sediment chemistry likely play the dominant controls in taphonomic variation observed between deposits.

\section{Conclusions}\label{Chapter2Conclusions}
The results of these experiments demonstrate that while minimal porewater iron is a necessary requirement for death mask style preservation, its presence alone is not a sufficient control. Death mask style preservation develops from a combination of available porewater iron, seawater sulfate, and the presence of nucleation sites for Fe--S associations. These results represent the first laboratory-produced iron sulfide veneers precipitated under death mask conditions, and they suggest this process occurs relatively rapidly on the order of weeks. While these veneers are likely not pure pyrite (based off crystal morphology), their development and ability to preserve tissue morphology demonstrates that the Gehling death mask model (1999) is not constrained solely to pyrite, but instead is more reliant on Fe--S associations in general.

\section{Acknowledgments}
The authors would like to thank Elli Ronay, Eva Biedron, Lydia Harmon, and Matthew Dietrich for assistance in the lab. BMG was supported by the Geological Society of America GSRG-11444-16, SEPM (Graduate Student Research Grant), and Sigma Xi GIAR-G2017100194597859. JDS is supported by NSF EAR CAREER-1652351, and acknowledges support of the X-ray Microanalysis Core Facility by NSF EAR I\&F-1636643.

\begin{thebibliography}{100}
	\bibitem{Anderson2011} Anderson, Evan P., James D. Schiffbauer, and Shuhai Xiao. 2011. Taphonomic study of Ediacaran organic-walled fossils confirms the importance of clay minerals and pyrite in Burgess Shale-type preservation. Geology 39: 643-646, doi: 10.1130/G31969.1.
	\bibitem{Bobrovskiy2018} Bobrovskiy, Ilya, Anna Krasnova, Andrey Ivantsov, Ekaterina Luzhnaya (Serezhnikova), and Jochen J. Brocks. 2018. Simple sediment rheology explains the Ediacara biota preservation. Nature Ecology \& Evolution 3: 582-589, doi:10.1038/s41559-019-0820-7.
	\bibitem{Brock2006} Brock, Fiona, R. John Parkes, and Derek E.G. Briggs. 2006. Experimental pyrite formation associated with decay of plant material. PALAIOS 21: 499–506.
	\bibitem{Buatois2014} Buatois, Luis A., Guy M. Narbonne, M. Gabriela M\'{a}ngano, Noelia B. Carmona, and Paul Myrow. 2014. Ediacaran matground ecology persisted into the earliest Cambrian. Nature Communications 5: doi:1038/ncomms5455.
	\bibitem{Cai2010} Cai, Yaoping, Hong Hua, Shuhai Xiao, James D. Schiffbauer, and Peng Li. 2010. Biostratinomy of the late Ediacaran pyritized Gaojiashan Lagerstätte from southern Shaanxi, South China: importance of event deposits. PALAIOS 25, 487-506, doi: 10.2110/palo.2009.p09-133r.
	\bibitem{Chen2018} Chen, Zhe, Xiang Chen, Chuanming Zhou, Xunlai Yuan, and Shuhai Xiao. 2018. Late Ediacaran trackways produced by bilaterian animals with paired appendages. Science Advances 4: eaao6691.
	\bibitem{Darroch2012} Darroch, Simon A.F., Marc Laflamme, James D. Schiffbauer, and Derek E.G. Briggs. 2012, Experimental formation of a microbial death mask. Palaios 27: 293–303, doi: 10.2110/palo.2011.p11-059r.
	\bibitem{Darroch2018} Darroch, Simon A.F., Marc Laflamme, and Peter J. Wagner. 2018. High ecological complexity in benthic Ediacaran communities. Nature Ecology \& Evolution 2: 1541-1547, doi: 10.1038/s41559-018-0663-7.
	\bibitem{Dunn2018} Dunn, Frances S., Alexander G. Liu, and Philip C.J. Donoghue. 2018. Ediacaran developmental biology. Biological Reviews 93: 914-932, doi: 10.1111/brv.12379.
	\bibitem{Gehling1999} Gehling, James G. 1999. Microbial mats in terminal Proterozoic siliciclastics: Ediacaran death masks. PALAIOS 14(1): 40–57.
	\bibitem{Gehling2005} Gehling, James G., Mary L. Droser, S\"{o}ren R. Jensen, and Bruce N Runnegar. 2005. Ediacaran organisms: relating form to function. In D.E.G. Briggs (ed.) Evolving Form and Function: Fossils and Development: Proceedings of a Symposium Honoring Adolf Seilacher for his Contributions to Paleontology, in Celebration of his 80th Birthday. Yale University, New Haven, Connecticut, 288p.
	\bibitem{Gibson2018} Gibson, Brandt M., James D. Schiffbauer, and Simon A.F. Darroch. 2018. Ediacaran--style decay experiments using mollusks and sea anemones. PALAIOS 33(5): 185–203, doi:10.2110/palo.2017.091.
	\bibitem{Gold2015} Gold, David A., Bruce Runnegar, James G. Gehling, and David K. Jacobs. 2015. Ancestral state reconstruction of ontogeny supports a bilaterian affinity for \textit{Dickinsonia}. Evolution \& Development 17: 315-324, doi: 10.1111/ede.12168.
	\bibitem{Goldhaber2003} Goldhaber, M.B. 2003. Sulfur-rich Sediments. In H.D. Holland and K.K. Turekian (eds). Treatise on Geochemistry, 2nd Edition, p. 257-288.
	\bibitem{Grimes} Grimes, Stephen T., Fiona Brock, David Rickard, Kevin L. Davies, Dianne Edwards, and Derek E.G. Briggs. 2001. Understanding fossilization: experimental pyritization of plants. Geology 29: 123-126, doi: 10.1130/0091-7613(2001)029<0123:UFEPOP>2.0.CO;2.
	\bibitem{Hagadorn} Hagadorn, J W., and David J. Bottjer. 1997. Wrinkle structures: microbially mediated sedimentary structures common in subtidal siliciclastic settings at the Proterozoic-Phanerozoic transition. Geology 25: 1047-1050, doi: 10.1130/0091-7613(1997)025<1047:WSMMSS>2.3.CO;2.
	\bibitem{Hancy} Hancy, Anthony D., and Jonathan B. Antcliffe. 2020. Anoxia can increase the rate of decay for cnidarian tissue: using \textit{Actinia equina} to understand the early fossil record. Geobiology 18: 167-184, doi:10.1111/gbi.12370.
	\bibitem{Hilton} Hilton, J., J.P. Lishman, and J.S. Chapman. 1986. Magnetic and chemical characterization of a diagenetic magnetic mineral formed in the sediments of productive lakes. Chemical Geology 56: 325-333, doi: 10.1016/0009-2541(86)90012-4.
	\bibitem{Hoekzema} Hoekzema, Renee S., Martin D. Brasier, Frances S. Dunn, and Alexander G. Liu. 2017. Quantitative study of developmental biology confirms \textit{Dickinsonia} as a metazoan. Proceedings of the Royal Society B 284: 20171348, doi: 10.1098/rspb.2017.1348.
	\bibitem{Jensen} Jensen, S\"{o}ren, James G. Gehling, and Mary L. Droser. 1998. Ediacara-type fossils in Cambrian sediments. Nature 393: 567-569, doi: 10.1038/31215.
	\bibitem{Laflamme2011} Laflamme, Marc, James D. Schiffbauer, Guy M. Narbonne, and Derek E.G. Briggs. 2011. Microbial biofilms and the preservation of the Ediacara biota. Lethaia 44: 203–213, doi: 10.1111/j.1502-3931.2010.00235.x.
	\bibitem{Liu2016} Liu, Alexander G. 2016. Framboidal pyrite shroud confirms the ``death mask" model for moldic preservation of Ediacaran soft-bodied organisms. PALAIOS 31: 259–274, doi:10.2110/palo.2015.095.
	\bibitem{Liu2019} Liu, Alexander G., Sean McMahon, Jack J. Matthews, John W. Still, and Alexander T. Brasier. 2019. Petrological evidence supports the death mask model for the preservation of Ediacaran soft-bodied organisms in South Australia. Geology 47(2): 215–218, doi:10.1130/G45918.1/4617348/g45918.
	\bibitem{MacGabhann} MacGabhann, Brend\'{a}n Anraio, James D. Schiffbauer, James W. Hagadorn, Peter Van Roy, Edward P. Lynch, Liam Morrison, and John Murray. 2019. Resolution of the earliest metazoan record: differential taphonomy of Ediacaran and Paleozoic fossil molds and casts. Palaeogeography, Palaeoclimatology, Palaeoecology 513: 146-165 doi: 10.1016/j.palaeo.2018.11.009.
	\bibitem{Morse} Morse, John W., and Qiwei Wang. 1997. Pyrite formation under conditions approximating those in anoxic sediments: II. Influence of precursor iron minerals and organic matter. Marine Chemistry 57, 187-193.
	\bibitem{Murowchick} Murowchick, James B. 1992. Marcasite inversion and the petrographic determination of pyrite ancestry. Economic Geology 87: 1141-1152, doi:10.2113/gsecongeo.87.4.1141.
	\bibitem{Murowchick2} Murowchick, James B., and H.L. Barnes. 1987. Effects of temperature and degree of supersaturation on pyrite morphology. American Mineralogist 72, 1241-1250.
	\bibitem{Narbonne} Narbonne, Guy M., 2005. The Ediacara biota: Neoproterozoic origin of animals and their ecosystems. Annual Review of Earth and Planetary Sciences 33: 421-422, doi: 10.1146/annurev.earth.33.092203.122519.
	\bibitem{Noffke2010} Noffke, Nora. 2010. Geobiology: Microbial Mats in Sandy Deposits from the Archean Era to Today: Springer-Verlag, Berlin, 194 p.
	\bibitem{Noffke} Noffke, Nora, Andrew H. Knoll, and John P. Grotzinger. 2002. Sedimentary controls on the formation and preservation of microbial mats in siliciclastic deposits: a case study from the upper Neoproterozoic Nama Group, Namibia. PALAIOS 17:  533-544, doi: 10.1669/0883-1351(2002)017,0533:SCOTFA.2.0.CO;2. 
	\bibitem{Ohjuji} Ohjuji, Hiroaki, and David Rickard. 2005. Experimental syntheses of framboids -- a review. Earth Science Reviews 71: 147-170.
	\bibitem{Petrovich} Petrovich, Radomir. 2001. Mechanisms of fossilization of the soft-bodied and lightly armored faunas of the Burgess Shale and of some other classical localities. American Journal of Science 301: 683-726, doi:10.2475/ajs.301.8.683.
	\bibitem{Schiffbauer} Schiffbauer, James D., Tara Selly, Sarah M. Jacquet, Rachel A. Merz, Lyle L. Nelson, Michael A. Strange, Yaoping Cai, and Emily F. Smith. 2020. Discovery of bilaterian-type through-guts in cloudinomorphs from the terminal Ediacaran Period. Nature Communications 11: 205(2020), doi:10.1038/s41467-019-13882-z.
	\bibitem{Seilacher1999} Seilacher, Adolf. 1999. Biomat-related lifestyles in the Precambrian. PALAIOS 14: 86-93, doi: 10.2307/3515363.
	\bibitem{Seilacher1994} Seilacher, Adolf, and F. Pfl\"{u}ger. 1994. From biomats to benthic agriculture: a biohistoric revolution, in W.E. Krumbein and L.J. Stal (eds.), Biostabilization of Sediments: Bibliotheks und Informations system der Carl von Ossietzky Universität, Oldenburg, p. 97–105.
	\bibitem{Steiner} Steiner, Michael, and Joachim Reitner. 2001. Evidence of organic microstructures in Ediacara-type fossils and associated microbial mats. Geology 29: 1119-1122.
	\bibitem{Tarhan} Tarhan, Lydia G., Ashleigh V.S. Hood, Mary L. Droser, James G. Gehling, and Derek E.G. Briggs. 2016. Exceptional preservation of soft-bodied Ediacara Biota promoted by silica-rich oceans. Geology 44: 951–954, doi: 10.1130/G38542.1
	\bibitem{Tarhan2017} Tarhan, Lydia G., Mary L. Droser, James G. Gehling, and Matthew P. Dzaugis. 2017. Microbial mat sandwiches and other anactualistic sedimentary features of the Ediacara Member (Rawnsley Quartzite, South Australia): implications for interpretation of the Ediacaran sedimentary record. Palaios 32: 181–194.
	\bibitem{Wang} Wang, Qiwei, and John W. Morse. 1996. Pyrite formation under conditions approximating those in anoxic sediments: I. Pathway and morphology. Marine Chemistry 52, 99-121.
	\bibitem{Xiao} Xiao, Shuhai and Marc Laflamme, 2009, On the eve of animal radiation: phylogeny, ecology and evolution of the Ediacara biota: Trends in Ecology \& Evolution 24: 31–40, doi: 10.1016/j.tree.2008.07.015.
	\bibitem{Zhu} Zhu, Maoyan, James G. Gehling, Shuhai Xiao, Yuanlong Zhao, and Mary L. Droser. 2008. Eight-armed Ediacara fossil preserved in contrasting taphonomic windows from China and Australia. Geology 36: 867-870, doi: 10.1130/G25203A.1.
\end{thebibliography}
\clearpage\newpage
\section{Appendix}
\begin{figure}[h!]
	\includegraphics[width=\textwidth]{Figure ESM1.jpeg}
	\centering
	\caption{Decay sediment grain analysis distribution collected using a Malvern Instruments Mastersizer 2000.}
	\label{fig:2S1}
\end{figure}

\subsection{EMS2: Decay Patterns}\label{text:2S2}
\textit{Sea anemone decay}. -- Decay rates and patterns varied based on tissue type, and were more rapid at higher Fe concentrations. Anterior tissues decayed most rapidly, while muscle tissues typically persisted the longest. Figure 2 shows the first and last occurrences of decay stages of broad scale anatomical features separated by Fe concentration. The anterior region incorporating the tentacles were completely missing from three of the Fe concentrations at the first removal (day 7), and all tissues were missing from the 5.00\% Fe concentration at the first removal (day 7). Only the 0.05\%, 0.10\%, and 1.00\% replicates still had some tentacle tissue left, and of those only the 0.05\% still had all replicates in DS1. Some 0.10\% replicates had already transitioned tentacle tissue to DS3, and all 1.00\% replicates were in DS2. By the third removal (day 28), only two concentrations (0.10\% and 1.00\%) still had tentacle tissue not in DS4.

Outer dermal tissue persisted in lower decay stages longer than the anterior tentacle region. At the first removal (day 7), all Fe concentrations still had replicates in DS1 except for the 5.00\% Fe experiments, which were missing. Only the 0.00\% and 1.00\% had outer dermal tissue of replicates that had transitioned beyond DS1, and they were in DS3. At the second removal (day14), at least one replicate from each Fe concentration had transitioned to a higher decay stage with only three concentrations (0.00\%, 0.05\%, and 0.50\%) having at least one replicate still in DS1. At the final sampling date (day 28), at least one replicate per Fe concentrations still had outer dermal tissue present in DS2 or DS3.

Muscle tissue decay patterns mimicked the broad scale outer dermal tissue decay patterns. At the first removal (day 7), all Fe concentrations had replicates with muscle tissue in DS1 except for the missing 5.00\% Fe experiment carcasses. Three Fe concentrations (0.00\%, 0.10\%, and 1.00\%) had replicates that transitioned into DS3. On the second removal (day 14), most Fe concentrations had replicates in DS1 and DS2. Higher concentrations had replicates mostly in DS2 and DS3, and the highest Fe concentration (5.00\%) had replicates already in DS4. At the final removal (day 28), some Fe concentrations still had muscle tissue in DS1 (0.00\% and 0.10\%), but all Fe concentrations had replicates that had at least transitioned to DS2 with some transitioning higher. The 5.00\% replicates muscle tissue had completely disappeared by day 28.
The pharynx tissue within the anemone had varied rates and patterns of decay with respect to Fe concentration. With the exception of the missing 5.00\% carcasses, all Fe concentrations had replicates still in DS1 at the first removal (day 7). Two concentrations (0.00\% and 1.00\%) had replicates that had transitioned into DS3. At the second removal (day 14), all concentrations had replicates that had transitioned at least to DS3 if not DS4. Only the 0.50\% Fe concentration replicates still had at least one carcass with pharynx tissue in DS1. At the final sampling date, most replicates had pharynx tissue in DS4 except for the 0.10\% Fe concentration.
\\ \\
\textit{Sea hare decay}. --  Decay rates and patterns varied among Fe concentrations, and tissues were mostly lost by the second time step (14 days). While the gut material was lost quickly, the muscle and dermal tissues were more recalcitrant. Figure 3 shows the first and last occurrences of decay stages of broad scale anatomical features separated by Fe concentration. During the first removal (day 7), only two concentrations had anterior regions still in DS1. Most Fe concentrations had replicates that had transitioned to at least DS2 or all the way to DS4. At the second removal (day 14), all Fe concentration experiments showed each replicate had transitioned to at least DS2 or further, usually in DS4. By the final removal (day 28), all Fe concentrations had replicates in DS4. Half of the concentrations had replicates in DS2 or DS3, with all but 0.50\% in DS3.

At the first removal at 7 days, all Fe concentrations had replicates with outer dermal tissues in DS1. Two Fe concentrations (0.05\% and 0.10\%) had replicates with outer dermal issues in DS4 though no Fe concentrations had replicates in DS2 or DS3. On the second sampling date (day 14), almost all replicates from each Fe concentration (notable exception of 0.10\% Fe) had entirely transitioned to DS2 or beyond. Furthermore, at least one replicate per Fe concentration had outer dermal tissue that had transitioned to DS4 with the exception of 0.50\% Fe, which had all replicates in DS3. At the final sampling date (day 28), every Fe concentration had replicates in DS4 or DS3.


After 7 days, half of the Fe concentrations had muscle tissue still in DS1 (0.00\%, 0.50\%, and 1.00\%), while replicates from all other concentrations had entirely transitioned to DS2 and beyond. All concentrations above 0.00\% Fe had replicates with muscle tissue in DS2, and three Fe concentrations (0.05\%, 0.10\%, and 1.00\%) had replicates with muscle tissue that had transitioned to DS4. Only the 5.00\% Fe concentration had a replicate with muscle tissue in DS3.

At the second sampling date (day 14), all Fe concentrations only had replicates in DS2 or DS4 except for the experiments without additional Fe. The experiments lacking supplemental Fe had replicates either in DS1 or DS4. Sea hare muscle tissue was lost rapidly between the second and third sampling dates, with half of the concentrations (0.05\%, 0.10\%, and 1.00\%) transitioning into DS4 for all replicates. By the final removal (day 28), no replicates for any Fe concentration were still in DS1, and only some replicates belonging to 0.50\% and 5.00\% had replicates still in DS2. A single replicate without supplemental Fe was still in DS3 at day 28.

Only two concentrations (0.50\% and 1.00\%) had gut tissue still in DS1 at the first sampling date (day 7). Two concentrations (0.00\% and 0.05\%) had all replicates missing observable gut tissues (DS4). The remaining Fe concentrations had replicates ranging in decay states from DS1 to DS4. On the second removal (day 14), all Fe concentrations except for 0.05\% had replicates in DS4. The two highest Fe concentrations (1.00\% and 5.00\%) had all replicates in DS4. The remaining replicates (not in DS4) were either in DS2 or DS3, with all 0.05\% Fe replicates in DS3. Between days 14 and 28 most of the replicates had tissues that transitioned to DS4 indicating a complete loss or recognizable tissue. Only replicates from 0.50\% supplemental Fe had replicates with tissues left, which were in DS2 or DS3.

Important for subsequent discussions is that sea anemone primary tissue material was absent for all characters in all replicates of 5.00\% supplemental Fe by day 28, with most of the material being lost by day 7 for replicates. This demonstrates a rapid loss of original organic material compared to lower Fe concentration experiments.

\begin{figure}[h!]
	\includegraphics[width=\textwidth]{Figure ESM3.jpeg}
	\centering
	\caption{Caribbean giant sea anemone \textit{Condylactis gigantea} iron recovered (mass normalized) based on initial iron concentrations. }
	\label{fig:2S3}
\end{figure}

\begin{figure}[h!]
	\includegraphics[width=\textwidth]{Figure ESM3.jpg}
	\centering
	\caption{Caribbean giant sea anemone \textit{Condylactis gigantea} SEM EDS maps for replicates removed at 7 days. Initial iron concentrations increase row-wise, replicates denoted in first column of respective data.}
	\label{fig:2S4}
\end{figure}

\begin{figure}[h!]
	\includegraphics[width=\textwidth]{Figure ESM4.jpg}
	\centering
	\caption{Caribbean giant sea anemone \textit{Condylactis gigantea} SEM EDS maps for replicates removed at 14 days. Initial iron concentrations increase row-wise, replicates denoted in first column of respective data.}
	\label{fig:2S5}
\end{figure}

\begin{figure}[h!]
	\includegraphics[width=\textwidth]{Figure ESM5.jpg}
	\centering
	\caption{Caribbean giant sea anemone \textit{Condylactis gigantea} SEM EDS maps for replicates removed at 28 days. Initial iron concentrations increase row-wise, replicates denoted in first column of respective data.}
	\label{fig:2S6}
\end{figure}

\begin{figure}[h!]
	\includegraphics[width=\textwidth]{Figure ESM6.jpeg}
	\centering
	\caption{Lettuce sea slug \textit{Elysia crispata} iron recovered (mass normalized) based on initial iron concentrations. }
	\label{fig:2S7}
\end{figure}

\begin{figure}[h!]
	\includegraphics[width=\textwidth]{Figure ESM7.jpg}
	\centering
	\caption{Lettuce sea slug \textit{Elysia crispata} SEM EDS maps for replicates removed at 7 days. Initial iron concentrations increase row-wise, replicates denoted in first column of respective data..}
	\label{fig:2S8}
\end{figure}

\begin{figure}[h!]
	\includegraphics[width=\textwidth]{Figure ESM8.jpg}
	\centering
	\caption{Lettuce sea slug \textit{Elysia crispata} SEM EDS maps for replicates removed at 14 days. Initial iron concentrations increase row-wise, replicates denoted in first column of respective data..}
	\label{fig:2S9}
\end{figure}

\begin{figure}[h!]
	\includegraphics[width=\textwidth]{Figure ESM9.jpg}
	\centering
	\caption{Lettuce sea slug \textit{Elysia crispata} SEM EDS maps for replicates removed at 28 days. Initial iron concentrations increase row-wise, replicates denoted in first column of respective data..}
	\label{fig:2S10}
\end{figure}
\newpage\clearpage
%---------------------------------------------------------------------------------------------------------------%
%------------------------------------------------SECTION------------------------------------------------%
%---------------------------------------------------------------------------------------------------------------%
\chapter{Gregarious suspension feeding in a modular Ediacaran organism}\label{Chapter3title}
\begin{center}
Previously published in \textit{Science Advances}
\end{center}
\vspace{-7mm}
\section{Abstract}
Reconstructing Precambrian eukaryotic paleoecology is pivotal to understanding the origins of the modern, animal- dominated biosphere. Here, we combine new fossil data from southern Namibia with computational fluid dynamics (CFD) to test between competing feeding models for the Ediacaran taxon \textit{Ernietta}. In addition, we perform simulations for multiple individuals, allowing us to analyze hydrodynamics of living communities. We show that \textit{Ernietta} lived gregariously, forming shallow marine aggregations in the latest Ediacaran, 548 to 541 million years (Ma) ago. We demonstrate enhanced vertical mixing of the water column above aggregations and preferential redirection of current into body cavities of downstream individuals. These results support the reconstruction of \textit{Ernietta} as a macroscopic suspension feeder and also provide a convincing paleoecological advantage to feeding in aggregations analogous to those recognized in many extant marine metazoans. These results provide some of the oldest evidence of facilitation facilitation by macroscopic eukaryotes yet recognized in the fossil record.
\section{Introduction}\label{Section3introduction}
The Ediacara biota [571 to 539 million years (Ma) ago] is an enigmatic group of soft-bodied organisms that represents the first major radiation of complex, macroscopic, and eukaryotic life. Although some of these organisms represent animals [Metazoa; e.g., Bobrovskiy et al., 2018; Cuthill and Han, 2018], others do not appear to share any synapomorphies with extant metazoan clades and thus may represent extinct groups with no modern representatives (Darroch et al., 2018). Reconstructing the paleobiology and paleoecology of these organisms has long been complicated by their non-analog body plans, which have no counterparts in the present day. Despite these difficulties, cutting-edge quantitative analyses and modeling techniques have provided a back door into understanding Ediacaran organisms, allowing us to better constrain their place in the eukaryotic tree of life (Mitchell et al., 2015; Rahman et al., 2015; Darroch et al., 2017; Mitchell and Kenchington, 2018; Mitchell and Butterfield, 2018). In particular, spatial analyses (Mitchell et al., 2015), inference of population-level habitat competition and partitioning (Mitchell and Kenchington, 2018; Mitchell and Butterfield, 2018), modeling of feeding mode (Rahman et al., 2015), and modeling of facultative motility [supported by field observations (Darroch et al., 2017; Paterson et al., 2017; Ivantsov and Malakhovskaya, 2002; Ivantsov, 2011; 2013)] in enigmatic taxa have provided new insights into their affinities, as well as nutrient cycling and the overall complexity of Ediacaran ecosystems. Here, we use computational fluid dynamics (CFD) to reconstruct the feeding ecology of the enigmatic Ediacaran taxon \textit{Ernietta plateauensis} Pflug 1966. Although CFD has previously been used to study the paleobiology and paleoecology of individual fossils (Rahman et al., 2015; Darroch et al., 2017), in this study, we use this method to test hypotheses surrounding the functioning of Ediacaran ecological communities for the first time.

\textit{Ernietta} is a late Ediacaran ($\sim$548 to 538 Ma ago) sack-like organism with a modular architecture consisting entirely of tubular elements alternatingly stitched along a basal medial seam (Fig. \ref{fig:4fig1}B and fig.\ref{fig:4S1}) (Elliott et al., 2016; Ivantsov et al., 2016). \textit{Ernietta} likely maintained a sessile and semi-infaunal lifestyle, with some portion of the body cavity buried beneath the sediment-water interface, leaving, at minimum, an upper frill exposed in the water column (Ivantsov et al., 2016). \textit{Ernietta} is one of the youngest Ediacaran taxa, with examples known right up until the Precambrian-Cambrian boundary (Laflamme et al., 2013), and therefore may provide insights into the character of Ediacaran ecosystems immediately before the second pulse of end-Ediacaran extinction (Darroch et al., 2018). In this study, we analyze accumulations of \textit{Ernietta} from the Witputs subbasin (Fig. \ref{fig:4fig1}A), Namibia, where disparate spatial aggregations of relatively undeformed individuals (fig. \ref{fig:4S1} and table \ref{tab:4ST1}) are found with the ventral portion (i.e., the suture) facing down into the sediment (Fig. \ref{fig:4fig1}B and fig. \ref{fig:4S1}). This consistent orientation and lack of deformation suggests that these individuals were preserved in situ and hence indicates a gregarious ecology similar to many modern marine invertebrates.
\begin{figure}[h!]
	\includegraphics[width=0.5\textwidth]{Ernietta_Figure1.jpg}
	\centering
	\caption{\textbf{Study locality.} (A) Generalized stratigraphic section of Hansburg, Namibia, showing the distribution of \textit{Ernietta}-bearing units [redrawn from (Bouougri et al., 2011)]. Bmt, Basement; Kliphoek mbr, Kliphoek member; Mooif, Mooifontein. (B) Close-up photograph of an overturned slab containing exceptionally preserved \textit{Ernietta} with detailed suture and individual tube elements. Photo credit: Marc Laflamme, University of Toronto.}
	\label{fig:4fig1}
\end{figure}

\subsection{Ediacaran feeding modes}
Modern shallow marine settings are home to a wide variety of organisms with varied feeding modes, including photoautotrophy, chemoautotrophy, suspension feeding, grazing, predation, and deposit feeding. Previous work (Laflamme et al., 2009; 2013) has proposed that most members of the Ediacara biota were restricted to one of two possible feeding modes: osmotrophy or suspension feeding. Deposit feeding and predation is limited because of little evidence for movement or sediment disruption (Narbonne, 2005), indirect evidence of facultative mobility in some taxa notwithstanding (Darroch et al., 2017; Paterson et al., 2017; Narbonne, 2005). Furthermore, these two feeding modes can be discounted because the Ediacaran soft-bodied fossil record is almost entirely devoid of definitive body fossils with specialized feeding structures. The probable bilaterian \textit{Kimberella} is alone among the Ediacara biota in being found associated with scratch marks, representing surficial grazing (Ivantsov and Malakhovskaya, 2002; Ivantsov, 2011; 2013; Gehling et al., 2014), while \textit{Dickinsonia} likely fed saprophytically via its ventral sole (Sperling and Vinther, 2010). Photoautotrophy can be discounted as a possible feeding ecology for \textit{Ernietta} based on the presence of Erniettomorpha in deeper-water settings below the photic zone (Narbonne et al., 2014). Given the highly consistent and relatively simple body plans in this clade (Dececchi et al., 2017), it is unlikely that species within the erniettomorphs used completely different feeding modes. Chemoautotrophy is also unlikely as an Ediacaran feeding ecology, because the necessary levels of methane and hydrogen sulfide for chemosynthesis, such as near deep-sea vent communities (Little et al., 1998), are not supported by geochemical studies (Canfield et al., 2007). In Namibia, in particular, there is no geological evidence for the types of deposits that would support a dense chemoautrophic ecosystem. Consequently, osmotrophy and suspension feeding are the most plausible feeding modes for sessile members of the Ediacara biota, including \textit{Ernietta}.

Osmotrophy is most often invoked as a potential feeding ecology on the basis of surface area--to--volume (SA/V) ratios similar to those of modern organisms that feed via passive absorption of dissolved organic matter (Laflamme et al., 2013). The potential for suspension feeding has been suggested for some of the frondose taxa (Singer et al., 2012) and demonstrated in the triradial taxon \textit{Tribrachidium} (Rahman et al., 2015). Rahman \textit{et al.} (2015) used computer simulations of fluid flow to establish robust criteria for testing between suspension feeding and osmotrophy in Ediacaran organisms. Macroscopic osmotrophs rely on passive absorption of organic matter through membranes and thus maximize feeding by distributing flow evenly across all exposed exterior surfaces (Singer et al., 2012). An osmotrophic feeding model for \textit{Ernietta} would therefore predict that the flow would be evenly distributed over the entire surface of the organism. In contrast, suspension feeders obtain nutrients by transporting water through, or past, structures specialized to entrap organic particles (J\o rgensen, 1966; LaBarbera, 1984; Vogel, 1994). Thus, if \textit{Ernietta} was a suspension feeder, then we would expect water flow to be directed to specific parts of the anatomy, which presumably represented sites of specialized feeding structures in the living organism. CFD allows us to test between these two hypothesized feeding modes by simulating fluid flows around three-dimensional (3D), semi-infaunal digital models of \textit{Ernietta} in a virtual flume tank. Furthermore, we use fluid-structure interaction (FSI) simulations to assess how the rigidity of the \textit{Ernietta} model might affect fluid flow and thus feeding efficiency. Last, we carry out an independent test of osmotrophy by calculating the SA/V ratio of our 3D models, comparing these to the SA/V ratios of extant osmotrophic organisms (Laflamme et al., 2013).

\subsection{Gregarious behavior and feeding ecologies}
\textit{Ernietta} fossils are found aggregated in life position (e.g., presumed ventral sutures all facing down; Fig. 1B) in assemblages, which is highly suggestive of a gregarious lifestyle. Modern organisms aggregate for many reasons, including predator avoidance, reduced exposure to nutrient-depleted water (via tiering), or as a by-product of reproduction and recruitment. Ghisalberti \textit{et al.} (2014) demonstrated the importance of tiering within Ediacaran tiered frondose communities for developing canopy flow and enhancing vertical mixing of the water column, although recent analyses have proposed this to be less common than previously assumed (Mitchell and Kenchington, 2018). Enhanced vertical mixing offsets any depletion of nutrients from upstream individuals, as well as diluting possible waste products. While \textit{Ernietta} communities do not demonstrate similar vertical size variations, their gregarious behavior would most likely affect individual feeding efficiency and ecology. 

Many extant sessile marine invertebrates have evolved gregarious benthic ecologies to help with aspects of nutrient acquisition. For example, mussels and oysters form dense benthic accumulations that provide measurable benefits to suspension feeding (Bertness and Grosholz, 1985; van de Koppel et al., 2005). Studies have demonstrated increased success in particle capture rates when living in aggregated populations (Okamura, 1985); however, it has also been shown that some down current individuals (or those situated toward the center of patches) may receive fewer nutrients due to depletion from higher competition (Fr\'echette et al., 1993; Svane and Ompi, 1993; Butman et al., 1994). In addition, both advection-diffusion models and experimental flume studies demonstrate that increasing the number of individuals generates turbulence near the bed, thickening the turbulent boundary layer, and thus playing an important role in nutrient delivery (Butman et al., 1994; Fr\'echette et al., 1989). Topography created by accumulations of mussels increases the size of the turbulent boundary layer around the overall populations (Butman et al., 1994; Smits and Wood, 1985; Denny, 1988), and this produces vertical and horizontal mixing of nutrients over the length of the bed, thereby increasing the concentration of nutrients within the water column above the living populations (Butman et al., 1994). Many passive suspension feeders rely on this increased turbulence, as it mixes the water column and delivers more nutrients than simple laminar flow (Denny, 1988). Consequently, if gregarious living in \textit{Ernietta} was an adaptation to aid feeding, then this would therefore predict the redirection of fluid flow toward areas of nutrient acquisition for all individuals in a population, and this redirection should be equally as strong as that seen in solitary individuals. We test this hypothesis through CFD simulations of flow for multiple individuals in spatial groupings.

\section{Results}\label{Section heading 3} 
\subsection{Flow patterns}
In all the CFD simulations performed, fluid velocity decreased rapidly where the flow first encountered the model(s), with a steep velocity gradient developed close to the bottom of the computational domain (Fig. \ref{fig:4fig2} and figs. \ref{fig:4S5} to \ref{fig:4S7}). A region of recirculating flow, characterized by much lower velocities than ambient flow, formed within the central cavity of the \textit{Ernietta} model, as well as directly downstream of the model (Fig. \ref{fig:4fig2} and figs. \ref{fig:4S5} and \ref{fig:4S7}).

\begin{figure}[h!]
	\includegraphics[width=\textwidth]{Ernietta_Figure2.jpg}
	\centering
	\caption{\textbf{CFD results.} Results of CFD simulations in horizontal (left column) and vertical (right column) cross-sections. All models oriented parallel to flow, at moderate burial depth, and simulations were performed using an inlet velocity of 0.2 m/s. (\textbf{Top}) Single-model simulation results. (\textbf{Middle}) Spaced multiple-model simulation results. (\textbf{Bottom}) Clumped multiple-model simulation results.}
	\label{fig:4fig2}
\end{figure}

In the single-model CFD simulations (fig. \ref{fig:4S5}), downstream flow patterns were conserved between simulations with models in the same orientation, but recirculation became stronger with increasing velocity. Comparing simulations with models at different orientations (0$\degree$ and 90$\degree$), overall water velocity downstream of perpendicularly oriented individuals was consistently slower compared to those in parallel orientation. Recirculation was generated for all simulated burial depths. In both orientations, downward vertical velocity in the cavity was consistently strongest at the downstream internal face, while upward vertical velocity was strongest at the upper tip of the upstream external face of the \textit{Ernietta} model. Turbulence was always strongest for perpendicularly oriented individuals and increased with faster velocities. 

In the multiple-model CFD simulations, the flow patterns produced for each of the individual \textit{Ernietta} models were generally similar to the other individuals within the same row, as well as to those obtained for individuals in the single-model simulations in the same orientation. In particular, the region of recirculation developed within the central cavity was observed in all the simulations but was typically enhanced in downstream individuals (Fig. \ref{fig:4fig2} and fig. \ref{fig:4S6}). In each multiple-model simulation, the row of individuals furthest from the inlet typically experienced slightly higher flow velocities on their downstream internal face compared to velocities experienced by upstream models. Downstream models also experienced more strongly negative vertical velocity than upstream ones at these same downstream internal faces, indicative of greater fluid flow downwards into the cavity. This downward velocity is balanced by a faster than ambient upward velocity at the upstream internal face of these same downstream individuals. Velocities for upstream individuals were comparable to those in the single-model simulations, and cavity recirculation patterns among individuals of the same orientation were typically mirrored row-wise. Multiple-model simulations with mixed orientations in up- and downstream individuals did not exhibit mirrored recirculation patterns row-wise, but in simulations of well-spaced, mixed-orientation individuals, the individual patterns were similar to single-model simulations of the same respective orientations. Plots of turbulent kinetic energy for the well-spaced multiple-model simulations (Fig. \ref{fig:4fig3} and fig. \ref{fig:4S6}) show some weak turbulence around the sides of \textit{Ernietta} individuals and near the top of the cavities, with stronger turbulence above downstream individuals where models were placed in perpendicular orientation (fig. \ref{fig:4S6}).

In the clumped multiple-model CFD simulations (Fig. \ref{fig:4fig2} and fig. \ref{fig:4S6}), all vertical velocity patterns were enhanced compared to the well-spaced multiple-model simulations (fig. \ref{fig:4S6}), and downstream individuals experienced much stronger recirculation compared to upstream individuals. Compared to the well-spaced multiple-model simulations, downstream individuals in the clumped multiple-model simulations experienced slower overall flow velocities and lower recirculation within their cavities. This was not conserved in the clumped-mixed orientation simulations, where overall recirculation patterns and flow velocities were stronger for downstream individuals. In the turbulent kinetic energy plots for the clumped individuals, a much stronger turbulence was created above and downstream of downstream individuals, as indicated in fig. \ref{fig:4S6}.

In the FSI simulation (movies S1 and S2), flow patterns were generally conserved throughout the 10 s duration of the simulation, with recirculation within the cavity observed once the flow had reached steady state. There was a very small displacement ($<0.2$ mm) of the upper part of the \textit{Ernietta} model during the first 0.1 s of the simulation; however, no additional displacement was observed under steady-state flow.

\begin{figure}[h!]
	\includegraphics[width=\textwidth]{Ernietta_Figure3.jpg}
	\centering
	\caption{\textbf{CFD results.} Results of CFD simulations in vertical cross-sections showing vertical velocity (left column) and kinetic energy (right column). All models oriented parallel to flow, at moderate burial depth, and simulations were performed using an inlet velocity of 0.2 m/s. (\textbf{A} and \textbf{B}) Single-model simulation. (\textbf{C} to \textbf{F}) Spaced multiple- model results, where (\textbf{C}) and (\textbf{D}) show left column of individuals and (\textbf{E}) and (\textbf{F}) show right column of individuals with respect to flow. (\textbf{G} to \textbf{J}) Clumped multiple-model results, where (\textbf{G}) and (\textbf{H}) show left column of individuals and (\textbf{I}) and (\textbf{J}) show right column of individuals with respect to flow.}
	\label{fig:4fig3}
\end{figure}


\subsection{Drag calculations}
Drag forces increased and the coefficients of drag decreased with increasing inlet velocity (Table \ref{tab:4T1} and fig. \ref{fig:4S8}). In addition, drag forces and their coefficients increased with decreasing burial depth (increased relative height in the water column) and were greatest when individuals were oriented perpendicular to the flow. In multiple-model simulations, drag was typically close to zero for downstream individuals but more similar to that seen in the single-model simulations for upstream individuals. The exception to this pattern was the mixed-orientation multiple-model simulation, in which downstream individuals are offset from upstream ones (fig. \ref{fig:4S7}). In the multiple-model simulations, drag forces and their coefficients were greater in the clumped simulations than in the well-spaced ones, which, in turn, produced slightly more drag than single-model simulations with individuals in the same orientation (Table \ref{tab:4T1} and fig. \ref{fig:4S8}).

\subsection{SA/V ratios}
SA/V ratios of the exposed model (e.g., above the sediment-water interface; fig. \ref{fig:4S4}) increased with increasing burial depth of the organism (fig. \ref{fig:4S8}). The whole model (e.g., epibenthic or entirely above the sediment-water interface) had an SA/V ratio of 0.59 mm$^2$/mm$^3$, and the deeply buried model (e.g., sediment-water interface halfway between midline suture and top most portion of the model) had the highest SA/V ratio of 0.77 mm$^2$/mm$^3$ (fig. \ref{fig:4S8}). 

%\clearpage\newpage
\vspace{1cm}
{\footnotesize\tiny
	\begin{longtable}{p{0.14\textwidth} p{0.1\textwidth}l p{0.06\textwidth} p{0.06\textwidth} p{0.06\textwidth} p{0.06\textwidth} ll}
		\caption{\textbf{Drag Results.} Results of CFD simulations for single- and multiple-model simulations of \textit{Ernietta}, varying the current velocity (0.1, 0.2, and 0.5 m/s), burial depth (shallow, moderate, and deep), and orientation with respect to flow (parallel and perpendicular).}\\ 
		\label{tab:4T1}
		Density of fluid (kg/m3)    & Dynamic viscosity of fluid (kg/(s·m)) & & & & & & & \\
		1000 & 0.001  &  &   & &  &   &   &   \\
		&    &    &    & &  &     &  &  \\
		Model& Burial depth& Orientation   & Characteristic dimension (m) & Reference area (m$^2$) & Velocity (m/s) & Reynolds number & Drag force (N)  & Drag coefficient\\
		Single individual & Shallow  & Parallel & 0.059         & 0.0032   & 0.10  & 5900             & 0.01115498717230990                & 0.697186698269369  \\
		&                  &                & 0.059          & 0.0032   & 0.20   &11800           & 0.04435156048105120                & 0.692993132516425  \\
		&                            &                   & 0.059   & 0.0032        & 0.50        & 29500   & 0.27451391432455000                & 0.686284785811375  \\
		&      Shallow                         &  Perpendicular& 0.064                        & 0.0038              & 0.10           & 6400            & 0.01640526727730790 & 0.863435119858310  \\
		&                              &  & 0.064                        & 0.0038              & 0.20           & 12800           & 0.06556131975167460 & 0.862648944100981  \\
		&                                &  & 0.064                        & 0.0038              & 0.50           & 32000           & 0.40547097969682800 & 0.853623115151217  \\
		& Moderate                              & Parallel      & 0.059                        & 0.0024              & 0.10           & 5900            & 0.00780989011491970 & 0.650824176243308  \\
		&                               &       & 0.059                        & 0.0024              & 0.20           & 11800           & 0.03095450738813410 & 0.644885570586127  \\
		&                               &       & 0.059                        & 0.0024              & 0.50           & 29500           & 0.19148327641114800 & 0.638277588037160  \\
		& Moderate                              & Perpendicular & 0.064                        & 0.0028              & 0.10           & 6400            & 0.01097594350218370 & 0.783995964441693  \\
		&                               &  & 0.064                        & 0.0028              & 0.20           & 12800           & 0.04385177326839820 & 0.783067379792825  \\
		&                               &  & 0.064                        & 0.0028              & 0.50           & 32000           & 0.27217976318145000 & 0.777656466232714  \\
		& Deep                                  & Parallel      & 0.059                        & 0.0016              & 0.10           & 5900            & 0.00510221637973906 & 0.637777047467382  \\
		&                                   &       & 0.059                        & 0.0016              & 0.20           & 11800           & 0.02002824322207540 & 0.625882600689856  \\
		&                                   &       & 0.059                        & 0.0016              & 0.50           & 29500           & 0.12240245033436900 & 0.612012251671845  \\
		& Deep                                  & Perpendicular & 0.064                        & 0.0018              & 0.10           & 6400            & 0.00665568976802439 & 0.739521085336043  \\
		&                                   &  & 0.064                        & 0.0018              & 0.20           & 12800           & 0.02659742614565730 & 0.738817392934925  \\
		&                                   &  & 0.064                        & 0.0018              & 0.50           & 32000           & 0.16418447680940500 & 0.729708785819578  \\
		Four Individuals & & & & & & & \\
		Top left             & Moderate                              & Parallel      & 0.059                        & 0.0024              & 0.20           & 11800           & 0.0337107511642232  & 0.702307315921317  \\
		Bottom left          & Moderate                              & Parallel      & 0.059                        & 0.0024              & 0.20           & 11800           & 0.0336249551239988  & 0.700519898416642  \\
		Top right            & Moderate                              & Parallel      & 0.059                        & 0.0024              & 0.20           & 11800           & 0.0039417469198683  & 0.082119727497256  \\
		Bottom right         & Moderate                              & Parallel      & 0.059                        & 0.0024              & 0.20           & 11800           & 0.0030375563506614  & 0.063282423972112  \\
		Four Individuals & & & & & & & \\
		Top left             & Moderate                              & Perpendicular & 0.064                        & 0.0028              & 0.20           & 12800           & 0.0504436221184845  & 0.900778966401509  \\
		Bottom left          & Moderate                              & Perpendicular & 0.064                        & 0.0028              & 0.20           & 12800           & 0.0491364809391965  & 0.877437159628509  \\
		Top right            & Moderate                              & Perpendicular & 0.064                        & 0.0028              & 0.20           & 12800           & -0.0008403062351596 & -0.015005468484993 \\
		Bottom right         & Moderate                              & Perpendicular & 0.064                        & 0.0028              & 0.20           & 12800           & -0.0056891902315857 & -0.101592682706888 \\
		Four Individuals & & & & & & & \\
		Top left       & Moderate                              & Perpendicular & 0.064                        & 0.0028              & 0.20           & 12800           & 0.0498790059537312  & 0.890696534888057  \\
		Bottom left    & Moderate                              & Parallel      & 0.059                        & 0.0024              & 0.20           & 11800           & 0.0332994715036173  & 0.693738989658694  \\
		Top right      & Moderate                              & Parallel      & 0.059                        & 0.0024              & 0.20           & 11800           & -0.0011524043075931 & -0.024008423074855 \\
		Bottom right   & Moderate                              & Perpendicular & 0.064                        & 0.0028              & 0.20           & 12800           & 0.0043642874977630  & 0.077933705317196  \\
		Four Individuals, clumped & & & & & & & \\
		Top left            & Moderate                              & Parallel      & 0.059                        & 0.0024              & 0.20           & 11800           & 0.0426060103328862  & 0.887625215268462  \\
		Bottom left         & Moderate                              & Parallel      & 0.059                        & 0.0024              & 0.20           & 11800           & 0.0426196085320831  & 0.887908511085065  \\
		Top right           & Moderate                              & Parallel      & 0.059                        & 0.0024              & 0.20           & 11800           & -0.0074879970079540 & -0.155999937665708 \\
		Bottom right        & Moderate                              & Parallel      & 0.059                        & 0.0024              & 0.20           & 11800           & -0.0027149188517437 & -0.056560809411327 \\
		Four Individuals, clumped & & & & & & & \\
		Top left            & Moderate                              & Perpendicular & 0.064                        & 0.0028              & 0.20           & 12800           & 0.0580070614238671  & 1.035840382569060  \\
		Bottom left         & Moderate                              & Perpendicular & 0.064                        & 0.0028              & 0.20           & 12800           & 0.0565483085671746  & 1.009791224413830  \\
		Top right           & Moderate                              & Perpendicular & 0.064                        & 0.0028              & 0.20           & 12800           & -0.0085171293959361 & -0.152091596356002 \\
		Bottom right        & Moderate                              & Perpendicular & 0.064                        & 0.0028              & 0.20           & 12800           & -0.0084508226386397 & -0.150907547118565 \\
		Four Individuals, clumped & & & & & & & \\
		Top left     & Moderate                              & Perpendicular & 0.064                        & 0.0028              & 0.20           & 12800           & 0.0580510254958707  & 1.036625455283410  \\
		Bottom left  & Moderate                              & Parallel      & 0.059                        & 0.0024              & 0.20           & 11800           & 0.0418699175305886  & 0.872289948553929  \\
		Top right    & Moderate                              & Parallel      & 0.059                        & 0.0024              & 0.20           & 11800           & -0.0040699100616795 & -0.084789792951656 \\
		Bottom right & Moderate                              & Perpendicular & 0.064                        & 0.0028              & 0.20           & 12800           & -0.0071175827072387 & -0.127099691200690 \\
		Five Individuals & & & & & & & \\
		Top left               & Moderate                              & Perpendicular & 0.064                        & 0.0028              & 0.20           & 12800           & 0.0491217229681063  & 0.877173624430470  \\
		Bottom left            & Moderate                              & Parallel      & 0.059                        & 0.0024              & 0.20           & 11800           & 0.0328310384436475  & 0.683979967575990  \\
		Top right              & Moderate                              & Parallel      & 0.059                        & 0.0024              & 0.20           & 11800           & 0.0261873415135867  & 0.545569614866390  \\
		Middle right           & Moderate                              & Perpendicular & 0.064                        & 0.0028              & 0.20           & 12800           & 0.0161636012318585  & 0.288635736283187  \\
		Bottom right           & Moderate                              & Parallel      & 0.059                        & 0.0024              & 0.20           & 11800           & 0.0275210268558887  & 0.573354726164348
\end{longtable}}

\section{Discussion}\label{Section heading 3}
\subsection{Competing feeding models for \textit{Ernietta}}
The results of the CFD simulations show that the flow was not distributed evenly over the entire surface of the organism, as predicted if \textit{Ernietta} was feeding osmotrophically (Laflamme et al., 2013; Singer et al., 2012). Instead, our simulations reveal that there was consistent and strong recirculation within the central cavity of the organism, regardless of the burial depth (deeply buried to midway between the suture and top of the model or shallowly buried to the midway point between the bottom and midline suture of the model), current velocity, and orientation with respect to flow (Fig. \ref{fig:4fig2} and figs. \ref{fig:4S5} to \ref{fig:4S7}), as expected if \textit{Ernietta} was a suspension feeder (Vogel, 1994). Even when the model was allowed to deform under fluid flow in the FSI simulation, recirculation was still apparent once the flow reached steady state. The ubiquity of recirculation in the presence of these varying conditions indicates that \textit{Ernietta} would have been capable of functioning as a passive suspension feeder in an environment with variable current velocities and directions, regardless of the burial depth and variously interpreted endobenthic lifestyles (i.e., fully endobenthic or semi-endobenthic or surficial epibenthic). Evidence for recirculation within the central cavities of individual \textit{Ernietta} is also apparent in fossil material; slow recirculation of fluid would likely lead to settling of sediment particles within the body cavity, which matches observations of graded sediment fill within \textit{Ernietta} fossils (Ivantsov et al., 2016). Recirculation would have cycled nutrient-depleted fluid out of the cavity, providing access to new, nutrient-rich flow. The observed recirculation indicates that the internal cavity of \textit{Ernietta} was the likely site of nutrient acquisition, although the precise mechanism of particle capture and processing remains uncertain, given the lack of specialized feeding structures preserved in fossils.

We also analyzed the SA/V ratios of our models as an independent test for osmotrophy. SA/V ratios for the three burial depths and whole model lie in a tight range (0.59 to 0.77 mm$^2$/mm$^3$) that falls far below the values exhibited by extant deep-sea osmotrophs [typical ranges of 8 to 20,000 mm$^2$/mm$^3$; (Schulz et al., 1999)] and modeled SA/V for the Ediacaran frond \textit{Fractofusus} [1 to 10,000 mm$^2$/mm$^3$; (Laflamme et al., 2013)]. Coupled with the inference of a semi-infaunal life habit for \textit{Ernietta} (Elliott et al., 2016; Ivantsov et al., 2016), these SA/V ratios suggest that an osmotrophic feeding ecology was unlikely. Even if a solitary \textit{Ernietta} individual was capable of absorbing nutrients from the surrounding porewater as well as the water column, it would likely deplete nutrients from the surrounding porewater within the sediment rapidly. These nutrients, in turn, would have a low replenishment rate due to the overlying microbial mat acting as a diffusive boundary. Depletion of the surrounding porewaters would have been further enhanced if we consider the inferred gregarious life habit of these organisms (Elliott et al., 2016; Ivantsov et al., 2016; Bouougri et al., 2011), indicating that only the exposed portions of the organism would likely be absorbing nutrients. Furthermore, our \textit{Ernietta} model comprised only a single layer of tubes, while some fossils show evidence for two layers (Elliott et al., 2016; Ivantsov et al., 2016). Incorporating this additional layer of tubes into the model would likely increase volume without drastically increasing surface area, thus lowering SA/V values even further (or at minimum maintain SA/V values if the inner tubes were not in direct contact with the other tubes). The only means by which \textit{Ernietta} could have attained the high SA/V necessary for osmotrophy is by limiting the active tissue in each tubular unit to a very thin layer surrounding an empty vacuole (\textit{15}), which is improbable given the structural rigidity necessary for the inferred semi-infaunal lifestyle.

\subsection{Gregarious behavior}
Our well-spaced multiple-model simulations (Fig. \ref{fig:4fig3} and fig. \ref{fig:4S6}) show that downstream individuals were exposed to comparatively faster flow velocities than upstream ones while maintaining stronger patterns of recirculation within the internal cavity compared to upstream individuals. Moreover, the strength of recirculation within the cavity in upstream individuals in the multiple-model simulations is very similar to that seen in the single-model simulations (fig. \ref{fig:4S5}). Having \textit{Ernietta} individuals grouped in tighter aggregates (i.e., clumped arrangements; Figs. \ref{fig:4fig2} and \ref{fig:4fig3} and fig. \ref{fig:4S5}) preserves the increased recirculation within the cavities in the downstream individuals and additionally creates increased turbulence above downstream individuals, both factors that would have likely enhanced nutrient delivery. This nutrient delivery to downstream individuals is further enhanced by the strong downward velocity at the downstream internal faces of their cavities in conjunction with the increased turbulence above downstream individuals. This turbulence remixes flow sourced from the cavities of upstream individuals with the surrounding ambient flow; some of this fluid is then redirected into the cavity of downstream individuals. This indicates that the nutrient-depleted flow from upstream cavities would be mixed with more nutrient-rich ambient flow above the aggregated individuals and then preferentially transported into the feeding cavities of the downstream organisms. These results provide a paleoecological and paleobiological explanation for the observation that \textit{Ernietta} lived gregariously within aggregated populations (Fig. \ref{fig:4fig1} and fig. \ref{fig:4S1}). The enhancement of recirculation within downstream cavities coupled with the hypothesized benefits of gregarious living for feeding, such as vertical mixing of nutrients in the water column and enhanced turbulence within the boundary layer (Butman et al., 1994; Smits and Wood, 1985; Denny, 1988), strongly suggests that a gregarious lifestyle would have aided feeding in \textit{Ernietta}.

There are several alternative explanations for gregarious behavior in extant marine invertebrates, but these can be dismissed for \textit{Ernietta}. For example, many extant aquatic organisms aggregate as a consequence of reproduction. If this was the sole driver, then we might expect to see smaller individuals in close association with larger individuals, as seen in the Ediacaran organism \textit{Fractofusus }[(Mitchell et al., 2015); though see (Droser and Gehling, 2008)]. However, in nearly all the studied assemblages of \textit{Ernietta}, there is no reported evidence of such a size distribution, and our beds show no such distribution (table \ref{tab:4ST1}). Moreover, under the velocity conditions in which \textit{Ernietta} likely lived (Maloney et al., 2018), offspring would have been transported substantial distances (meters to kilometers) from their parents (Gaylord et al., 2002), which would likely result in more dispersed colonization sites. Even if their settling rate was exceedingly fast, we would anticipate a degree of current alignment within the offspring (Shanks, 2009), which we do not observe in the fossil communities preserved at Farm Hansburg (Gaylord et al., 2002). Thus, while the initial placement of these organisms is likely influenced by dispersal from reproduction, their ecological success in aggregations was likely driven by factors other than reproductive dispersal alone. Avoidance of predation is another possible explanation for aggregating, but there is currently no evidence for any predation within the soft-bodied Ediacara biota (Paterson et al., 2017; Narbonne, 2005). A final possibility involves aggregation as a means of elevating one-self within the water column, thereby partitioning feeding among individuals at different tiering heights, as has been documented in barnacles (Bertness et al., 1998) and oysters (Lenihan, 1999). While this arrangement has been demonstrated in a single community of older age (Mitchell and Kenchington, 2018; Ghisalberti et al., 2014; Clapham and Narbonne, 2002), none of these features were observed at Farm Hansburg and Kuibis Farm, Namibia, or in our individual size data (table \ref{tab:4ST1}). We do note a large size range within collected \textit{Ernietta}, but we do not see defined size classes such as what might be observed in tiering. Furthermore, we see no evidence for attachment to other individuals for tiering as often seen in modern organisms (Bertness et al., 1998).

Consequently, we infer that the gregarious lifestyle of \textit{Ernietta} was primarily an adaptation to aid in feeding, and more specifically a facilitatory interaction. Our CFD results demonstrate that downstream individuals consistently experienced less drag than upstream individuals, which would buffer fluid-derived strain on downstream organisms. The minimization of drag bestows a number of protective benefits to the organism, including decreased chance of tissue tears from faster water velocities, reduced chance of abrasion from larger particles within the water, and the ability to capture nutrients in less stressful conditions. However, increased turbulence from overall topography generated by aggregated individuals (Fig. \ref{fig:4fig3} and fig. \ref{fig:4S6}), as also outlined above for some modern mussels (Butman et al., 1994; Smits and Wood, 1985; Denny, 1988), would disrupt fluid flow around them and aid in transporting organic particles from microbial mats into the water column. While this is not explicitly observed in our simulations, one limitation in assessing this feature in our simulations is that the virtual seafloor is not characterized by any degree of surface topography or roughness. At all other locations of nonuniform topography (e.g., where the models are located), we do see mixing and turbulent energy, indicating that this mixing would likely occur but is not accurately portrayed because of limitations in the experimental design. This vertical mixing would replenish water currents depleted in nutrients following feeding by upstream individuals, ensuring that downstream individuals had access to nutrient-rich currents. In modern epibenthic mussels, this phenomenon is pivotal for communities (Butman et al., 1994), and survival of downstream individuals has been hypothesized to be unlikely without this flow characteristic (Denny, 1988).

Last, our CFD analyses provide a convincing mechanism for the accumulation of layered sediments seen inside fossil \textit{Ernietta} (Ivantsov et al., 2016). Simulations illustrate significant recirculation of current around communities of \textit{Ernietta}, as well as lower-velocity recirculation inside the cavities of individual organisms. In a tidally and storm-influenced paleoenvironment (Ivantsov et al., 2016; Maloney et al.,  2018), the suspended sediment would therefore have settled out over \textit{Ernietta} populations, forming layered deposits inside cavities and accumulating around the outside of individuals. Hence, these communities of \textit{Ernietta} would likely have contributed to forming low-relief mounds on the seafloor (in support of this, in situ \textit{Ernietta} accumulations on Farm Hansburg often form discrete clumps). Further, the gregarious nature of these organisms and associated benefits for feeding represents one of the oldest examples of facilitation, which emphasizes that Ediacaran ecosystems were much more complex than has been previously imagined, and provides a paleoecological link to the animal-dominated ecosystems of the Paleozoic (Darroch et al., 2018).

\section{Materials and Methods}\label{Section heading 3}
\subsection{Geological setting}
Fossil outcrops at Farm Hansburg (Fig. \ref{fig:4fig1}B) preserve communities of \textit{Ernietta} within 20- to 30-cm-thick medium- to fine-grained planar-bedded sandstones (Bouougri et al., 2011). \textit{Ernietta} was restricted to storm-influenced muddy tidal flats, suggesting that these organisms thrived in environments with periodic sediment supply, fluctuating salinity, and medium- to low-flow velocities (Maloney et al., 2018). Although these fossiliferous horizons were thought to belong to the Kanies Member of the Kuibis Formation (Bouougri et al., 2011), new chemostratigraphic data instead suggest that they belong to the Kliphoek Member (Maloney et al., 2018), thus placing them as stratigraphically equivalent to the iconic fossil horizons preserved at Farm Aar (Fig. \ref{fig:4fig1}A) Maloney et al., 2018). Within the fossiliferous horizons, the vast majority of \textit{Ernietta} that we found are in disparate spatial aggregations (fig. \ref{fig:4S1} and table \ref{tab:4ST1}), although we cannot discount the presence of rare, isolated individuals. Most individuals within communities are found preserved in a common orientation, with the ventral portion (i.e., the suture) facing down into the sediment (Fig. \ref{fig:4fig1}B and fig. \ref{fig:4S1}). This common orientation and relative lack of deformation comprise strong evidence that \textit{Ernietta} were preserved in life position, rather than transported. Typical accumulations consist of 5 to 15 closely spaced individuals (fig. \ref{fig:4S1}), with rare larger slabs preserving less dense populations.

\subsection{\textit{Ernietta} model construction}
A 3D digital model of \textit{Ernietta} was constructed in COMSOL Multiphysics v. 5.3a through box modeling. The model was built from multiple cylindrical elements, which were iteratively added, moved, rotated, and scaled to approximate the modular shape of the organism (fig. \ref{fig:4S2}). The model was scaled on the basis of measurements reported for published fossil material (Ivantsov et al., 2016) and incomplete specimens collected during fieldwork from Namibia (fig. \ref{fig:4S3}). To avoid adding additional interpretive biases, the model was based solely off fossil material and not previous artistic reconstructions. Hence, some smaller features, such as specialized feeding structures, are likely missed because of taphonomic overprint. Surface area and volume measurements were obtained using VGStudio Max 2.2.

\subsection{Computational fluid dynamics}
CFD simulations were carried out using COMSOL Multiphysics v. 5.3a. The \textit{Ernietta} model was fixed to the lower surface of the computational domain, which consisted of a cuboid (fig. \ref{fig:4S3}). Models were oriented upright in/on the sediment; this decision was based both on observations made in the field on Farm Hansburg (where the overwhelming majority of our specimens were found in an upright orientation) and the nature of sediment infill reported by Ivantsov (2013), who inferred that the sediment accumulated inside \textit{Ernietta} cavities during life (and so also supported an upright orientation). Portions of the model considered to be buried were subtracted from the domain, leaving only the exhumed regions of the model, thereby approximating different burial depths possible for a semi-infaunal lifestyle. An inlet with a normal inflow velocity boundary condition was assigned to one end of the domain, with a zero-pressure boundary condition assigned to the opposing end. Slip boundary conditions were assigned to the top and sides of the domain, allowing inviscid flow along the walls, and a no-slip boundary condition was assigned to the lower surface of the domain and the surfaces of the fossil, fixing the fluid velocity at zero. The fluid properties of water [density = 1000 kg/m$^3$; dynamic viscosity ($\mu$) = 0.001 kg/(s⋅m)] were assigned to the model. The domain was meshed using free tetrahedral elements, which varied in size according to the distance from the fossil (larger elements used in regions further away from the fossil). We conducted a sensitivity analysis to identify the optimal mesh size (table \ref{tab:4ST2}) and, based on this, selected COMSOL's ``normal" mesh parameter for use in all the simulations. Simulations were run using the shear stress transport turbulence model, which solves the Reynolds- averaged Navier-Stokes equations, and a stationary solver was used to compute the steady-state flow patterns.

CFD simulations were carried out with inlet velocities of 0.1, 0.2, and 0.5 m/s (Reynolds numbers, 5900 to 32,000) (Table \ref{tab:4T1} and section \ref{sec:SuppRe}), which encompass typical current velocities in shallow marine conditions on modern continental shelves (Valle-Levinson and Matsuno, 2003). Because the orientation of \textit{Ernietta} with respect to the current is poorly constrained based on the fossil record, we ran simulations with models oriented at both 0$\degree$ and 90$\degree$ to the inlet (figs. \ref{fig:4S3} and \ref{fig:4S4}). The life mode of \textit{Ernietta} is debated, and it has been interpreted as fully endobenthic (Crimes and Fedonkin, 1996), surficial epibenthic (Dzik, 1999), and semi-endobenthic (Elliott et al., 2016; Ivantsov et al., 2016; Seilacher, 1992). To address the different interpretations of burial depths of \textit{Ernietta}, we performed simulations at three positions relative to the sediment-water interface, all of which correspond to semi-infaunal lifestyles, with the most shallowly buried model closely resembling an epibenthic lifestyle (fig. \ref{fig:4S4}).

We carried out a series of simulations using multiple \textit{Ernietta} individuals to evaluate the impact of a gregarious lifestyle on fluid flow. Six of these simulations were set up, with four individuals ar- ranged in a square in different orientations and positions relative to the inlet, walls, and other individuals (fig. \ref{fig:4S6}). These six simulations were divided into ``clumped" (fig. \ref{fig:4S6}) and ``spaced" (fig. \ref{fig:4S6}) arrangements, where interindividual distances were adjusted. The fifth simulation included five individuals, which were arranged with a row of three individuals downstream of a row of two individuals (fig. \ref{fig:4S7}). All of these simulations were conducted using an inlet velocity of 0.2 m/s and with \textit{Ernietta} individuals at a ``moderate" burial depth (Table \ref{tab:4T1}). This allowed us to assess the impact of orientation and spacing on flow patterns in multi-individual assemblages.

Last, we conducted an FSI simulation (\textcolor{red}{movies S1 and S2}) to evaluate the extent to which the \textit{Ernietta} model was deformed by fluid flow. The material properties of silicone rubber [density = 1100 kg/m$^3$; Poisson's ratio = 0.47; Young's modulus = 1,000,000 Pa; (Cambridge University Engineering Department, 2003)] were assigned to a single individual of \textit{Ernietta} oriented at 90$\degree$ to the inlet with a moderate burial depth, and an FSI simulation was carried out using a normal mesh size and a simple algebraic yPlus turbulence model. A time-dependent simulation was run over a period of 10 s, with the inlet velocity increased from 0 to 0.2 m/s during the first 0.1 s of the simulation. 

Simulation results were visualized as 2D plots showing overall flow velocity magnitude ($U$), flow velocity in the vertical axis ($w$), and turbulent kinetic energy magnitude ($k$) at horizontal and vertical cross-sections through the domain to characterize flow patterns. In addition, drag forces and their coefficients were calculated to quantify the forces exerted by the fluid on \textit{Ernietta} in different positions (fig. \ref{fig:4S4}).

\section{Acknowledgments} \label{Section heading 3}
We thank B. Viljoen and L. Viljoen for their extraordinary hospitality and for access to the field localities at Farm Hansburg. We thank D. J. Furbish for insightful discussion in fluid mechanics and D. Mazierski for artistic reconstruction. We also thank J. Hoyal-Cuthill, two anonymous reviewers, and the editor R. Wood for constructive comments and criticisms. \textbf{Funding:} M.L. was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant (RGPIN 435402) and the National Geographic (grant no. 9241-14). I.A.R. was funded by the Oxford University Museum of Natural History. S.A.F.D. acknowledges generous funding from the National Geographic (grant no. 9968-16) and a Paleontological Society Arthur Boucot Award. \textbf{Data and materials availability:} All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. CFD simulations are on Dryad (doi:10.5061/dryad.v9s0hk5).
\clearpage\newpage
\begin{thebibliography}{100}\label{Section heading 3}
	\bibitem{Bobrovskiy2018} I. Bobrovskiy, J. M. Hope, A. Ivantsov, B. J. Nettersheim, C. Hallmann, J. J. Brocks, Ancient steroids establish the Ediacaran fossil \textit{Dickinsonia} as one of the earliest animals. \textit{Science} \textbf{361}, 1246--1249 (2018).
	\bibitem{Cuthill2018} J. F. H. Cuthill, J. Han, Cambrian petalonamid \textit{Stromatoveris phylogenetically} links Ediacaran biota to later animals. \textit{Palaentology} \textbf{61}, 813--823 (2018).
	\bibitem{Darroch2018} S. A. F. Darroch, E. F. Smith, M. Laflamme, D. H. Erwin, Ediacaran extinction and Cambrian explosion. \textit{Trends Ecol. Evol.} \textbf{33}, 653--663 (2018).
	\bibitem{Mitchell2015} E. G. Mitchell, C. G. Kenchington, A. G. Liu, J. J. Matthews, N. J. Butterfield, Reconstructing the reproductive mode of an Ediacaran macro-organism. \textit{Nature} \textbf{524}, 343--346 (2015).
	\bibitem{Rahman2015} I. A. Rahman, S. A. F. Darroch, R. A. Racicot, M. Laflamme, Suspension feeding in the enigmatic Ediacaran organism \textit{Tribrachidium} demonstrates complexity of Neoproterozoic ecosystems. \textit{Sci. Adv.} \textbf{1}, e1500800 (2015).
	\bibitem{Darroch2017} S. A. F. Darroch, I. A. Rahman, B. M. Gibson, R. A. Racicot, M. Laflamme, Inference of facultative mobility in the enigmatic Ediacaran organism \textit{Parvancorina}. \textit{Biol. Lett.} \textbf{13}, 20170033 (2017).
	\bibitem{Mitchell2018} E. G. Mitchell, C. G. Kenchington, The utility of height for the Ediacaran organisms of Mistaken Point. \textit{Nat. Ecol. Evol.} \textbf{2}, 1218--1222 (2018).
	\bibitem{Mitchell2018b} E. G. Mitchell, N. J. Butterfield, Spatial analyses of Ediacaran communities at Mistaken Point. \textit{Paleobiology} \textbf{44}, 40--57 (2018).
	\bibitem{Paterson2017} J. R. Paterson, J. G. Gehling, M. L. Droser, R. D. C. Bicknell, Rheotaxis in the Ediacaran epibenthic organism \textit{Parvancorina} from South Australia. \textit{Sci. Rep.} \textbf{7}, 45539 (2017).
	\bibitem{Ivantsov2002} A. Y. Ivantsov, Y. E. Malakhovskaya, Giant traces of Vendian animals. \textit{Dokl. Earth Sci.} \textbf{385}, 618--622 (2002).
	\bibitem{Ivantsov2011} A. Y. Ivantsov, Feeding traces of proarticulata—The Vendian metazoa. \textit{Paleontol. J.} \textbf{45}, 237--248 (2011).
	\bibitem{Ivantsov2013} A. Y. Ivantsov, Trace fossils of Precambrian metazoans ``Vendobionta" and ``Mollusks". \textit{Stratrigr. Geol. Corr.} \textbf{21}, 252--264 (2013).
	\bibitem{Elliott2016} D. A. Elliott, P. W. Trusler, G. M. Narbonne, P. Vickers-Rich, N. Morton, M. Hall, K. H. Hoffmann, G. I. C. Schneider, \textit{Ernietta} from the late Ediacaran Nama Group, Namibia. \textit{J. Paleontol.} \textbf{90}, 1017--1026 (2016).
	\bibitem{Ivantsov2016} A. Y. Ivantsov, G. M. Narbonne, P. W. Trusler, C. Greentree, P. Vickers-Rich, Elucidating \textit{Erniettia}: New insights from exceptionally preserved specimens in the Ediacaran of Namibia. \textit{Lethaia} \textbf{49}, 540--554 (2016).
	\bibitem{Laflamme2013} M. Laflamme, S. A. F. Darroch, S. M. Tweedt, K. J. Peterson, D. H. Erwin, The end of the Ediacara biota: Extinction, biotic replacement, or Cheshire Cat? \textit{Gondwana Res.} \textbf{23}, 558--573 (2013).
	\bibitem{Laflamme2009} M. Laflamme, S. Xiao, M. Kowalewski, Osmotrophy in modular Ediacara organisms. \textit{Proc. Natl. Acad. Sci. U.S.A.} \textbf{106}, 14438--14443 (2009).
	\bibitem{Narbonne2005} G. M. Narbonne, The Ediacara biota: Neoproterozoic origin of animals and their ecosystems. \textit{Annu. Rev. Earth Planet. Sci.} \textbf{33}, 421--442 (2005).
	\bibitem{Gehling2014} J. G. Gehling, B. N. Runnegar, M. L. Droser, Scratch traces of large Ediacara bilaterian animals. \textit{J. Paleontol.} \textbf{88}, 284--298 (2014).
	\bibitem{Sperling2014} E. A. Sperling, J. Vinther, A placozoan affinity for \textit{Dickinsonia} and the evolution of late Proterozoic metazoan feeding modes. \textit{Evol. Dev.} \textbf{12}, 201--209 (2010).
	\bibitem{Narbonne2014} G. M. Narbonne, M. Laflamme, P. W. Trusler, R. W. Dalrymple, C. Greentree, Deep-water Ediacaran fossils from northwestern Canada: Taphonomy, ecology, and evolution. \textit{J. Paleontol.} \textbf{88}, 207--223 (2014).
	\bibitem{Deceechi2017} T. A. Dececchi, G. M. Narbonne, C. Greentree, M. Laflamme, Relating Ediacaran fronds. \textit{Paleobiology} \textbf{43}, 171--180 (2017).
	\bibitem{Little1998} C. T. S. Little, R. J. Herrington, V. V. Maslennikov, V. V. Zaykov, The fossil record of hydrothermal vent communities, in \textit{Modern Ocean Floor Processes and the Geological Record}, R. A. Mills, K. Harrison, Eds. (Geologic Society, London, Special Publications, 1998), vol. 148, pp. 259--270.
	\bibitem{Canfield2007} D. E. Canfield, S. W. Poulton, G. M. Narbonne, Late-Neoproterozoic deep-ocean oxygenation and the rise of animal life. \textit{Science} \textbf{315}, 92--95 (2007).
	\bibitem{Singer2012} A. Singer, R. Plotnick, M. Laflamme, Experimental fluid mechanics of an Ediacaran frond. \textit{Paleontol. Electron.} \textbf{15}, 19A (2012).
	\bibitem{Jorgensen1984} C. B. J\o rgensen, \textit{Biology of Suspension Feeding} (Pergamon Press, 1966). 
	\bibitem{LaBarbera1984} M. LaBarbera, Feeding currents and particle capture mechanisms in suspension feeding animals. \textit{Integr. Comp. Biol.} \textbf{24}, 71--84 (1984).
	\bibitem{Vogel1994} S. Vogel, \textit{Life in Moving Fluids: The Physical Biology of Flow} (Princeton Univ. Press, 1994). 
	\bibitem{Ghisalberti2014} M. Ghisalberti, D. A. Gold, M. Laflamme, M. E. Clapham, G. M. Narbonne, R. E. Summons, D. T. Johnston, D. K. Jacobs, Canopy flow analysis reveals the advantage of size in the oldest communities of multicellular eukaryotes. \textit{Curr. Biol.} \textbf{24}, 305--309 (2014).
	\bibitem{Bertness1985} M. D. Bertness, E. D. Grosholz, Population dynamics of the ribbed mussel, \textit{Geukensia demissa}: The costs and benefits of an aggregated distribution. \textit{Oecologia} \textbf{67}, 192--204 (1985).
	\bibitem{Koppel2005} J. van de Koppel, M. Rietkerk, N. Dankers, P. M. J. Herman, Scale-dependent feedback and regular spatial patterns in young mussel beds. \textit{Am. Nat.} \textbf{165}, E66--E77 (2005).
	\bibitem{Okamura1985} B. Okamura, The effects of ambient flow velocity, colony size, and upstream colonies on the feeding success of Bryozoa. II. \textit{Conopeum reticulum} (Linnaeus), an encrusting species. \textit{J. Exp. Mar. Biol. Ecol.} \textbf{89}, 69--80 (1985).
	\bibitem{Frechette1993} M. Fr\'{e}chette, D. Lefaivre, C. A. Butman, Bivalve feeding and the benthic boundary layer, in \textit{Bivalve Filter Feeders in Estuarine and Coastal Ecosystem Processes}, R. F. Dame, Ed. (Springer, 1993), pp. 325--369.
	\bibitem{Svane1993} I. Svane, M. Ompi, Patch dynamics in beds of the blue mussel \textit{Mytilu edulis} L.: Effects of site, patch size, and position within a patch. \textit{Ophelia} \textbf{37}, 187--202 (1993).
	\bibitem{Butman1994} C. A. Butman, M. Fr\'{e}chette, W. R. Geyer, V. R. Starczak, Flume experiments on food supply to the blue mussel \textit{Mytilus edulis} L. as a function of boundary-layer flow. \textit{Limnol. Oceanogr.} \textbf{39}, 1755--1768 (1994).
	\bibitem{Frechette1989} M. Fr\'{e}chette, C. A. Butman, W. R. Geyer, The importance of boundary-layer flows in supplying phytoplankton to the benthic suspension feeder, \textit{Mytilus edulis} L.. \textit{Limnol. Oceanogr.} \textbf{34}, 19--36 (1989).
	\bibitem{Smits1985} A. J. Smits, D. H. Wood, The response of turbulent boundary layers to sudden perturbations. \textit{Annu. Rev. Fluid Mech.} \textbf{17}, 321--358 (1985).
	\bibitem{Denny1988} M. W. Denny, \textit{Biology and the Mechanics of the Wave-Swept Environment} (Princeton Univ. Press, 1988).
	\bibitem{Schulz1999} H. N. Schulz, T. Brinkhoff, T. G. Ferdelman, M. Hern\'{a}ndez Marin\'{e}, A. Teske, B. B. J\o rgensen, Dense populations of a giant sulfur bacterium in Namibian shelf sediments. \textit{Science} \textbf{284}, 493--495 (1999).
	\bibitem{Bouougouri2011} E. H. Bouougri, H. Porada, K. Weber, J. Reitner, Sedimentology and palaeocology of \textit{Ernietta}-bearing Ediacaran deposits in southern Namibia: Implications for infaunal vendobiont communities, in \textit{Advances in Stromatolite Geobiology} (Springer, 2011), pp. 473--506.
	\bibitem{Droser2008} M. L. Droser, J. G. Gehling, Synchronous aggregate growth in an abundant new Ediacaran tubular organism. \textit{Science} \textbf{319}, 1660--1662 (2008).
	\bibitem{Maloney2018} K. M. Maloney, A. J. Facciol, B. M. Gibson, A. Cribb, B. E. Koester, C. G. Kenchington, T. H. Boag, R. A. Racicot, S. A. F. Darroch, M. Laflamme, Facies analysis of fossiliferous ediacaran deposits in southern Namibia, paper presented at the International Sedimentological Congress, Quebec City, QuebecC, Canada, 2018.
	\bibitem{Gaylord2002} B. Gaylord, D. C. Reed, P. T. Raimondi, L. Washburn, S. R. McLean, A physically based model of macroagal spore dispersal in the wave and current-dominated nearshore. \textit{Ecology} \textbf{83}, 1239--1251 (2002).
	\bibitem{Shanks2009} A. L. Shanks, Pelagic larval duration and dispersal distance revisited. \textit{Biol. Bull.} \textbf{216}, 373--385 (2009).
	\bibitem{Bertness1998} M. D. Bertness, S. D. Gaines, S. M. Yeh, Making mountains out of barnacles: The dynamics of acorn barnacle hummocking. \textit{Ecology} \textbf{79}, 1382--1394 (1998).
	\bibitem{Lenihan1999} H. S. Lenihan, Physical-biological coupling on oyster reefs: How habitat structure influences individual performance. \textit{Ecol. Monogr.} \textbf{69}, 251--275 (1999).
	\bibitem{Clapham2002} M. E. Clapham, G. M. Narbonne, Ediacaran epifaunal tiering. \textit{Geology} \textbf{30}, 627--630 (2002). 
	\bibitem{Darroch2018} S. A. F. Darroch, M. Laflamme, P. J. Wagner, High ecological complexity in benthic Ediacaran communities. \textit{Nat. Ecol. Evol.} \textbf{2}, 1541--1547 (2018).
	\bibitem{Valle} A. Valle-Levinson, T. Matsuno, Tidal and subtidal flow along a cross-shelf transect on the East China Sea. \textit{J. Oceanogr.} \textbf{59}, 573--584 (2003).
	\bibitem{Crimes1996} T. P. Crimes, M. A. Fedonkin, Biotic changes in platform communities across the Precambrian-Phanerozoic boundary. \textit{Riv. Ital. Paleontol. S.} \textbf{102}, 317--332 (1996).
	\bibitem{Dzik1999} J. Dzik, Organic membranous skeleton of the Precambrian metazoans from Namibia. \textit{Geology} \textbf{27}, 519--522 (1999).
	\bibitem{Seilacher1992} A. Seilacher, Vendobionta and Psammocorallia: Lost constructions of Precambrian evolution. \textit{J. Geol. Soc.} \textbf{149}, 607--613 (1992).
	\bibitem{Cambridge} Cambridge University Engineering Department, Materials Data Book (Cambridge University Engineering Department, 2003).
\end{thebibliography}
\clearpage\newpage
\section{Appendix}\label{Section heading 3}
\begin{figure}[h!]
	\includegraphics[width=\textwidth]{Ernietta_FigureS1.jpg}
	\centering
	\caption{Field photographs of \textit{Ernietta} aggregations likely representing bioherms. Photo credit A-D: Marc Laflamme, University of Toronto Mississauga }
	\label{fig:4S1}
\end{figure}
\newpage
\begin{figure}
	\includegraphics{Ernietta_FigureS2.jpg}
	\centering
	\caption{\textit{Ernietta} model construction for CFD analyses. Three-dimensional digital model of the Ediacaran organism \textit{Ernietta}was created in COMSOL Multiphysics version 5.3a by iteratively adding and modifying cylindrical elements. The dimensions of the model (45 mm long, 45 mm wide, and 10 mm high) were derived from Ivantsov et al.'s (2016) complete specimen (NESM-F722 - 4) and the average dimensions of specimens recorded from original field work in Kuibis Farm (26$\deg$37'35.00"S, $16\deg$41'07.00"E) and Hansburg, Namibia (26$\deg$17'52.00"S, $16\deg$54'13.00"E). Specimens from Kuibis Farm only preserved the lower-most portions of the organisms, but were consistent among the samples for overall ventral morphology. Following construction of the model in COMSOL, smoothing and removal of overlapping elements was carried out in VG Studio Max version 2.2.}
	\label{fig:4S2}
\end{figure}
\newpage
%\newgeometry{margin=1cm}
\begin{landscape}
	%\begin{small}
	{\footnotesize\tiny
		\begin{longtable}{ p{0.03\textwidth} p{0.03\textwidth} p{0.03\textwidth} p{0.06\textwidth} p{0.08\textwidth} p{0.08\textwidth} p{0.025\textwidth} p{0.025\textwidth} p{0.05\textwidth} p{0.05\textwidth} p{0.05\textwidth} p{0.05\textwidth} p{0.05\textwidth} p{0.05\textwidth} p{0.05\textwidth} p{0.05\textwidth} p{0.05\textwidth} p{0.05\textwidth} p{0.05\textwidth} p{0.05\textwidth}}%{cccccccccccccccccccc} 
			\caption{Size measurements of \textit{Ernietta} from Farm Hansburg and Farm Kuibis in Namibia, collected summer 2016.}\\
			\label{tab:4ST1}
			&           &      &                 &            &            &                     &                 & a           & b    & c    & ellipsoid                      & elliptic cylinder              & ellipsoid                  & elliptic cylinder          & ellipsoid & elliptic cylinder & Tube Width   &      &          \\
			Location & MajorSite & Site & Specimen        & GPS        & GPS        & Est. Size (cm) & No. of Stars & L           & W    & H    & Volume (cm\textasciicircum{}3) & Volume (cm\textasciicircum{}3) & SA (cm\textasciicircum{}2) & SA (cm\textasciicircum{}2) & SA:V      & SA:V              & Min          & Max  & \# tubes \\
			\endfirsthead
			HB       & HB1       & HB1A & HB1A-01         & 26 17 23.4 & 16 52 55.6 & 10                  & 2               & 11.72       & 6.85 & 2.29 & 96.26                          & 144.39                         & 145.68                     & 192.91                     & 1.51      & 1.34              & 0.28         & 0.33 & 15       \\
			HB       & HB1       & HB1A & HB1A-02         & 26 17 23.4 & 16 52 55.6 & 6-7                 & 2               & 7.99        & 5.18 & 2.76 & 59.81                          & 89.72                          & 85.98                      & 122.11                     & 1.44      & 1.36              & 0.11         & 0.15 & 17       \\
			HB       & HB1       & HB1A & HB1A-03         & 26 17 23.4 & 16 52 55.6 & 5                   & 0               & 5.89        & 5.1  & 1.14 & 17.93                          & 26.90                          & 52.20                      & 66.87                      & 2.91      & 2.49              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1A & HB1A-04         & 26 17 23.4 & 16 52 55.6 & 6                   & 0               & 8.17        & 5.09 & 2.08 & 45.29                          & 67.93                          & 79.35                      & 108.65                     & 1.75      & 1.60              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1A & HB1A-05         & 26 17 23.4 & 16 52 55.6 & 8-9                 & 3               & 9.86        & 6.4  & 1.96 & 64.76                          & 97.14                          & 113.32                     & 149.18                     & 1.75      & 1.54              & 0.18         & 0.22 & 20       \\
			HB       & HB1       & HB1A & HB1A-06         & 26 17 23.4 & 16 52 55.6 & 10                  & 1               & 10.62       & 9.56 & 2.52 & 133.96                         & 200.94                         & 181.63                     & 239.36                     & 1.36      & 1.19              & 0.21         & 0.26 & 10       \\
			HB       & HB1       & HB1A & HB1A-07         & 26 17 23.4 & 16 52 55.6 & 5-6                 & 0               & 8.46        & 6.4  & 2.88 & 81.65                          & 122.47                         & 108.31                     & 152.27                     & 1.33      & 1.24              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1A & HB1A-08         & 26 17 23.4 & 16 52 55.6 & 4-5                 & 1               & 3.95        & 3.25 & 2.25 & 15.12                          & 22.69                          & 30.93                      & 45.61                      & 2.04      & 2.01              & 0.19         & 0.22 & 10       \\
			HB       & HB1       & HB1A & HB1A-09         & 26 17 23.4 & 16 52 55.6 & 4-5                 & 0               & 5.2         & 3.75 & 1.69 & 17.26                          & 25.88                          & 38.81                      & 54.39                      & 2.25      & 2.10              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1A & HB1A-10         & 26 17 23.4 & 16 52 55.6 & 8                   & 0               & 2.93        & 2.75 & 2.6  & 10.97                          & 16.45                          & 23.92                      & 35.85                      & 2.18      & 2.18              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1A & HB1A-11         & 26 17 23.4 & 16 52 55.6 & 5                   & 0               & 5.82        & 3.73 & 2.2  & 25.01                          & 37.51                          & 46.77                      & 67.10                      & 1.87      & 1.79              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1A & HB1A-12         & 26 17 23.4 & 16 52 55.6 & 5                   & 0               & 5.18        & 3.92 & 2.78 & 29.56                          & 44.34                          & 48.68                      & 71.63                      & 1.65      & 1.62              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1A & HB1A-13         & 26 17 23.4 & 16 52 55.6 & 5                   & 0               & 5.84        & 3.48 & 2.27 & 24.16                          & 36.23                          & 45.18                      & 65.16                      & 1.87      & 1.80              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1A & HB1A-14         & 26 17 23.4 & 16 52 55.6 & 6                   & 1               & 6.43        & 2.95 & 2.79 & 27.71                          & 41.56                          & 48.78                      & 70.90                      & 1.76      & 1.71              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1A & HB1A-15         & 26 17 23.4 & 16 52 55.6 & 7                   & 1               & 7.21        & 4.4  & 1.73 & 28.74                          & 43.10                          & 59.84                      & 81.38                      & 2.08      & 1.89              & 0.18         & 0.21 & 14       \\
			HB       & HB1       & HB1A & HB1A-16         & 26 17 23.4 & 16 52 55.6 & 4                   & 2               & 4.44        & 2.38 & 1.92 & 10.62                          & 15.93                          & 25.53                      & 37.17                      & 2.40      & 2.33              & 0.17         & 0.21 & 16       \\
			HB       & HB1       & HB1A & HB1A-17         & 26 17 23.4 & 16 52 55.6 & 3-4                 & 0               & 4.29        & 3.08 & 1.44 & 9.96                           & 14.94                          & 26.59                      & 37.43                      & 2.67      & 2.50              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1A & HB1A-18         & 26 17 23.4 & 16 52 55.6 & 3-4                 & 0               & 4.52        & 3.37 & 0.66 & 5.26                           & 7.90                           & 25.85                      & 32.11                      & 4.91      & 4.07              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1A & HB1A-19         & 26 17 23.4 & 16 52 55.6 & 3-4                 & 2               & 4.17        & 2.07 & 2.04 & 9.22                           & 13.83                          & 22.94                      & 33.55                      & 2.49      & 2.43              & 0.17         & 0.2  & 5        \\
			HB       & HB1       & HB1A & HB1A-20         & 26 17 23.4 & 16 52 55.6 & 5                   & 0               & 5.03        & 3.65 & 0.86 & 8.27                           & 12.40                          & 31.82                      & 40.56                      & 3.85      & 3.27              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1A & HB1A-21         & 26 17 23.4 & 16 52 55.6 & 2                   & 0               & 2.71        & 2.64 & 2.09 & 7.83                           & 11.74                          & 19.28                      & 28.80                      & 2.46      & 2.45              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1A & HB1A-22         & 26 17 23.4 & 16 52 55.6 & 3                   & 0               & 3.83        & 2.92 & 0.95 & 5.56                           & 8.34                           & 20.56                      & 27.64                      & 3.70      & 3.31              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1A & HB1A-23         & 26 17 23.4 & 16 52 55.6 & 1                   & 0               & 3.03        & 2.97 & 0.58 & 2.73                           & 4.10                           & 15.48                      & 19.60                      & 5.66      & 4.78              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1A & HB1A-24         & 26 17 23.4 & 16 52 55.6 & 2-3                 & 2               & 2.79        & 1.92 & 0.93 & 2.61                           & 3.91                           & 10.85                      & 15.30                      & 4.16      & 3.91              & 0.2          & 0.19 & 9        \\
			HB       & HB1       & HB1A & HB1A-25         & 26 17 23.4 & 16 52 55.6 & 3-4                 & 0               & 4.21        & 3.62 & 1.34 & 10.69                          & 16.04                          & 29.26                      & 40.42                      & 2.74      & 2.52              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1A & HB1A-26         & 26 17 23.4 & 16 52 55.6 & 3                   & 1               & 3.54        & 3.51 & 1.93 & 12.56                          & 18.83                          & 28.00                      & 40.89                      & 2.23      & 2.17              & 0.17         & 0.15 & 5        \\
			HB       & HB1       & HB1A & HB1A-27         & 26 17 23.4 & 16 52 55.6 & 5-6                 & 1               & 6.92        & 6.7  & 2.48 & 60.20                          & 90.31                          & 90.36                      & 125.89                     & 1.50      & 1.39              & 0.17         & 0.23 & 9        \\
			HB       & HB1       & HB1A & HB1A-28         & 26 17 23.4 & 16 52 55.6 & 5-6                 & 0               & 6.25        & 3.29 & 1.35 & 14.53                          & 21.80                          & 38.79                      & 52.53                      & 2.67      & 2.41              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1A & HB1A-29         & 26 17 23.4 & 16 52 55.6 & 4-5                 & 1               & 5.5         & 4.89 & 0.9  & 12.67                          & 19.01                          & 45.69                      & 56.94                      & 3.61      & 2.99              & 0.16         & 0.2  & 10       \\
			HB       & HB1       & HB1A & HB1A-30         & 26 17 23.4 & 16 52 55.6 & 6-7                 & 0               & 7.03        & 6.1  & 2.73 & 61.30                          & 91.95                          & 87.23                      & 123.67                     & 1.42      & 1.34              & 0.19         & 0.23 & 9        \\
			HB       & HB1       & HB1A & HB1A-31         & 26 17 23.4 & 16 52 55.6 & 3-4                 & 0               & 4.64        & 3.42 & 1.91 & 15.87                          & 23.80                          & 34.12                      & 49.11                      & 2.15      & 2.06              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1A & HB1A-32         & 26 17 23.4 & 16 52 55.6 & 4-5                 & 0               & 5.19        & 3.98 & 3.15 & 34.07                          & 51.10                          & 52.51                      & 77.82                      & 1.54      & 1.52              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1A & HB1A-33         & 26 17 23.4 & 16 52 55.6 & 4-5                 & 1               & 5.45        & 3.04 & 2.5  & 21.69                          & 32.53                          & 40.63                      & 59.37                      & 1.87      & 1.82              & 0.2          & 0.23 & 16       \\
			HB       & HB1       & HB1B & HB1B-01         & 26 17 23.2 & 16 52 58.9 & 6                   & 0               & 7.18        & 4.37 & 3.89 & 63.91                          & 95.86                          & 81.32                      & 119.86                     & 1.27      & 1.25              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1B & HB1B-02         & 26 17 23.2 & 16 52 58.9 & 3                   & 0               & 4.29        & 2.46 & 1.96 & 10.83                          & 16.25                          & 25.58                      & 37.36                      & 2.36      & 2.30              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1B & HB1B-03         & 26 17 23.2 & 16 52 58.9 & 3                   & 1               & 5.65        & 2.3  & 2.14 & 14.56                          & 21.84                          & 32.69                      & 47.14                      & 2.25      & 2.16              & 0.18         & 0.21 & 11       \\
			HB       & HB1       & HB1B & HB1B-04         & 26 17 23.2 & 16 52 58.9 & 2-3                 & 3               & 3.68        & 2.55 & 2.35 & 11.55                          & 17.32                          & 25.41                      & 37.74                      & 2.20      & 2.18              & 0.17         & 0.22 & 15       \\
			HB       & HB1       & HB1B & HB1B-05         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 1               & 4.43        & 2.22 & 0.87 & 4.48                           & 6.72                           & 18.30                      & 24.54                      & 4.08      & 3.65              & 0.13         & 0.15 & 13       \\
			HB       & HB1       & HB1B & HB1B-06         & 26 17 23.2 & 16 52 58.9 & 4-5                 & 1               & 5.47        & 2.63 & 1.98 & 14.91                          & 22.37                          & 33.20                      & 47.79                      & 2.23      & 2.14              & 0.21         & 0.24 & 15       \\
			HB       & HB1       & HB1B & HB1B-07         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 1               & 4.07        & 2.03 & 2.09 & 9.04                           & 13.56                          & 22.53                      & 33.00                      & 2.49      & 2.43              & 0.19         & 0.22 & 14       \\
			HB       & HB1       & HB1B & HB1B-08         & 26 17 23.2 & 16 52 58.9 & 3                   & 0               & 3.75        & 2.16 & 1.44 & 6.11                           & 9.16                           & 18.10                      & 26.09                      & 2.96      & 2.85              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1B & HB1B-09         & 26 17 23.2 & 16 52 58.9 & 2-3                 & 0               & 3.37        & 2.77 & 1.52 & 7.43                           & 11.14                          & 20.28                      & 29.32                      & 2.73      & 2.63              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1B & HB1B-10         & 26 17 23.2 & 16 52 58.9 & 4-5                 & 2               & 4.73        & 2.18 & 1.77 & 9.56                           & 14.33                          & 24.54                      & 35.41                      & 2.57      & 2.47              & 0.17         & 0.22 & 14       \\
			HB       & HB1       & HB1B & HB1B-11         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 2               & 3.72        & 2.84 & 2.04 & 11.28                          & 16.93                          & 25.53                      & 37.62                      & 2.26      & 2.22              & 0.16         & 0.21 & 14       \\
			HB       & HB1       & HB1B & HB1B-12         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 0               & 4.11        & 2.44 & 1.72 & 9.03                           & 13.55                          & 23.05                      & 33.45                      & 2.55      & 2.47              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1B & HB1B-13         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 1               & 3.73        & 1.57 & 2.31 & 7.08                           & 10.62                          & 19.60                      & 28.43                      & 2.77      & 2.68              & 0.16         & 0.23 & 9        \\
			HB       & HB1       & HB1B & HB1B-14         & 26 17 23.2 & 16 52 58.9 & 2-3                 & 0               & 2.94        & 1.6  & 1.41 & 3.47                           & 5.21                           & 11.91                      & 17.44                      & 3.43      & 3.35              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1B & HB1B-15         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 2               & 4.05        & 2.47 & 1.71 & 8.96                           & 13.44                          & 22.89                      & 33.23                      & 2.56      & 2.47              & 0.11         & 0.2  & 17       \\
			HB       & HB1       & HB1B & HB1B-16         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 0               & 4.4         & 2.34 & 1.36 & 7.33                           & 11.00                          & 21.60                      & 30.57                      & 2.95      & 2.78              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1B & HB1B-17         & 26 17 23.2 & 16 52 58.9 & 4-5                 & 1               & 4.14        & 3.31 & 0.72 & 5.17                           & 7.75                           & 23.62                      & 29.95                      & 4.57      & 3.87              & 0.17         & 0.18 & 11       \\
			HB       & HB1       & HB1B & HB1B-18         & 26 17 23.2 & 16 52 58.9 & 1-2                 & 1               & 2.74        & 1.97 & 1.77 & 5.00                           & 7.50                           & 14.52                      & 21.57                      & 2.90      & 2.88              & 0.18         & 0.22 & 8        \\
			HB       & HB1       & HB1B & HB1B-19         & 26 17 23.2 & 16 52 58.9 & 2-3                 & 1               & 3.47        & 2.42 & 1.03 & 4.53                           & 6.79                           & 16.37                      & 22.72                      & 3.61      & 3.34              & 0.17         & 0.22 & 7        \\
			HB       & HB1       & HB1B & HB1B-20         & 26 17 23.2 & 16 52 58.9 & 5-6                 & 1               & 4.96        & 3.56 & 2.95 & 27.27                          & 40.91                          & 45.38                      & 67.22                      & 1.66      & 1.64              & 0.19         & 0.22 & 12       \\
			HB       & HB1       & HB1B & HB1B-21         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 1               & 3.62        & 2.97 & 0.69 & 3.88                           & 5.83                           & 18.72                      & 24.03                      & 4.82      & 4.12              & 0.13         & 0.18 & 11       \\
			HB       & HB1       & HB1B & HB1B-21 Rock    & 26 17 23.2 & 16 52 58.9 & 1-2                 & 0               & 0.9         & 0.6  & 0.15 & 0.04                           & 0.06                           & 0.94                       & 1.20                       & 22.16     & 18.89             & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1B & HB1B-22         & 26 17 23.2 & 16 52 58.9 & 5                   & 1               & 3.46        & 2.79 & 0.59 & 2.98                           & 4.47                           & 16.59                      & 20.96                      & 5.56      & 4.68              & 0.25         & 0.3  & 9        \\
			HB       & HB1       & HB1B & HB1B-23         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 1               & 3.88        & 2.69 & 1.68 & 9.18                           & 13.77                          & 23.27                      & 33.73                      & 2.53      & 2.45              & 0.22         & 0.25 & 13       \\
			HB       & HB1       & HB1B & HB1B-24         & 26 17 23.2 & 16 52 58.9 & 1-2                 & 0               & 1.82        & 1.61 & 0.66 & 1.01                           & 1.52                           & 5.81                       & 8.16                       & 5.74      & 5.37              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1B & HB1B-25         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 1               & 5           & 2.87 & 1.89 & 14.20                          & 21.30                          & 31.88                      & 45.91                      & 2.25      & 2.16              & 0.18         & 0.23 & 9        \\
			HB       & HB1       & HB1B & HB1B-26         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 2               & 4.13        & 2.63 & 1.8  & 10.24                          & 15.36                          & 24.88                      & 36.18                      & 2.43      & 2.36              & 0.14         & 0.19 & 8        \\
			HB       & HB1       & HB1B & HB1B-27         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 0               & 4.01        & 2.66 & 1.78 & 9.94                           & 14.91                          & 24.34                      & 35.40                      & 2.45      & 2.37              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1B & HB1B-28         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 0               & 3.36        & 3.09 & 1.73 & 9.40                           & 14.11                          & 23.21                      & 33.84                      & 2.47      & 2.40              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1B & HB1B-29         & 26 17 23.2 & 16 52 58.9 & 2-3                 & 0               & 2.54        & 1.68 & 1.56 & 3.49                           & 5.23                           & 11.50                      & 17.04                      & 3.30      & 3.26              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1B & HB1B-30         & 26 17 23.2 & 16 52 58.9 & 2-3                 & 2               & 1.86        & 1.09 & 0.94 & 1.00                           & 1.50                           & 5.13                       & 7.54                       & 5.14      & 5.04              & 0.19         & 0.25 & 7        \\
			HB       & HB1       & HB1B & HB1B-31         & 26 17 23.2 & 16 52 58.9 & 4-5                 & 2               & 4.45        & 1.76 & 1.12 & 4.59                           & 6.89                           & 16.58                      & 23.23                      & 3.61      & 3.37              & 0.12         & 0.19 & 11       \\
			HB       & HB1       & HB1B & HB1B-32         & 26 17 23.2 & 16 52 58.9 & 2-3                 & 1               & 2.14        & 1.99 & 1.71 & 3.81                           & 5.72                           & 11.89                      & 17.78                      & 3.12      & 3.11              & 0.16         & 0.18 & 8        \\
			HB       & HB1       & HB1B & HB1B-33         & 26 17 23.2 & 16 52 58.9 & 1-2                 & 1               & 1.37        & 1.29 & 1.7  & 1.57                           & 2.36                           & 6.61                       & 9.88                       & 4.20      & 4.19              & 0.15         & 0.18 & 6        \\
			HB       & HB1       & HB1B & HB1B-34         & 26 17 23.2 & 16 52 58.9 & 1-2                 & 1               & 2.33        & 1.18 & 0.4  & 0.58                           & 0.86                           & 4.96                       & 6.52                       & 8.62      & 7.55              & 0.19         & 0.24 & 8        \\
			HB       & HB1       & HB1B & HB1B-35         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 0               & 3.2         & 1.95 & 0.83 & 2.71                           & 4.07                           & 12.01                      & 16.52                      & 4.43      & 4.06              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1B & HB1B-36         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 1               & 3.13        & 2.63 & 1.05 & 4.53                           & 6.79                           & 16.09                      & 22.43                      & 3.56      & 3.30              & 0.14         & 0.17 & 9        \\
			HB       & HB1       & HB1B & HB1B-37         & 26 17 23.2 & 16 52 58.9 & 5-6                 & 1               & 4.09        & 2.28 & 0.44 & 2.15                           & 3.22                           & 15.65                      & 19.05                      & 7.28      & 5.91              & 0.19         & 0.23 & 8        \\
			HB       & HB1       & HB1B & HB1B-38         & 26 17 23.2 & 16 52 58.9 & 4-5                 & 2               & 4.62        & 2.58 & 0.78 & 4.87                           & 7.30                           & 21.18                      & 27.54                      & 4.35      & 3.77              & 0.2          & 0.25 & 9        \\
			HB       & HB1       & HB1B & HB1B-39         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 1               & 2.89        & 1.66 & 1.49 & 3.74                           & 5.61                           & 12.37                      & 18.18                      & 3.31      & 3.24              & 0.14         & 0.21 & 6        \\
			HB       & HB1       & HB1B & HB1B-40         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 0               & 3.44        & 2.28 & 1.29 & 5.30                           & 7.95                           & 16.70                      & 23.91                      & 3.15      & 3.01              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1B & HB1B-41         & 26 17 23.2 & 16 52 58.9 & 2-3                 & 2               & 2.14        & 2.13 & 1.33 & 3.17                           & 4.76                           & 10.90                      & 16.08                      & 3.43      & 3.38              & 0.13         & 0.18 & 11       \\
			HB       & HB1       & HB1B & HB1B-42         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 2               & 3.54        & 3.18 & 2.42 & 14.26                          & 21.40                          & 29.05                      & 43.23                      & 2.04      & 2.02              & 0.16         & 0.2  & 9        \\
			HB       & HB1       & HB1B & HB1B-43         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 1               & 2.54        & 1.57 & 2.62 & 5.47                           & 8.21                           & 15.73                      & 23.18                      & 2.88      & 2.82              & 0.23         & 0.27 & 7        \\
			HB       & HB1       & HB1B & HB1B-44         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 0               & 4.06        & 2.68 & 1    & 5.70                           & 8.55                           & 20.39                      & 27.68                      & 3.58      & 3.24              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1B & HB1B-45         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 1               & 3.4         & 3.12 & 1.33 & 7.39                           & 11.08                          & 21.41                      & 30.28                      & 2.90      & 2.73              & 0.23         & 0.27 & 9        \\
			HB       & HB1       & HB1B & HB1B-46         & 26 17 23.2 & 16 52 58.9 & 1-2                 & 0               & 0.8         & 0.67 & 1.21 & 0.34                           & 0.51                           & 2.46                       & 3.64                       & 7.25      & 7.14              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1B & HB1B-47A        & 26 17 23.2 & 16 52 58.9 & 3-4                 & 2               & 2.82        & 1.9  & 1.42 & 3.98                           & 5.98                           & 12.91                      & 18.94                      & 3.24      & 3.17              & 0.15         & 0.18 & 12       \\
			HB       & HB1       & HB1B & HB1B-47B        & 26 17 23.2 & 16 52 58.9 & 1-2                 & 2               & 1.83        & 0.66 & 0.41 & 0.26                           & 0.39                           & 2.52                       & 3.50                       & 9.72      & 9.00              & 0.26         & 0.32 & 3        \\
			HB       & HB1       & HB1B & HB1B-48         & 26 17 23.2 & 16 52 58.9 & 2-3                 & 0               & 2.5         & 1.1  & 1.35 & 1.94                           & 2.92                           & 8.20                       & 11.95                      & 4.22      & 4.10              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1B & HB1B-49         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 0               & 2.99        & 2.36 & 2.14 & 7.91                           & 11.86                          & 19.49                      & 29.07                      & 2.46      & 2.45              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1B & HB1B-50         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 0               & 2.62        & 1.84 & 1.9  & 4.80                           & 7.19                           & 14.02                      & 20.88                      & 2.92      & 2.90              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1B & HB1B-51         & 26 17 23.2 & 16 52 58.9 & 2-3                 & 0               & 2.95        & 1.46 & 2.02 & 4.56                           & 6.83                           & 14.16                      & 20.76                      & 3.11      & 3.04              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1B & HB1B-52         & 26 17 23.2 & 16 52 58.9 & 3-4                 & 0               & 3.84        & 2.37 & 0.93 & 4.43                           & 6.65                           & 17.17                      & 23.37                      & 3.88      & 3.52              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-01         & 26 17 23.4 & 16 52 59.9 & 1-2                 & 1               & 2.31        & 1.58 & 1.32 & 2.52                           & 3.78                           & 9.33                       & 13.80                      & 3.70      & 3.65              & 0.07         & 0.09 & 14       \\
			HB       & HB1       & HB1C & HB1C-02         & 26 17 23.4 & 16 52 59.9 & 1-2                 & 0               & 2.64        & 1.51 & 0.96 & 2.00                           & 3.01                           & 8.73                       & 12.52                      & 4.35      & 4.17              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-03         & 26 17 23.4 & 16 52 59.9 & 4-5                 & 0               & 4.57        & 2.43 & 1.58 & 9.19                           & 13.78                          & 24.33                      & 34.82                      & 2.65      & 2.53              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-04         & 26 17 23.4 & 16 52 59.9 & 2-3                 & 0               & 3.26        & 2.11 & 1.1  & 3.96                           & 5.94                           & 14.18                      & 20.08                      & 3.58      & 3.38              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-05         & 26 17 23.4 & 16 52 59.9 & 1-2                 & 0               & 2.8         & 1.55 & 0.76 & 1.73                           & 2.59                           & 8.63                       & 12.01                      & 5.00      & 4.64              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-06         & 26 17 23.4 & 16 52 59.9 & 1-2                 & 1               & 2.15        & 1.31 & 0.75 & 1.11                           & 1.66                           & 5.96                       & 8.50                       & 5.39      & 5.12              & 0.08         & 0.13 & 11       \\
			HB       & HB1       & HB1C & HB1C-07         & 26 17 23.4 & 16 52 59.9 & 1-2                 & 0               & 2.08        & 1.32 & 1.18 & 1.70                           & 2.54                           & 7.19                       & 10.61                      & 4.24      & 4.17              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-08         & 26 17 23.4 & 16 52 59.9 & 1-2                 & 0               & 1.99        & 1.42 & 0.75 & 1.11                           & 1.66                           & 5.92                       & 8.46                       & 5.34      & 5.08              & 0.06         & 0.09 & 9        \\
			HB       & HB1       & HB1C & HB1C-09         & 26 17 23.4 & 16 52 59.9 & 2-3                 & 1               & 2.51        & 1.48 & 1.82 & 3.54                           & 5.31                           & 11.65                      & 17.24                      & 3.29      & 3.25              & 0.06         & 0.09 & 13       \\
			HB       & HB1       & HB1C & HB1C-10         & 26 17 23.4 & 16 52 59.9 & 1-2                 & 1               & 1.84        & 1.53 & 1.93 & 2.84                           & 4.27                           & 9.79                       & 14.64                      & 3.44      & 3.43              & 0.06         & 0.1  & 11       \\
			HB       & HB1       & HB1C & HB1C-11         & 26 17 23.4 & 16 52 59.9 & 1-2                 & 0               & 2.23        & 1.17 & 1.09 & 1.49                           & 2.23                           & 6.77                       & 9.92                       & 4.55      & 4.44              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-12         & 26 17 23.4 & 16 52 59.9 & 1-2                 & 0               & 2.26        & 1.47 & 1.15 & 2.00                           & 3.00                           & 8.14                       & 11.96                      & 4.07      & 3.98              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-13         & 26 17 23.4 & 16 52 59.9 & 4-5 (1-2)           & 0               & 1.64        & 0.92 & 0.72 & 0.57                           & 0.85                           & 3.61                       & 5.27                       & 6.35      & 6.17              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-14         & 26 17 23.4 & 16 52 59.9 & 1-2                 & 0               & 2.06        & 1.33 & 1.26 & 1.81                           & 2.71                           & 7.43                       & 11.01                      & 4.11      & 4.06              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-15         & 26 17 23.4 & 16 52 59.9 & 1                   & 0               & 1.82        & 1.51 & 1.11 & 1.60                           & 2.40                           & 6.84                       & 10.12                      & 4.28      & 4.23              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-16         & 26 17 23.4 & 16 52 59.9 & 2-3                 & 0               & 2.38        & 1.88 & 1.72 & 4.03                           & 6.04                           & 12.42                      & 18.54                      & 3.08      & 3.07              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-17         & 26 17 23.4 & 16 52 59.9 & 1                   & 0               & 2.11        & 1    & 1.03 & 1.14                           & 1.71                           & 5.71                       & 8.35                       & 5.02      & 4.89              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-18         & 26 17 23.4 & 16 52 59.9 & 2-3                 & 1               & 3.43        & 1.59 & 0.62 & 1.77                           & 2.66                           & 10.09                      & 13.46                      & 5.70      & 5.07              & 0.08         & 0.12 & 13       \\
			HB       & HB1       & HB1C & HB1C-19         & 26 17 23.4 & 16 52 59.9 & 1-2                 & 1               & 1.63        & 1.44 & 0.86 & 1.06                           & 1.59                           & 5.35                       & 7.83                       & 5.07      & 4.94              & 0.07         & 0.11 & 11       \\
			HB       & HB1       & HB1C & HB1C-20         & 26 17 23.4 & 16 52 59.9 & 2-3                 & 0               & 2.17        & 1.46 & 1.26 & 2.09                           & 3.14                           & 8.22                       & 12.16                      & 3.93      & 3.88              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-21         & 26 17 23.4 & 16 52 59.9 & 2-3                 & 0               & 2.34        & 1.6  & 1.04 & 2.04                           & 3.06                           & 8.47                       & 12.32                      & 4.16      & 4.03              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-22         & 26 17 23.4 & 16 52 59.9 & 3-4                 & 2               & 4.24        & 2.47 & 2.58 & 14.15                          & 21.22                          & 29.53                      & 43.64                      & 2.09      & 2.06              & 0.14         & 0.17 & 14       \\
			HB       & HB1       & HB1C & HB1C-23         & 26 17 23.4 & 16 52 59.9 & 1-2                 & 0               & 2.37        & 1.77 & 1.09 & 2.39                           & 3.59                           & 9.41                       & 13.68                      & 3.93      & 3.81              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-24         & 26 17 23.4 & 16 52 59.9 & 1-2                 & 0               & 2.07        & 1.51 & 1.43 & 2.34                           & 3.51                           & 8.70                       & 12.95                      & 3.72      & 3.69              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-25 A       & 26 17 23.4 & 16 52 59.9 & 2-3                 & 1               & 2.68        & 1.48 & 0.72 & 1.50                           & 2.24                           & 7.87                       & 10.94                      & 5.26      & 4.88              & 0.09         & 0.13 & 8        \\
			HB       & HB1       & HB1C & HB1C-25B        & 27 17 23.4 & 17 52 59.9 & 2-3                 & 0               & 2.38        & 1.17 & 0.72 & 1.05                           & 1.57                           & 5.92                       & 8.39                       & 5.64      & 5.33              & 0.1          & 0.14 & 13       \\
			HB       & HB1       & HB1C & HB1C-26         & 26 17 23.4 & 16 52 59.9 & 1-2                 & 0               & 1.51        & 1.13 & 0.83 & 0.74                           & 1.11                           & 4.15                       & 6.12                       & 5.60      & 5.50              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-27         & 26 17 23.4 & 16 52 59.9 & 1-2                 & 0               & 1.82        & 1.01 & 0.75 & 0.72                           & 1.08                           & 4.29                       & 6.22                       & 5.94      & 5.75              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-28         & 26 17 23.4 & 16 52 59.9 & 1-2                 & 1               & 1.69        & 0.93 & 0.99 & 0.81                           & 1.22                           & 4.44                       & 6.54                       & 5.45      & 5.35              & 0.9          & 0.13 & 10       \\
			HB       & HB1       & HB1C & HB1C-29         & 26 17 23.4 & 16 52 59.9 & 2-3                 & 0               & 3.52        & 2.66 & 0.86 & 4.22                           & 6.32                           & 17.18                      & 23.06                      & 4.08      & 3.65              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-30         & 26 17 23.4 & 16 52 59.9 & 2-3                 & 0               & 2.14        & 1.33 & 1.8  & 2.68                           & 4.02                           & 9.64                       & 14.28                      & 3.59      & 3.55              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-31         & 26 17 23.4 & 16 52 59.9 & 2-3                 & 1               & 1.9         & 1.31 & 1.1  & 1.43                           & 2.15                           & 6.39                       & 9.46                       & 4.46      & 4.40              & 0.12         & 0.17 & 9        \\
			HB       & HB1       & HB1C & HB1C-32         & 26 17 23.4 & 16 52 59.9 & 2-3                 & 0               & 2.41        & 1.56 & 1.07 & 2.11                           & 3.16                           & 8.64                       & 12.58                      & 4.10      & 3.98              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-33         & 26 17 23.4 & 16 52 59.9 & 1-2                 & 1               & 1.58        & 1.33 & 1.71 & 1.88                           & 2.82                           & 7.44                       & 11.12                      & 3.95      & 3.94              & 0.09         & 0.14 & 11       \\
			HB       & HB1       & HB1C & HB1C-34         & 26 17 23.4 & 16 52 59.9 & 1-2                 & 2               & 2.15        & 1.58 & 0.98 & 1.74                           & 2.61                           & 7.62                       & 11.08                      & 4.37      & 4.24              & 0.1          & 0.12 & 13       \\
			HB       & HB1       & HB1C & HB1C-35         & 26 17 23.4 & 16 52 59.9 & 2-3                 & 1               & 2.3         & 1.75 & 1.11 & 2.34                           & 3.51                           & 9.17                       & 13.38                      & 3.92      & 3.81              & 0.9          & 0.13 & 7        \\
			HB       & HB1       & HB1C & HB1C-36         & 26 17 23.4 & 16 52 59.9 & 1-2                 & 1               & 1.98        & 1.51 & 2.06 & 3.22                           & 4.84                           & 10.72                      & 15.99                      & 3.33      & 3.31              & 0.13         & 0.18 & 8        \\
			HB       & HB1       & HB1C & HB1C-37         & 26 17 23.4 & 16 52 59.9 & 2-3                 & 0               & 2.21        & 1.62 & 0.79 & 1.48                           & 2.22                           & 7.32                       & 10.38                      & 4.94      & 4.67              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-38         & 26 17 23.4 & 16 52 59.9 & 2-3                 & 1               & 2.1         & 1.94 & 1.67 & 3.56                           & 5.34                           & 11.36                      & 17.00                      & 3.19      & 3.18              & 0.12         & 0.16 & 8        \\
			HB       & HB1       & HB1C & HB1C-39         & 26 17 23.4 & 16 52 59.9 & 1-2                 & 0               & 1.75        & 1.02 & 1.1  & 1.03                           & 1.54                           & 5.13                       & 7.59                       & 4.99      & 4.92              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1C & HB1C-40         & 26 17 23.4 & 16 52 59.9 & 1-2                 & 0               & 2.37        & 1.92 & 0.43 & 1.02                           & 1.54                           & 7.88                       & 10.05                      & 7.69      & 6.54              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1D & HB1D-01         & 26 17 23.3 & 16 53 01.2 & 5-6                 & 0               & 5.4         & 3.27 & 1.01 & 9.34                           & 14.01                          & 31.63                      & 41.49                      & 3.39      & 2.96              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1D & HB1D-02         & 26 17 23.3 & 16 53 01.2 & 6-7                 & 0               & 5.78        & 4.27 & 0.94 & 12.15                          & 18.22                          & 42.43                      & 53.61                      & 3.49      & 2.94              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1D & HB1D-03         & 26 17 23.3 & 16 53 01.2 & 7-8                 & 0               & 7.67        & 5.52 & 1.58 & 35.03                          & 52.54                          & 75.60                      & 99.24                      & 2.16      & 1.89              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1D & HB1D-04         & 26 17 23.3 & 16 53 01.2 & 5-6                 & 2               & 5.26        & 4.4  & 2.12 & 25.69                          & 38.54                          & 48.02                      & 68.52                      & 1.87      & 1.78              & Split into 2 &      &          \\
			HB       & HB1       & HB1D & HB1D-04A        & 27 17 23.3 & 17 53 01.2 & 4-5                 & 1               & 5.35        & 2.16 & 2.03 & 12.28                          & 18.42                          & 29.20                      & 42.10                      & 2.38      & 2.28              & 0.16         & 0.21 & 7        \\
			HB       & HB1       & HB1D & HB1D-04B        & 28 17 23.3 & 18 53 01.2 & 4-5                 & 2               & 4.77        & 2.15 & 1.78 & 9.56                           & 14.34                          & 24.58                      & 35.46                      & 2.57      & 2.47              & 0.16         & 0.2  & 18       \\
			HB       & HB1       & HB1D & HB1D-05         & 26 17 23.3 & 16 53 01.2 & 10                  & 0               & 7.17        & 5.67 & 2.67 & 56.83                          & 85.25                          & 83.01                      & 117.71                     & 1.46      & 1.38              & 0.2          & 0.25 & 8        \\
			HB       & HB1       & HB1D & Sample and Rock & 27 17 23.3 & 17 53 01.2 & 7-8                 & 0               & 7.69        & 7.66 & 2.67 & 82.35                          & 123.53                         & 113.35                     & 156.91                     & 1.38      & 1.27              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1D & HB1D-06         & 26 17 23.3 & 16 53 01.2 & 10                  & 0               & 3.8         & 3.29 & 2.03 & 13.29                          & 19.93                          & 28.82                      & 42.25                      & 2.17      & 2.12              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1D & Sample and Rock & 27 17 23.3 & 17 53 01.2 & 8-9                 & 0               & 8.69        & 4.6  & 0.81 & 16.95                          & 25.43                          & 66.49                      & 79.70                      & 3.92      & 3.13              & N/A          & N/A  & N/A      \\
			HB       & HB1       & HB1E & HB1E-01         & 26 17 23.4 & 16 53 04.1 & 2-3                 & 3               & 3.39        & 2.6  & 3.34 & 15.41                          & 23.12                          & 30.32                      & 45.27                      & 1.97      & 1.96              & 0.09         & 0.13 & 13       \\
			HB       & HB5       & HB5  & HB5-01          & 26 17 3.94 & 16 54 21.1 & 4-5                 & 3               & 3.74        & 2.33 & 1.11 & 5.06                           & 7.60                           & 17.37                      & 24.27                      & 3.43      & 3.19              & 0.1          & 0.16 & 17       \\
			HB       & HB5       & HB5  & HB5-02          & 26 17 3.94 & 16 54 21.1 & 3-4                 & 3               & 2.54        & 2.46 & 0.53 & 1.73                           & 2.60                           & 10.88                      & 13.98                      & 6.28      & 5.37              & 0.18         & 0.25 & 14       \\
			KB       & KB        & KB   & KB-01           & 26 38 09.4 & 16 41 21.6 & 5-6                 & 0               & 4.45        & 2.54 & 0.98 & 5.80                           & 8.70                           & 21.12                      & 28.51                      & 3.64      & 3.28              & N/A          & N/A  & N/A      \\
			KB       & KB        & KB   & Sample and Rock & 27 38 09.4 & 17 41 21.6 & 7-8                 & 0               & 10.05       & 9.08 & 1.65 & 78.84                          & 118.26                         & 154.94                     & 192.92                     & 1.97      & 1.63              & N/A          & N/A  & N/A      \\
			KB       & KB        & KB   & KB-02           & 26 38 09.4 & 16 41 21.6 & 4-5                 & 0               & 7.82        & 4.93 & 1    & 20.19                          & 30.28                          & 65.25                      & 80.59                      & 3.23      & 2.66              & N/A          & N/A  & N/A      \\
			KB       & KB        & KB   & KB-03           & 26 38 09.4 & 16 41 21.6 & 2-3                 & 0               & 2.36        & 1.94 & 0.81 & 1.94                           & 2.91                           & 9.04                       & 12.66                      & 4.66      & 4.35              & 0.08         & 0.12 & 8        \\
			KB       & KB        & KB   & Sample and Rock & 27 38 09.4 & 17 41 21.6 & 3-4                 & 0               & 3.55        & 1.56 & 0.7  & 2.03                           & 3.04                           & 10.57                      & 14.32                      & 5.21      & 4.70              & N/A          & N/A  & N/A      \\
			KB       & KB        & KB   & KB-04           & 26 38 09.4 & 16 41 21.6 & 6-7                 & 0               & 2.58        & 2.31 & 1.12 & 3.50                           & 5.24                           & 12.53                      & 17.96                      & 3.58      & 3.43              & N/A          & N/A  & N/A      \\
			KB       & KB        & KB   & KB-05           & 26 17 59.8 & 16 54 35.6 & 8-9                 & 0               & 5.4         & 3.69 & 1.16 & 12.10                          & 18.15                          & 36.08                      & 47.86                      & 2.98      & 2.64              & N/A          & N/A  & N/A      \\
			HB       & HB4       & HB4  & HB4C-01         & 26 17 59.8 & 16 54 35.6 & 6-7                 & 0               & 6.71        & 4.55 & 1.52 & 24.30                          & 36.45                          & 55.94                      & 74.84                      & 2.30      & 2.05              & N/A          & N/A  & N/A      \\
			HB       & HB4       & HB4  & HB4C-02         & 26 17 59.8 & 16 54 35.6 & 5-6                 & 0               & 8.02        & 3.58 & 1.9  & 28.56                          & 42.85                          & 57.58                      & 79.72                      & 2.02      & 1.86              & N/A          & N/A  & N/A      \\
			HB       & HB4       & HB4  & HB4C-03         & 26 17 59.8 & 16 54 35.6 & 4-5                 & 0               & 6.13        & 3.55 & 1.69 & 19.26                          & 28.88                          & 43.07                      & 59.88                      & 2.24      & 2.07              & N/A          & N/A  & N/A      \\
			HB       & HB4       & HB4  & HB4C-04         & 26 17 59.8 & 16 54 35.6 & 6                   & 0               & 5.52        & 3.2  & 1.23 & 11.38                          & 17.06                          & 33.02                      & 44.59                      & 2.90      & 2.61              & N/A          & N/A  & N/A      \\
			HB       & HB4       & HB4  & HB4C-05         & 26 17 59.8 & 16 54 35.6 & 6-7                 & 0               & 7.24        & 4.46 & 2.23 & 37.70                          & 56.55                          & 65.28                      & 91.71                      & 1.73      & 1.62              & N/A          & N/A  & N/A      \\
			HB       & HB4       & HB4  & HB4C-06         & 26 17 59.8 & 16 54 35.6 & 4-5                 & 0               & 6.2         & 3.04 & 1.13 & 11.15                          & 16.73                          & 34.62                      & 46.01                      & 3.10      & 2.75              & N/A          & N/A  & N/A      \\
			HB       & HB4       & HB4  & HB4C-07         & 26 17 59.8 & 16 54 35.6 & 8-9                 & 0               & 5.25        & 1.81 & 2.1  & 10.45                          & 15.67                          & 26.63                      & 38.22                      & 2.55      & 2.44              & N/A          & N/A  & N/A      \\
			HB       & HB4       & HB4  & HB4C-08         & 26 17 59.8 & 16 54 35.6 & 6-7                 & 0               & 8.88        & 4.46 & 1.72 & 35.67                          & 53.50                          & 73.42                      & 98.25                      & 2.06      & 1.84              & N/A          & N/A  & N/A      \\
			HB       & HB4       & HB4  & HB4C-09         & 26 17 59.8 & 16 54 35.6 & 8-9                 & 0               & 7.64        & 4.14 & 1.42 & 23.52                          & 35.28                          & 57.44                      & 75.96                      & 2.44      & 2.15              & N/A          & N/A  & N/A      \\
			HB       & HB4       & HB4  & HB4C-10         & 26 17 59.8 & 16 54 35.6 & 4-5                 & 0               & 9.94        & 5.89 & 1.26 & 38.63                          & 57.94                          & 99.44                      & 123.30                     & 2.57      & 2.13              & N/A          & N/A  & N/A      \\
			HB       & HB4       & HB4  & HB4C-11         & 26 17 59.8 & 16 54 35.6 & 5-6                 & 0               & 5.88        & 1.7  & 1.15 & 6.02                           & 9.03                           & 21.27                      & 29.39                      & 3.53      & 3.26              & N/A          & N/A  & N/A      \\
			HB       & HB4       & HB4  & HB4C-12         & 26 17 59.8 & 16 54 35.6 & 5-6                 & 0               & 5.01        & 2.93 & 1.55 & 11.91                          & 17.87                          & 30.08                      & 42.39                      & 2.52      & 2.37              & N/A          & N/A  & N/A      \\
			HB       & HB4       & HB4  & HB4C-13         & 26 17 59.8 & 16 54 35.6 & 4-5                 & 0               & 5.63        & 1.76 & 2.13 & 11.05                          & 16.58                          & 28.25                      & 40.29                      & 2.56      & 2.43              & N/A          & N/A  & N/A      \\
			HB       & HB4       & HB4  & HB4C-14         & 26 17 59.8 & 16 54 35.6 & 5-6                 & 0               & 5.31        & 2.16 & 0.8  & 4.80                           & 7.21                           & 20.87                      & 27.40                      & 4.34      & 3.80              & N/A          & N/A  & N/A      \\
			HB       & HB4       & HB4  & HB4C-15         & 26 17 59.8 & 16 54 35.6 & 4-5                 & 0               & 4.9         & 2    & 0.95 & 4.87                           & 7.31                           & 18.92                      & 25.69                      & 3.88      & 3.51              & N/A          & N/A  & N/A      \\
			HB       & HB4       & HB4  & HB4C-16         & 26 17 59.8 & 16 54 35.6 & 5-6                 & 0               & 4.93        & 3.29 & 1.1  & 9.34                           & 14.01                          & 29.69                      & 39.68                      & 3.18      & 2.83              & N/A          & N/A  & N/A      \\
			HB       & HB4       & HB4  & HB4C-17         & 26 16 54.6 & 16 52 48.4 & 3-4                 & 0               & 5.37        & 2.09 & 1.95 & 11.46                          & 17.19                          & 28.15                      & 40.48                      & 2.46      & 2.36              & N/A          & N/A  & N/A      \\
			HB       & HB3       & HB3  & HB3-01          & 26 16 54.6 & 16 52 48.4 & 2-3                 & 0               & 3.16        & 2.66 & 1.43 & 6.29                           & 9.44                           & 18.19                      & 26.28                      & 2.89      & 2.78              & N/A          & N/A  & N/A      \\
			HB       & HB3       & HB3  & HB3-02          & 26 16 54.6 & 16 52 48.4 & 2-3                 & 1               & 2.82        & 2.57 & 2.21 & 8.39                           & 12.58                          & 20.13                      & 30.10                      & 2.40      & 2.39              & 0.13         & 0.19 & 6        \\
			HB       & HB3       & HB3  & HB3-03          & 26 16 54.6 & 16 52 48.4 & 3-4                 & 1               & 1.85        & 1.84 & 1.57 & 2.80                           & 4.20                           & 9.65                       & 14.45                      & 3.45      & 3.44              & 0.14         & 0.18 & 6        \\
			HB       & HB3       & HB3  & HB3-04          & 26 16 54.6 & 16 52 48.4 & 3-4                 & 0               & 2.93        & 2.2  & 1.43 & 4.83                           & 7.24                           & 14.81                      & 21.65                      & 3.07      & 2.99              & N/A          & N/A  & N/A      \\
			HB       & HB3       & HB3  & HB3-05          & 26 16 54.6 & 16 52 48.4 & 5-6                 & 1               & 2.74        & 2.65 & 0.85 & 3.23                           & 4.85                           & 13.63                      & 18.60                      & 4.22      & 3.84              & 0.09         & 0.12 & 9        \\
			HB       & HB3       & HB3  & HB3-06          & 26 16 54.6 & 16 52 48.4 & 3-4                 & 0               & 4.31        & 2.55 & 0.97 & 5.58                           & 8.37                           & 20.52                      & 27.72                      & 3.68      & 3.31              & N/A          & N/A  & N/A      \\
			HB       & HB3       & HB3  & HB3-07          & 26 16 54.6 & 16 52 48.4 & 3-4                 & 2               & 3.13        & 2.03 & 0.76 & 2.53                           & 3.79                           & 11.90                      & 16.14                      & 4.71      & 4.26              & 0.14         & 0.18 & 6        \\
			HB       & HB3       & HB3  & HB3-08          & 26 16 54.6 & 16 52 48.4 & 2-3                 & 0               & 4.05        & 3.5  & 1.32 & 9.80                           & 14.70                          & 27.36                      & 37.92                      & 2.79      & 2.58              & 0.15         & 0.2  & 14       \\
			HB       & HB3       & HB3  & HB3-09          & 26 16 54.6 & 16 52 48.4 & 2-3                 & 0               & 2.99        & 2.1  & 0.5  & 1.64                           & 2.47                           & 10.88                      & 13.86                      & 6.62      & 5.62              & N/A          & N/A  & N/A      \\
			HB       & HB3       & HB3  & HB3-10          & 26 16 54.6 & 16 52 48.4 & 2-3                 & 0               & 2.8         & 1.83 & 0.78 & 2.09                           & 3.14                           & 9.93                       & 13.72                      & 4.75      & 4.37              & 0.09         & 0.13 & 16       \\
			HB       & HB3       & HB3  & HB3-11          & 26 16 54.6 & 16 52 48.4 & 1-2                 & 0               & 2.01        & 1.55 & 1.22 & 1.99                           & 2.99                           & 7.91                       & 11.72                      & 3.97      & 3.92              & N/A          & N/A  & N/A      \\
			HB       & HB3       & HB3  & HB3-12          & 26 16 54.6 & 16 52 48.4 & 1                   & 0               & 1.5         & 0.94 & 0.85 & 0.63                           & 0.94                           & 3.71                       & 5.47                       & 5.90      & 5.81              & N/A          & N/A  & N/A      \\
			HB       & HB3       & HB3  & HB3-13          & 26 16 54.6 & 16 52 48.4 & 3-4                 & 0               & 1.26        & 1.04 & 0.69 & 0.47                           & 0.71                           & 3.09                       & 4.55                       & 6.54      & 6.41              & N/A          & N/A  & N/A      \\
			HB       & HB3       & HB3  & HB3-14          & 26 16 54.6 & 16 52 48.4 & 4-5                 & 0               & 3.34        & 3.01 & 0.83 & 4.37                           & 6.55                           & 18.14                      & 24.07                      & 4.15      & 3.67              & 0.1          & 0.18 & 8        \\
			HB       & HB3       & HB3  & HB3-15          & 26 16 54.6 & 16 52 48.4 & 5-6                 & 0               & 3.99        & 3.15 & 1.09 & 7.17                           & 10.76                          & 23.51                      & 31.97                      & 3.28      & 2.97              & 0.16         & 0.17 & 3        \\
			HB       & HB3       & HB3  & HB3-16          & 26 16 54.6 & 16 52 48.4 & 5-6                 & 0               & 4.19        & 2.98 & 1.49 & 9.74                           & 14.61                          & 25.66                      & 36.39                      & 2.63      & 2.49              & 0.08         & 0.12 & 13       \\
			HB       & HB3       & HB3  & HB3-17          & 26 16 54.6 & 16 52 48.4 & 7-8                 & 0               & 4.82        & 3.56 & 1.11 & 9.97                           & 14.96                          & 31.20                      & 41.56                      & 3.13      & 2.78              & 0.12         & 0.17 & 13       \\
			HB       & HB3       & HB3  & HB3-18          & 26 18 49.0 & 16 53 40.2 & 3-4                 & 2               & 5.52        & 4.59 & 2.94 & 39.00                          & 58.50                          & 58.95                      & 86.49                      & 1.51      & 1.48              & 0.13         & 0.21 & 10       \\
			HB       & HBGS      & HBGS & HBGS-01         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 1               & 3.98        & 2.91 & 1.93 & 11.70                          & 17.56                          & 26.74                      & 39.08                      & 2.28      & 2.23              & 0.12         & 0.18 & 9        \\
			HB       & HBGS      & HBGS & HBGS-02         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 1               & 3.76        & 2.78 & 1.73 & 9.47                           & 14.20                          & 23.50                      & 34.19                      & 2.48      & 2.41              & 0.13         & 0.19 & 9        \\
			HB       & HBGS      & HBGS & HBGS-03         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 1               & 3.01        & 2.57 & 2.93 & 11.87                          & 17.80                          & 25.26                      & 37.83                      & 2.13      & 2.13              & 0.15         & 0.19 & 7        \\
			HB       & HBGS      & HBGS & HBGS-04         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 2               & 4.21        & 2.41 & 2.46 & 13.07                          & 19.60                          & 28.13                      & 41.52                      & 2.15      & 2.12              & 0.16         & 0.19 & 10       \\
			HB       & HBGS      & HBGS & HBGS-05         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 2               & 2.76        & 1.9  & 2.35 & 6.45                           & 9.68                           & 17.08                      & 25.44                      & 2.65      & 2.63              & 0.14         & 0.18 & 7        \\
			HB       & HBGS      & HBGS & HBGS-06         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 1               & 3.46        & 1.63 & 1.5  & 4.43                           & 6.64                           & 14.34                      & 20.85                      & 3.24      & 3.14              & 0.16         & 0.21 & 15       \\
			HB       & HBGS      & HBGS & HBGS-07         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 0               & 4.11        & 2.96 & 3.05 & 19.43                          & 29.14                          & 35.53                      & 52.98                      & 1.83      & 1.82              & N/A          & N/A  & N/A      \\
			HB       & HBGS      & HBGS & HBGS-08         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 0               & 2.8         & 2.64 & 5.93 & 22.95                          & 34.43                          & 42.78                      & 62.28                      & 1.86      & 1.81              & N/A          & N/A  & N/A      \\
			HB       & HBGS      & HBGS & HBGS-09         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 1               & 2.72        & 2.56 & 2.11 & 7.69                           & 11.54                          & 19.03                      & 28.44                      & 2.47      & 2.46              & 0.12         & 0.17 & 7        \\
			HB       & HBGS      & HBGS & HBGS-10         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 0               & 3.56        & 2.68 & 2.33 & 11.64                          & 17.46                          & 25.43                      & 37.82                      & 2.19      & 2.17              & N/A          & N/A  & N/A      \\
			HB       & HBGS      & HBGS & HBGS-11         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 2               & 3.02        & 2.13 & 5.01 & 16.87                          & 25.31                          & 34.86                      & 50.63                      & 2.07      & 2.00              & 0.12         & 0.19 & 7        \\
			HB       & HBGS      & HBGS & HBGS-12         & 26 18 49.0 & 16 53 40.2 & 4-5                 & 0               & 3.36        & 1.97 & 2.17 & 7.52                           & 11.28                          & 19.31                      & 28.57                      & 2.57      & 2.53              & N/A          & N/A  & N/A      \\
			HB       & HBGS      & HBGS & HBGS-13         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 0               & 4.81        & 4.26 & 4.56 & 48.92                          & 73.39                          & 64.82                      & 97.15                      & 1.32      & 1.32              & N/A          & N/A  & N/A      \\
			HB       & HBGS      & HBGS & HBGS-14         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 2               & 2.63        & 2.04 & 2.73 & 7.67                           & 11.50                          & 19.07                      & 28.45                      & 2.49      & 2.47              & 0.14         & 0.2  & 8        \\
			HB       & HBGS      & HBGS & HBGS-15         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 1               & 2.73        & 1.85 & 2.09 & 5.53                           & 8.29                           & 15.43                      & 22.97                      & 2.79      & 2.77              & 0.12         & 0.17 & 12       \\
			HB       & HBGS      & HBGS & HBGS-16         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 1               & 3.05        & 2.84 & 1.39 & 6.30                           & 9.46                           & 18.39                      & 26.47                      & 2.92      & 2.80              & 0.13         & 0.16 & 9        \\
			HB       & HBGS      & HBGS & HBGS-17         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 1               & 2.86        & 2.41 & 1.78 & 6.42                           & 9.64                           & 17.24                      & 25.56                      & 2.68      & 2.65              & 0.16         & 0.22 & 9        \\
			HB       & HBGS      & HBGS & HBGS-18         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 1               & 3.32        & 2.5  & 1.93 & 8.39                           & 12.58                          & 20.75                      & 30.68                      & 2.47      & 2.44              & 0.13         & 0.2  & 8        \\
			HB       & HBGS      & HBGS & HBGS-19         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 3               & 2.39        & 1.84 & 2.04 & 4.70                           & 7.05                           & 13.69                      & 20.46                      & 2.91      & 2.90              & 0.12         & 0.18 & 6        \\
			HB       & HBGS      & HBGS & HBGS-20         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 3               & 3.5         & 2.16 & 2.47 & 9.78                           & 14.67                          & 22.81                      & 33.84                      & 2.33      & 2.31              & 0.16         & 0.21 & 12       \\
			HB       & HBGS      & HBGS & HBGS-21         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 0               & 3.85        & 2.42 & 2.55 & 12.44                          & 18.66                          & 26.80                      & 39.75                      & 2.15      & 2.13              & 0.17         & 0.22 & 18       \\
			HB       & HBGS      & HBGS & HBGS-22         & 26 18 49.0 & 16 53 40.2 & 1-2                 & 1               & 3.34        & 2.81 & 2.73 & 13.42                          & 20.12                          & 27.47                      & 41.12                      & 2.05      & 2.04              & 0.15         & 0.19 & 6        \\
			HB       & HBGS      & HBGS & HBGS-23         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 1               & 2.22        & 1.98 & 0.8  & 1.84                           & 2.76                           & 8.69                       & 12.18                      & 4.72      & 4.41              & 0.13         & 0.19 & 8        \\
			HB       & HBGS      & HBGS & HBGS-24         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 1               & 2.22        & 1.99 & 0.91 & 2.10                           & 3.16                           & 9.10                       & 12.96                      & 4.32      & 4.10              & 0.16         & 0.19 & 8        \\
			HB       & HBGS      & HBGS & HBGS-25         & 26 18 49.0 & 16 53 40.2 & 1-2                 & 1               & 2.95        & 1.48 & 1.25 & 2.86                           & 4.29                           & 10.70                      & 15.56                      & 3.74      & 3.63              & 0.13         & 0.2  & 7        \\
			HB       & HBGS      & HBGS & HBGS-26         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 1               & 2.45        & 1.5  & 1.85 & 3.56                           & 5.34                           & 11.63                      & 17.25                      & 3.27      & 3.23              & 0.14         & 0.2  & 8        \\
			HB       & HBGS      & HBGS & HBGS-27         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 1               & 2.98        & 2.5  & 1.24 & 4.84                           & 7.26                           & 15.62                      & 22.38                      & 3.23      & 3.08              & 0.12         & 0.14 & 10       \\
			HB       & HBGS      & HBGS & HBGS-28         & 26 18 49.0 & 16 53 40.2 & 1-2                 & 1               & 4.21        & 3.2  & 2.66 & 18.76                          & 28.15                          & 35.10                      & 52.12                      & 1.87      & 1.85              & 0.11         & 0.15 & 12       \\
			HB       & HBGS      & HBGS & HBGS-29         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 0               & 1.94        & 1.6  & 1.54 & 2.50                           & 3.75                           & 8.99                       & 13.44                      & 3.59      & 3.58              & N/A          & N/A  & N/A      \\
			HB       & HBGS      & HBGS & HBGS-30         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 3               & 3.36        & 2.24 & 1.2  & 4.73                           & 7.09                           & 15.72                      & 22.38                      & 3.32      & 3.15              & 0.14         & 0.19 & 18       \\
			HB       & HBGS      & HBGS & HBGS-31         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 0               & 3.14        & 2.31 & 0.71 & 2.70                           & 4.04                           & 13.15                      & 17.47                      & 4.88      & 4.32              & N/A          & N/A  & N/A      \\
			HB       & HBGS      & HBGS & HBGS-32         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 0               & 2.64        & 1.74 & 1.48 & 3.56                           & 5.34                           & 11.78                      & 17.40                      & 3.31      & 3.26              & N/A          & N/A  & N/A      \\
			HB       & HBGS      & HBGS & HBGS-33         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 0               & 3.37        & 2.37 & 2.05 & 8.57                           & 12.86                          & 20.93                      & 31.03                      & 2.44      & 2.41              & N/A          & N/A  & N/A      \\
			HB       & HBGS      & HBGS & HBGS-34         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 0               & 2.63        & 1.65 & 2.31 & 5.25                           & 7.87                           & 15.08                      & 22.35                      & 2.87      & 2.84              & 0.12         & 0.2  & 7        \\
			HB       & HBGS      & HBGS & HBGS-35         & 26 18 49.0 & 16 53 40.2 & 1-2                 & 2               & 2.55        & 1.43 & 1.58 & 3.02                           & 4.53                           & 10.57                      & 15.61                      & 3.50      & 3.45              & 0.14         & 0.18 & 10       \\
			HB       & HBGS      & HBGS & HBGS-36         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 0               & 2.97        & 2.31 & 1.06 & 3.81                           & 5.71                           & 13.86                      & 19.57                      & 3.64      & 3.43              & 0.14         & 0.19 & 13       \\
			HB       & HBGS      & HBGS & HBGS-37         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 0               & 2.88        & 1.99 & 0.82 & 2.46                           & 3.69                           & 11.06                      & 15.28                      & 4.50      & 4.14              & N/A          & N/A  & N/A      \\
			HB       & HBGS      & HBGS & HBGS-38         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 1               & 2.42        & 2.06 & 1.41 & 3.68                           & 5.52                           & 12.03                      & 17.75                      & 3.27      & 3.22              & 0.13         & 0.17 & 9        \\
			HB       & HBGS      & HBGS & HBGS-39         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 0               & 2.36        & 1.64 & 2.02 & 4.09                           & 6.14                           & 12.60                      & 18.77                      & 3.08      & 3.06              & 0.13         & 0.19 & 13       \\
			HB       & HBGS      & HBGS & HBGS-40         & 26 18 49.0 & 16 53 40.2 & 1-2                 & 2               & 4.17        & 2.63 & 3.09 & 17.74                          & 26.62                          & 33.83                      & 50.23                      & 1.91      & 1.89              & 0.18         & 0.23 & 9        \\
			HB       & HBGS      & HBGS & HBGS-41         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 1               & 2.39        & 1.94 & 1.73 & 4.20                           & 6.30                           & 12.76                      & 19.05                      & 3.04      & 3.02              & 0.13         & 0.17 & 10       \\
			HB       & HBGS      & HBGS & HBGS-42         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 2               & 2.95        & 2.45 & 1.79 & 6.77                           & 10.16                          & 17.92                      & 26.54                      & 2.65      & 2.61              & 0.12         & 0.15 & 9        \\
			HB       & HBGS      & HBGS & HBGS-43         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 2               & 2.62        & 2.01 & 1.2  & 3.31                           & 4.96                           & 11.71                      & 17.00                      & 3.54      & 3.43              & 0.15         & 0.2  & 9        \\
			HB       & HBGS      & HBGS & Sample and Rock & 27 18 49.0 & 17 53 40.2 & 3-4                 & 0               & 4.18        & 2.37 & 1.2  & 6.22                           & 9.34                           & 19.95                      & 27.91                      & 3.20      & 2.99              & N/A          & N/A  & N/A      \\
			HB       & HBGS      & HBGS & HBGS-44         & 28 18 49.0 & 18 53 40.2 & 3-4                 & 1               & 3.19        & 2    & 2.36 & 7.88                           & 11.83                          & 19.71                      & 29.26                      & 2.50      & 2.47              & 0.17         & 0.21 & 10       \\
			HB       & HBGS      & HBGS & HBGS-45         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 1               & 3.58        & 3.26 & 2.44 & 14.91                          & 22.37                          & 29.95                      & 44.55                      & 2.01      & 1.99              & 0.07         & 0.14 & 12       \\
			HB       & HBGS      & HBGS & HBGS-46         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 1               & 3.71        & 2    & 1.49 & 5.79                           & 8.68                           & 17.27                      & 25.02                      & 2.98      & 2.88              & 0.18         & 0.22 & 5        \\
			HB       & HBGS      & HBGS & HBGS-47         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 1               & 4.18        & 2.9  & 2.31 & 14.66                          & 21.99                          & 30.31                      & 44.73                      & 2.07      & 2.03              & 0.16         & 0.21 & 11       \\
			HB       & HBGS      & HBGS & HBGS-48         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 0               & 3.52        & 2.6  & 2.16 & 10.35                          & 15.53                          & 23.69                      & 35.14                      & 2.29      & 2.26              & N/A          & N/A  & N/A      \\
			HB       & HBGS      & HBGS & HBGS-49         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 2               & 3.14        & 2.58 & 1.03 & 4.37                           & 6.55                           & 15.79                      & 21.98                      & 3.61      & 3.35              & 0.1          & 0.14 & 9        \\
			HB       & HBGS      & HBGS & HBGS-50         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 0               & 3.63        & 2.49 & 1.3  & 6.15                           & 9.23                           & 18.77                      & 26.70                      & 3.05      & 2.89              & N/A          & N/A  & N/A      \\
			HB       & HBGS      & HBGS & HBGS-51         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 0               & 3.52        & 2.33 & 1.72 & 7.39                           & 11.08                          & 19.58                      & 28.69                      & 2.65      & 2.59              & N/A          & N/A  & N/A      \\
			HB       & HBGS      & HBGS & HBGS-52         & 26 18 49.0 & 16 53 40.2 & 1-2                 & 1               & 3.58        & 2.08 & 1.91 & 7.45                           & 11.17                          & 19.48                      & 28.68                      & 2.62      & 2.57              & 0.15         & 0.18 & 11       \\
			HB       & HBGS      & HBGS & HBGS-53         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 1               & 2.71        & 2.06 & 1.98 & 5.79                           & 8.68                           & 15.82                      & 23.60                      & 2.73      & 2.72              & 0.14         & 0.18 & 15       \\
			HB       & HBGS      & HBGS & HBGS-54         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 2               & 2.52        & 1.89 & 2.08 & 5.19                           & 7.78                           & 14.65                      & 21.89                      & 2.82      & 2.81              & 0.14         & 0.2  & 9        \\
			HB       & HBGS      & HBGS & HBGS-55         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 1               & 3.24        & 2.48 & 3.38 & 14.22                          & 21.33                          & 28.83                      & 42.99                      & 2.03      & 2.02              & 0.16         & 0.2  & 11       \\
			HB       & HBGS      & HBGS & HBGS-56         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 0               & 3.99        & 2.89 & 1.48 & 8.94                           & 13.40                          & 23.95                      & 34.11                      & 2.68      & 2.54              & 0.18         & 0.23 & 11       \\
			HB       & HBGS      & HBGS & HBGS-57         & 26 18 49.0 & 16 53 40.2 & 2                   & 0               & 3.15        & 2.35 & 1.99 & 7.71                           & 11.57                          & 19.41                      & 28.82                      & 2.52      & 2.49              & N/A          & N/A  & N/A      \\
			HB       & HBGS      & HBGS & HBGS-58         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 0               & 2.83        & 2.35 & 0.83 & 2.89                           & 4.34                           & 12.56                      & 17.20                      & 4.35      & 3.97              & N/A          & N/A  & N/A      \\
			HB       & HBGS      & HBGS & HBGS-59         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 0               & 4.04        & 3.2  & 1.34 & 9.07                           & 13.61                          & 25.44                      & 35.55                      & 2.80      & 2.61              & 0.13         & 0.19 & 9        \\
			HB       & HBGS      & HBGS & HBGS-60         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 0               & 2.66        & 3.01 & 1.6  & 6.71                           & 10.06                          & 18.32                      & 26.83                      & 2.73      & 2.67              & N/A          & N/A  & N/A      \\
			HB       & HBGS      & HBGS & HBGS-61         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 2               & 3.53        & 3.28 & 1.46 & 8.85                           & 13.28                          & 23.76                      & 33.81                      & 2.68      & 2.55              & 0.9          & 0.11 & 8        \\
			HB       & HBGS      & HBGS & HBGS-62         & 26 18 49.0 & 16 53 40.2 & 1-2                 & 1               & 3.43        & 1.72 & 3.11 & 9.61                           & 14.41                          & 23.66                      & 34.43                      & 2.46      & 2.39              & 0.13         & 0.17 & 11       \\
			HB       & HBGS      & HBGS & HBGS-63         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 1               & 2.7         & 2.33 & 1.44 & 4.74                           & 7.11                           & 14.51                      & 21.26                      & 3.06      & 2.99              & 0.1          & 0.17 & 11       \\
			HB       & HBGS      & HBGS & HBGS-64         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 1               & 3.86        & 3.18 & 1.4  & 9.00                           & 13.50                          & 24.65                      & 34.76                      & 2.74      & 2.58              & 0.14         & 0.2  & 14       \\
			HB       & HBGS      & HBGS & HBGS-65         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 1               & 3.64        & 3    & 1.2  & 6.86                           & 10.29                          & 21.31                      & 29.67                      & 3.11      & 2.88              & 0.13         & 0.18 & 15       \\
			HB       & HBGS      & HBGS & HBGS-66         & 26 18 49.0 & 16 53 40.2 & 2-3                 & 1               & 3.53        & 2.61 & 2.83 & 13.65                          & 20.48                          & 27.97                      & 41.77                      & 2.05      & 2.04              & 0.12         & 0.18 & 17       \\
			HB       & HBGS      & HBGS & HBGS-67         & 26 18 49.0 & 16 53 40.2 & 1-2                 & 1               & 3.46        & 2.3  & 1.79 & 7.46                           & 11.19                          & 19.51                      & 28.70                      & 2.62      & 2.56              & 0.12         & 0.17 & 11       \\
			HB       & HBGS      & HBGS & HBGS-68         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 0               & 2.65        & 2.17 & 1.02 & 3.07                           & 4.61                           & 11.79                      & 16.76                      & 3.84      & 3.64              & N/A          & N/A  & N/A      \\
			HB       & HBGS      & HBGS & HBGS-69         & 26 18 49.0 & 16 53 40.2 & 3-4                 & 0               & 4.12        & 2.59 & 2.05 & 11.45                          & 17.18                          & 26.14                      & 38.37                      & 2.28      & 2.23              & N/A          & N/A  & N/A      \\
			HB       & HBGS      & HBGS & HBGS-70         & 27 18 49.0 & 17 53 40.2 & 3-4                 & 1               & 4.17        & 3.07 & 2.99 & 20.04                          & 30.06                          & 36.30                      & 54.11                      & 1.81      & 1.80              & 0.13         & 0.19 & 12       \\
			&           &      &                 &            &            &                     &                 & 3.834212598 &      &      &                                &                                &                            &                            &           &                   &              &      &          
	\end{longtable}}
	%\end{small}
\end{landscape}
%\restoregeometry
\newpage
\begin{figure}
	\includegraphics[width = \textwidth]{Ernietta_FigureS3.jpg}
	\centering
	\caption{Select examples of CFD simulation setup. a) Parallel clumped. b) Perpendicular clumped. c) Mixed offset setup showing slip/no-slip conditions and flow direction.}
	\label{fig:4S3}
\end{figure}
\newpage
%\begin{landscape}
\begin{table}[h!]
	\caption{\textbf{Sensitivity analyses for meshing.} To establish the optimal mesh size to use in our CFD simulations, we repeated simulations for a single individual of \textit{Ernietta} oriented parallel to the current with shallow burial using different mesh sizes. We compared the drag forces for these different mesh sizes to identify the coarsest mesh that would guarantee the computational accuracy of the simulation (i.e. the results were not substantially different from a finer mesh).}
	\label{tab:4ST2}
	\tiny
	\begin{tabular} {p{0.1\textwidth} p{0.1\textwidth} p{0.03\textwidth} p{0.06\textwidth} p{0.08\textwidth} p{0.08\textwidth} p{0.025\textwidth} p{0.025\textwidth} p{0.05\textwidth} p{0.05\textwidth} p{0.05\textwidth} p{0.05\textwidth}}%{llllllllllll}
		Density of fluid (kg/m3) & Dynamic viscosity of fluid (kg/(s·m)) &             &                              &                     &              &                    &                &                 &                &                  &                              \\
		1000                     & 0.001                                 &             &                              &                     &              &                    &                &                 &                &                  &                              \\
		&                                       &             &                              &                     &              &                    &                &                 &                &                  &                              \\
		Model                    & Burial depth                          & Orientation & Characteristic dimension (m) & Reference area (m2) & Mesh size    & Number of elements & Velocity (m/s) & Reynolds number & Drag force (N) & Drag coefficient & Difference from coarser mesh \\
		Single individual        & Shallow                               & Parallel    & 0.059                        & 0.0032              & Extra coarse & 116454             & 0.1            & 5900            & 0.011971647    & 0.748227916      &                              \\
		&                                       &             &                              &                     &              &                    & 0.2            & 11800           & 0.045839045    & 0.716235076      &                              \\
		&                                       &             &                              &                     &              &                    & 0.5            & 29500           & 0.255772117    & 0.639430293      &                              \\
		&                                       &             &                              &                     &              &                    &                &                 &                &                  &                              \\
		&                                       &             &                              &                     & Coarser      & 212727             & 0.1            & 5900            & 0.011716099    & 0.732256168      & -2.13\%                      \\
		&                                       &             &                              &                     &              &                    & 0.2            & 11800           & 0.045700431    & 0.714069227      & -0.30\%                      \\
		&                                       &             &                              &                     &              &                    & 0.5            & 29500           & 0.266639061    & 0.666597652      & 4.25\%                       \\
		&                                       &             &                              &                     &              &                    &                &                 &                &                  &                              \\
		&                                       &             &                              &                     & Coarse       & 400421             & 0.1            & 5900            & 0.011355367    & 0.709710438      & -3.08\%                      \\
		&                                       &             &                              &                     &              &                    & 0.2            & 11800           & 0.044687687    & 0.698245116      & -2.22\%                      \\
		&                                       &             &                              &                     &              &                    & 0.5            & 29500           & 0.267184777    & 0.667961943      & 0.20\%                       \\
		&                                       &             &                              &                     &              &                    &                &                 &                &                  &                              \\
		&                                       &             &                              &                     & Normal       & 783250             & 0.1            & 5900            & 0.011154987    & 0.697186698      & -1.76\%                      \\
		&                                       &             &                              &                     &              &                    & 0.2            & 11800           & 0.04435156     & 0.692993133      & -0.75\%                      \\
		&                                       &             &                              &                     &              &                    & 0.5            & 29500           & 0.274513914    & 0.686284786      & 2.74\%                      
	\end{tabular}
\end{table}
%\end{landscape}
\newpage
\subsection{Reynolds Calculation}\label{sec:SuppRe}
Reynolds number and drag coefficient calculations for characterizing flow regimes. Reynolds numbers (Re) were calculated using the following equation:
\begin{equation}
\textrm{Re} = \rho u L/ \mu
\end{equation}

where $\rho$ is the density of water (1000 kg m$^{-3}$), $u$ is the inlet velocity (0.1, 0.2, or 0.5 m s$^{-1}$), $L$ is the characteristic dimension (frontal surface area exposed to flow; S. Fig. 7.1), and $\mu$ is the dynamic viscosity of water (0.001 kg m$^{-1}$ s$^{-1}$).

Drag forces were calculated to quantify the forces exerted by the fluid on \textrm{Ernietta}.  The results were used to calculate the coefficients of drag by solving the following equation:
\begin{equation}
C_d = 2F_d / \rho u^2 A
\end{equation}
where $C_d$ is the drag coefficient, $F_d$ is the drag force (N), $\rho$ is the fluid density (kg/m$^3$), $u$ is the inlet velocity (m/s), and $A$ is the characteristic area (m$^2$). Here, the characteristic area is the surface area of \textit{Ernietta} exposed above the sediment water interface, which varied depending on the burial depth.
\begin{figure}
	\includegraphics[width = \textwidth]{Ernietta_FigureS4.jpg}
	\centering
	\caption{Frontal surface area at respective burial depth for calculations. a) Parallel orientation with respect to flow. b) Perpendicular orientation with respect to flow. Characteristic length scale was frontal area with respect to flow.}
	\label{fig:4S4}
\end{figure}
\newpage
\begin{figure}
	\includegraphics[width=\textwidth]{Ernietta_FigureS5.jpg}
	\centering
	\caption{CFD results for single individual model. Results visualized as two-dimensional plots of vertical velocity magnitude, average flow velocity magnitude with flow vectors (gray arrows; length of arrows proportional to the natural logarithm of the flow velocity magnitude), and kinetic energy.}
	\label{fig:4S5}
\end{figure}
\newpage
\begin{figure}
	\includegraphics[width=\textwidth]{Ernietta_FigureS6.jpg}
	\centering
	\caption{CFD results for multiple individual model. Results visualized as two-dimensional plots of vertical velocity magnitude, average flow velocity magnitude with flow vectors (gray arrows; length of arrows proportional to the natural logarithm of the flow velocity magnitude), and kinetic energy.}
	\label{fig:4S6}
\end{figure}
\newpage
\begin{figure}
	\includegraphics[width=\textwidth]{Ernietta_FigureS7.jpg}
	\centering
	\caption{CFD results for offset multiple individual model. Results visualized as two-dimensional plots of vertical velocity magnitude, average flow velocity magnitude with flow vectors (gray arrows; length of arrows proportional to the natural logarithm of the flow velocity magnitude), and kinetic energy.}
	\label{fig:4S7}
\end{figure}
\newpage
\begin{figure}
	\includegraphics[width=\textwidth]{Ernietta_FigureS8.jpg}
	\centering
	\caption{a) Coefficients of drag for multiple model simulations. b) Coefficients of drag for single model simulations. c) SA/V ratios for individual models at four burial depths.}
	\label{fig:4S8}
\end{figure}
\newpage

%---------------------------------------------------------------------------------------------------------------%
%------------------------------------------------SECTION------------------------------------------------%
%---------------------------------------------------------------------------------------------------------------%
\chapter{Ancient Life in Moving Fluids: how fluid dynamics can help us understand Precambrian ecosystems}\label{Chapter4 title}
\vspace{-7mm}
\section{Abstract}
Over 3.7 billion years of Earth history, life has evolved complex adaptations to help navigate and interact with the fluid environment. Consequently, fluid dynamics (and fluid dynamics modeling in particular) has become a powerful tool for studying ancient fossils, providing insights into the paleobiology and -ecology of extinct organisms from a wide variety of positions across the tree of life. In recent years, this approach has been extended to the Ediacara biota, an enigmatic assemblage of Neoproterozoic soft-bodied organisms that represent the first major radiation of macroscopic eukaryotes. Understanding what the Ediacara biota represent, as well as the structure and function of their ecosystems, is key to illuminating the origins of the modern, animal-dominated biosphere. Reconstructing the ways in which Ediacaran organisms interacted with the fluids has thus become a rich area of paleobiological research, providing new insights into how these organisms may have fed, moved, and interacted within communities. In this paper we describe the evolution of this field, starting with a review of fluid physics aimed at paleobiologists, in which we dispel misconceptions related to the Reynolds number and associated flow conditions. We also review recent advancements in Ediacaran paleobiology resulting from the application of computational fluid dynamics (CFD). We provide a worked example and account of best practices in CFD analyses of fossils, including the first large eddy simulation (LES) performed on Ediacaran communities. Lastly, we outline key questions, barriers, and emerging techniques in fluid physics approaches which will not only help us to understand the earliest animal ecosystems, but also develop new paleobiological tools for studying ancient life.
\section{Introduction}\label{Section heading 4}
Since the beginning of life on Earth, organisms have evolved in environments characterized by moving fluids. Fluids and their physical properties have been fundamental constraints throughout many key step-changes in the evolution of life, including the emergence of coordinated behavior (Drescher \textit{et al.}, 2011), the acquisition of multicellularity (Goldstein, 2015), and locomotion among macroscopic aquatic organisms (Gazzola \textit{et al.}, 2014). In modern oceans eukaryotes have evolved morphologies and behaviors that take advantage of fluid motion to aid feeding, locomotion, inter- and intra-specific community interactions, and more (Rubenstein \& Koehl, 1977; Chia \textit{et al.}, 1984, Arkema, 2009; Full, 2010). The fossil record itself preserves a large number of bizarre and unusual forms, which are hypothesized to have evolved as a means to mitigate, or take advantage of, the effects of fluid flow (Furbish \& Arnold, 1997). Thus, understanding the ways in which organisms interact with moving fluids can provide a fundamental window into evolutionary processes, but requires a knowledge base of the underlying fluid physics. 

In recent years this approach has become particularly important for reconstructing the paleobiology and -ecology of the latest Neoproterozoic Ediacara biota ($\sim571-539$ Ma), which is an enigmatic group of soft-bodied multicellular organisms that represents the first radiation of complex, eukaryotic macroscopic life (Xiao \& Laflamme, 2009; Liu \textit{et al.}, 2015; Darroch \textit{et al.}, 2018a). These organisms first appear in late Ediacaran sediments ($\sim571-566$ Ma) preserved around Mistaken Point, Newfoundland, Canada (Liu \textit{et al.}, 2015; Pu \textit{et al.}, 2016), become more diverse and widespread in younger and shallower-water sediments ($\sim558-550$ Ma) from South Australia and the White Sea area of Russia (Martin \textit{et al.}, 2000; Droser \textit{et al.}, 2019), and persist right up until the Cambrian boundary $\sim539$ Ma in both Namibia (Grotzinger \textit{et al.}, 1995; Narbonne \textit{et al.}, 1997; Darroch \textit{et al.}, 2015; Linnemann \textit{et al.}, 2019) and the southwestern USA (Smith \textit{et al.}, 2016; 2017). Following nearly 30 million years as the dominant components of benthic ecosystems, the Ediacara biota disappear at the base of the Cambrian in what some have suggested represents the first mass extinction of complex life (Amthor \textit{et al.}, 2003; Laflamme \textit{et al.}, 2013; Darroch \textit{et al.}, 2015; 2018\textit{a,b}; Muscente \textit{et al.}, 2018; Zhang \textit{et al.}, 2018; although see Hoyal-Cuthill \& Han, 2018 for an opposing view). Reconstructing the paleobiology, paleoecology, and biological affinities of the Ediacara biota is thus key to understanding the origins of the modern marine biosphere (Darroch \textit{et al.}, 2018\textit{b}). %However, given the array of strange (and at times, quite unique) morphological constructions that characterize the Ediacara biota (Figure \ref{fig:EPanel}), these organisms have been plagued by controversial assignments to modern metazoan clades, leaving aspects of their functional morphology as one of the few independent means of evaluating their likely biological affinities. 

While some Ediacara biota likely represent metazoans (Fedonkin \textit{et al.}, 2007; Gold \textit{et al.}, 2015; Dunn \textit{et al.}, 2017; Bobrovskiy, \textit{et al.}, 2018), many members do not appear to share synapomorphies with extant metazoan clades (Budd \& Jensen, 2000; Xiao \& Laflamme, 2009; Darroch \textit{et al.}, 2018a), and are characterized by bizarre body plans that hamper our ability to understand their relationships to extant eukaryotic groups (see Figure \ref{fig:EPanel}). Despite these challenges, the application of fluid physics studies have shed new light on the Ediacara biota, providing testable hypotheses for how these organisms moved, fed, and reproduced, despite not being able to observe them in life. These studies rely on physics-based approaches using fluid mechanics (Schopf \& Baumiller, 1998; Singer \textit{et al.}, 2012), and increasingly employ complex numerical algorithms such as computational fluid dynamics (CFD; Rahman \textit{et al.}, 2015; Darroch \textit{et al.}, 2017; Gibson \textit{et al.}, 2019). 

\begin{figure}[h!]
	\includegraphics[width=\textwidth]{EdiacaranPanel.jpg}
	\centering
	\caption{Enigmatic fossils from the late Ediacaran: a) \textit{Dickinsonia costata} (N4853; White Sea area, Russia) b) \textit{Tribrachidium heraldicum} (N3993/5056; White Sea area, Russia) c) \textit{Charniodiscus sp.} (Mistaken Point, Canada) d) \textit{Bradgatia sp.} (Mistaken Point, Canada) e) \textit{Kimberella quadrata} (N4853/57; White Sea area, Russia) f) \textit{Ernietta plateauensis} (Karas Region, southern Namibia) g) \textit{Archaeichnium} (Karas Region, southern Namibia). All scale bars are 1 cm.}
	\label{fig:EPanel}
\end{figure}

In this paper, we discuss several aspects of fluid physics that are fundamental to designing, conducting, and interpreting flume and CFD studies of fossil organisms. We provide a brief overview of fluid physics theory and address several misconceptions in the paleontological and biological literature. We review advances in Ediacaran paleobiology stemming from fluid mechanics approaches, while considering similar examples from more modern organisms. We then present a case study of CFD applied to an Ediacaran organism, outlining a sophisticated experimental design that has not yet been used in paleontological studies. Lastly, we discuss future directions in paleobiological fluid mechanics studies focused on the Ediacaran, and outline key research questions that will help discern the role of these enigmatic organisms in the proliferation of animal ecosystems. 

\section{Ediacaran paleobiology and paleoecology}\label{Section heading 4}
Historically the latest Ediacaran has been depicted as being characterized by ecologically simple communities with a relatively low number of ecologies and few mobile taxa (see `the Garden of Ediacara'; McMenamin, 1986), but more recent studies are highlighting increasing behavioral and ecological complexities during this time. Behaviors, particularly feeding and movement, are crucial facets to reconstructing Ediacaran ecosystems because they provide pivotal information for the grade of biological organization, the complexity of potential ecological interactions, the level of ecosystem engineering, and patterns of nutrient cycling. For example, previous studies have set rigid constraints on phylogenetic placements such as for \textit{Dickinsonia} purely on the basis of inferred feeding ecology, which can then be used to begin reconstructing total group phylogeny (Sperling \& Vinther, 2010). Other studies have also demonstrated that some modern feeding ecologies have likely been co-opted from those necessary to survive Proterozoic environments (Rothman \textit{et al.}, 2003; Sperling \textit{et al.}, 2007), emphasizing that roots for many Phanerozoic behaviors must be viewed from their original geologic and paleoenvironmental context (Peterson, 2005), and they firmly lie in the Precambrian (Sperling \& Vinther, 2010).

\subsection{Ediacaran feeding modes}
The soft-bodied Ediacara biota are characterized by a range of non-analogue body plans, many of which have no parallels amongst extant animal groups (Erwin \textit{et al.}, 2011). Irrespective of their phylogenetic affinities, the discovery of many fossilized Ediacaran organisms preserved in deep-water sediments (in particular in Newfoundland and NW Canada -- Wood \textit{et al.}, 2003; Narbonne \textit{et al.}, 2014; Liu \textit{et al.}, 2015) deposited far below the presumed photic zone, implies they were unlikely to have been photoautotrophic (or to have possessed photosynthetic symbionts; Clapham \& Narbonne, 2002; Laflamme \textit{et al.}, 2009). Concurrently, few feeding appendages or internal digestive structures have been recognized in Ediacaran organisms (e.g. Fedonkin \textit{et al.}, 2007; Schiffbauer \textit{et al.}, 2020), although this may be in part due to taphonomic bias (see Wade, 1968; Norris, 1989; Liu \textit{et al.}, 2011; Gibson \textit{et al.}, 2018). As such, morphological studies in isolation have offered little help in determining how some of the more enigmatic Ediacaran groups may have fed. Current suggestions for various Ediacaran feeding ecologies include chemoautotrophy (McMenamin \& McMenamin, 1990; Dufour \& McIlroy, 2017), symbiosis (McMenamin, 1986), osmotrophy (McMenamin, 1993; Sperling \textit{et al.}, 2007; Laflamme \textit{et al.}, 2009), and suspension feeding (Clapham \textit{et al.}, 2003; Wood \& Curtis, 2015), however several of these feeding ecologies need to be tested to fully determine feeding ecologies present during the Ediacaran.

\subsection{Ediacaran mobility}
Ediacaran mobility has traditionally been viewed through the trace fossil record using either sediment traces or preserved microbial mat disturbances (Fedonkin \& Waggoner, 1997; Gehling \textit{et al.}, 2005; Ivantsov \& Malkhovskaya, 2002; Jensen, 2003; Seilacher, 1989), which has provided a limited view given that tracemakers are rarely preserved in direct association with their respective traces. While originally thought to be overwhelmingly sessile (McMenamin, 1986), Ediacaran benthic ecosystems are now thought to have been more dynamic than previously stated (Droser \textit{et al.}, 2017; 2019; Gehling \& Droser, 2009; Evans \textit{et al.}, 2018; Tarhan \textit{et al.}, 2018). Evidence for Ediacaran locomotion has been reported as far back as the Avalonian assemblage from Mistaken Point (Liu \textit{et al.}, 2010), but abundant evidence of resting, movement, and grazing traces exists in White Sea assemblage material from Russia and South Australia. Iconic \textit{Dickinsonia} (Figure \ref{fig:EPanel}a) and \textit{Yorgia} resting and movement traces are common with some slabs preserving both trace and body fossils (see Gehling \textit{et al.}, 2005; Ivantsov, 2011; Ivantsov \& Malakhovskaya, 2002). Ichnological and body fossil evidence suggests \textit{Kimberella} was capable of movement given abundant grazing traces including some body fossils in coincidence with associated trace fossils (Fedonkin \textit{et al.}, 2007; Gehling \textit{et al.}, 2014). In South Australia, surfaces with abundant \textit{Parvancorina} illustrate a unidirectional orientation that is unlikely to be the result of passive current alignment, indicating that these organisms possessed the ability to move and reorient themselves with respect to flow (Paterson \textit{et al.}, 2017). Most recently, the trilobate bilaterian \textit{Yilingia} was reported in material from China where body fossils were discovered in direct association with traces (Chen \textit{et al.}, 2019). While the trace fossil record has allowed us to definitively show that at least five Ediacara taxa were mobile, the record is still limited by the unusual nature of the Ediacaran substrate (i.e., widespread and thick microbial mats) and body fossil taphonomy (Sappenfield \textit{et al.}, 2011). This has led authors to disagree over the criteria for distinguishing ``true" biogenic Ediacaran traces (Droser \textit{et al.}, 2005; Jensen \textit{et al.}, 2006). Thus, discerning alternative methods for determining potential mobility is useful. 

%	\subsection{\textcolor{red}{Snappy title}}
Direct evidence of Ediacaran feeding and mobility exist within the fossil record (Fedonkin \textit{et al.}, 2007; Gehling \textit{et al.}, 2014; Chen \textit{et al.}, 2019), but they are still limited. To fully address Ediacaran behavior and associated biomechanics, we require alternative approaches. Fortunately, the fidelity of preservation in these deposits permits understanding on key biomechanical controls for behaviors like locomotion, such as tissue rigidity (see e.g. Evans \textit{et al.}, 2015; 2019). Taking these approaches one step forward, we can use physics-based models to fill in information gaps that are left in the fossil record. Fluid mechanics and other modeling techniques provide unique opportunities with which we can understand how organisms may have lived and behaved in their environments without being constrained by the information directly preserved within a fossil. 


\section{Computational Fluid Dynamics as a Method}\label{Section heading 4}
Paleontologists interested in fluid flow problems frequently look to works of Vogel (1984), which has been foundational in our understanding of fluid life interactions. While Vogel's simplified approach to fluid problems has laid the foundation for tackling (paleo)biological fluid experiments, the reality is that fluid motions and interactions with life are far more complicated than what has been offered there and elsewhere. To rigorously investigate the questions that are often of interest while using tools like CFD, we recognize that we cannot simply use a plug-and-play approach with fluid modeling software for the high probability risk of yielding unrealistic and incorrect results in the same manner as conducting statistical analyses without understand the basics of statistics. For this reason, we provide a brief overview of key physical and mathematical concepts used to describe fluid motions. Our intent is to offer a sense of the complexities of fluid flow systems that are valuable for interpreting paleontological CFD studies, and to correct misunderstandings that are repeatedly presented in literature. However, we emphasize that this section does not provide a sufficient background for conducting CFD analyses, and those lacking a formal training in fluid mechanics who wish to use these methods will benefit from close collaboration with experts in fluid mechanics. 

%\subsection{History}
%The field of fluid mechanics has a deep history, possibly starting with experiments performed by Archimedes in ancient Greece (287--212 BCE). The field saw rapid growth during the 17$^{\mathrm{th}}$ century when developments were made in understanding continuity, wind flow, fluid pressures, and viscosity of linear fluids by Benedetto Castelli, Edme Mariotte, Blaise Pascal, and Sir Issac Newton, respectively. The 18$^{\mathrm{th}}$ century produced Euler's differential equation of motion for inviscid fluids, it's integral form known as Bernoulli's equation, and Jacob Bernoulli developed the energy equation for inviscid flow. In the 19$^{\mathrm{th}}$ century dimensional analysis was used to supplement much of fluid mechanics theory to develop solutions for many of the equations that were previously too complex to solve analytically. Osborne Reynolds conducted and published his famous experiments on the transition from laminar to turbulent flow regimes.  Claude-Louis Navier and George Gabriel Stokes developed the differential form of Newton's second law of motion to describe the motion of viscous fluids (known as the Navier-Stokes equations). Stokes additionally developed much of our foundational knowledge on forces of drag on small objects in viscous fluids. By the beginning of the 20th century, the continuity, momentum and energy equations were central in studies of fluid motion, and dimensional analysis was frequently implemented to simplify much of the mathematics involved in fluid experiments. However, the Navier-Stokes equations were still too difficult to solve analytically for most problems. Prandtl experimentally demonstrated how low viscosity fluid flows is divided into a viscous sublayer near boundaries transitioning to the turbulent boundary layer, before developing into more inviscid flow further away from solid boundaries. Lastly, with the advent of computational power, fluid mechanics rapidly developed a suite of numerical models known as computational fluid dynamics (CFD) that could be implemented on early computers and later on high-power workstations.

\subsection{Basic Elements}
We normally consider ordinary fluids, including water, to be continuous substances; however, when viewed at the molecular scale fluids are comprised of discrete particles (molecules). At ordinary pressures and temperatures there are about $3 \times 10^{22}$ molecules in one cm$^{3}$ of water. The mean free path $\lambda$ of liquid water molecules is on the order of $10^{-10}$ m. Average molecular speeds between collisions are on the order of hundreds of meters per second. Let $L$ denote a characteristic length scale, which may be defined by the resolution scale at which we observe the fluid, by the size of a flow domain (e.g., the size of a particle within the fluid or the diameter of a flow conduit), or by the size of a computational grid cell. We then define the Knudsen number as $\mathit{Kn} = \lambda / L$. When $\mathit{Kn} \ll 1$, it is then permissible to define ``local'' thermodynamic quantities such as the fluid mass density $\rho$, the temperature $T$, and the pressure $p$. Kinetic theory also yields the dynamic viscosity $\mu$, and we may additionally define the local fluid velocity -- effectively the average molecular velocity at the characteristic length scale $L$. We may view these quantities as smoothly varying functions of space and time, and in doing so the fluid is considered a continuum which permits us to use differential calculus in describing these quantities and the fluid continuum behavior without focusing on the individual particles. Under continuum conditions, fluid velocities vanish at solid boundaries providing the ``no-slip'' condition where all velocities vanish. For $\mathit{Kn} \ge 0.01$ the continuum assumption is not necessarily satisfied. Slip conditions may occur at solid boundaries and describing the behavior of the fluid requires kinetic theory or methods of statistical mechanics.

When fluid viscous (frictional) forces are large relative to other forces, fluid motion is laminar such that streamlines are quasi-parallel as they converge and diverge in the vicinity of an irregular object (organism) within the flow. When inertial forces (see below) are large relative to viscous forces, the flow becomes unstable leading to the onset of turbulent motions, where streamlines are now unsteady and complex across spatial and temporal scales (Figure \ref{fig:Re}). In this context it is useful to describe flows in terms of the dimensionless Reynolds number $\mathit{Re}$, conventionally defined as
\begin{equation}
\mathit{Re} = \frac{\rho U L}{\mu} = \frac{U L}{\nu}\, ,
\label{eq:Re}
\end{equation}
\begin{figure}[h!]
	\includegraphics[width=\textwidth]{ReFigure.jpg}
	\centering
	\caption{Development of the turbulent boundary layer. a) Direct Numerical Simulation (DNS) solution where velocity increases from blue to red (scale right). b) Theoretical development modified from COMSOL.com and Furbish (1997). Gray arrows represent instantaneous velocities of the boundary layer. Black arrows and profiles represent time averaged velocities. Boundary layer is initially fully laminar until is separates into the viscous sublayer (straight gray arrows) and turbulent boundary layer as indicated by the curved gray arrows.}
	\label{fig:Re}
\end{figure}
where $U$ is a characteristic fluid velocity, $L$ is a characteristic length, $\mu$ is the dynamic viscosity of the fluid, and $\nu = \mu/\rho$ is the kinematic viscosity (a molecular momentum diffusivity; see below). The Reynolds number can be interpreted several ways. Often it is described as the ratio of inertial to viscous forces, although this importantly does not imply that this ratio is fixed at all locations within a flow. Rather, under this description the Reynolds number represents a characteristic ratio of these forces in defining the dynamical similarity, or dissimilarity, of flow systems (see below). Here it is important to distinguish between a systems scale Reynolds number $\mathit{Re_s}$ and a particle Reynolds number $\mathit{Re_p}$. For example, with flow through a conduit (Figure \ref{fig:conduit}), $U$ normally is selected to be the magnitude of the average velocity and $L$ is the conduit diameter, yielding a system scale value of $\mathit{Re_s}$. With flow around a particle (Figure \ref{fig:sphere}), $U$ is the magnitude of the relative velocity between the particle and surrounding fluid outside the velocity boundary layer (i.e., the far-field velocity) and $L$ is the sphere radius or diameter, yielding a particle Reynolds number $\mathit{Re_p}$. Moreover, for a specified flow system, there is no prescribed value of $\mathit{Re}$ indicating the onset of turbulence. This onset can vary within an individual system depending on details of initial and boundary conditions, and it varies between geometrically dissimilar systems.
\begin{figure}[h!]
	\includegraphics[width=0.75\textwidth]{Conduit-Figure.jpg}
	\centering
	\caption{Stationary analytical solution of laminar flow through a conduit from left to right with 0.05 m/s inlet velocity. Black line represents velocity profile and with flow direction arrows.}
	\label{fig:conduit}
\end{figure}
\begin{figure}[h!]
	\includegraphics[width=0.75\textwidth]{Sphere.jpg}
	\centering
	\caption{$k-\omega$ RANS flow around a sphere from left to right with inlet velocity of 0.5 m/s. }
	\label{fig:sphere}
\end{figure}
Expanding on the latter point, objects are geometrically similar if they are scaled versions of each other, such as different sizes of spheres and cubes, respectively. Steady fluid motions around spheres of different sizes are geometrically similar if the streamlines are geometrically similar. The same holds for cubes, which additionally requires that the orientations of the cubes relative to the mean motion are the same. Two flows are dynamically similar if the Reynolds number is the same for geometrically similar systems. Importantly, this means that the Reynolds numbers for geometrically dissimilar objects are not comparable; a given Reynolds number for dissimilar systems does not imply the systems behave the same mechanically. That is, the meaning and significance of a Reynolds number $\mathit{Re}=1$ for flow around a brachiopod has little to do with the meaning and significance of a Reynolds number $\mathit{Re}=1$ for flow around a crinoid. Similarly, a given Reynolds number for two identical objects, one within a free stream and one next to a solid boundary, does not involve dynamic similitude and therefore does not imply that the systems behave the same mechanically.

Of particular interest is the drag force $F_D$ that fluid motion exerts on an organism. This drag force is equal to the integral of the pressure and the viscous stress acting on the surface of the object, measured in a direction parallel to the mean relative motion. By Newton's first law the object exerts a force on the fluid that is equal in magnitude to the drag force. Dimensional analysis leads to the conclusion that the drag force can be expressed in terms of a dimensionless coefficient of drag defined by 
\begin{equation}
C_D = \frac{F_D}{\frac{1}{2} \rho U^2 A}\, .
\end{equation}
Here, $U$ is a characteristic flow velocity, normally defined by the relative velocity between the object and surrounding far-field velocity, or by a well-defined approach velocity for an object attached to a solid boundary. The quantity $A$ is a characteristic area such as the frontal (silhouette) area of the object normal to the mean fluid flow, or more simply, an area defined by the square of the characteristic length of the object. The quantity $(1/2) \rho U^2$ defines a characteristic dynamic pressure acting on the object.

Theory and experiments indicate that for laminar flows at small Reynolds number $\mathit{Re}$, the coefficient $C_D$ varies inversely with $\mathit{Re}$ as $C_D = C/\mathit{Re}$ for geometrically similar objects; where the constant $C$ varies with object shape. Following a transition over intermediate Reynolds number, the coefficient of drag becomes approximately constant at large $\mathit{Re}$ with fully developed turbulence, although this is an average value. That is, the coefficient $C_D$ fluctuates with turbulence. Moreover, like the Reynolds number, the coefficient of drag for two identical objects, one within a free stream and one next to a solid boundary, are not the same.

Organisms suspended within a fluid may passively move with the fluid motion or, if sufficiently massive, inertially detach from the fluid motion during acceleration of the fluid. The fluid-particle coupling can be characterized by the dimensionless Stokes number defined as
\begin{equation}
\mathit{St} = \frac{U \tau}{L} \, ,
\end{equation}
where $U$ now is the fluid velocity surrounding the particle (organism), $L$ is the characteristic length (e.g., diameter) of the particle, and $\tau$ is the relaxation time of the particle due to drag. If flow surrounding the particle is laminar (small $\mathit{Re}$), then the relaxation time is $\tau = \rho_p L^2/C \mu$ where $\rho_p$ is the density of the particle and $C$ is a constant (equal to 18 for spherical particles). For $\mathit{St} \ll 1$, particles behave as passive tracers, closely following streamlines. For $\mathit{St} \gg 1$, particles inertially detach from the fluid motion during fluid accelerations and tend to continue their initial trajectories. The relaxation time $\tau$ must be modified when the particle Reynolds number is large.

Of interest is the relative contribution of advection and diffusion to the transport of a dissolved substance, notably in relation to delivery of nutrients to an organism or removal of waste products released by an organism. Starting with the advection-diffusion equation, dimensional analysis leads to the conclusion that this relative contribution can be characterized by the dimensionless compositional P\'{e}clet number $\mathit{Pe}$ defined by
\begin{equation}
\mathit{Pe} =\frac{UL}{\kappa}\, ,
\label{eq:Pe}
\end{equation}
where $\kappa$ is the molecular diffusivity of the substance within the fluid. As with the Reynolds number, $U$ is a characteristic relative velocity. The characteristic length $L$ is the thickness of the compositional boundary layer, normally approximated by the characteristic particle size. A suspended particle passively moving with the fluid $(\mathit{St} \ll 1)$ does not ``see'' advection toward or away from it so that $\mathit{Pe} \ll 1$. Conversely the small diffusivities of common ions in water mean that small relative velocities $U$ yield large $\mathit{Pe}$. Advective transport is far more effective than diffusive transport in delivering dissolved nutrients or removing waste products.

Returning to the Reynolds number $\mathit{Re}$ given in Eq. (\ref{eq:Re}), note that the kinematic viscosity is in fact a diffusivity. Thus the Reynolds number also is a momentum P\'{e}clet number. It can be interpreted as the rate of advection of momentum at the macroscopic (continuum) scale to diffusion of momentum at the molecular scale.

Whereas there are numerous quantities and dimensionless numbers frequently cited in the literature, the quantities described above are potentially the most widely utilized among paleontologists and evolutionary biologists.

\subsection{Equations of Motion}
\subsubsection{Navier-Stokes Equations}
Newton's second law for the motion of ordinary Newtonian fluids is expressed by the Navier-Stokes equations, also referred to as the momentum equations. Letting $\mathbf u = \mathbf i u_1 + \mathbf j u_2 + \mathbf k u_3$ denote the local (continuum) fluid velocity with components $u_1$, $u_2$ and $u_3$ parallel to the Cartesian $x_1$, $x_2$ and $x_3$ coordinate axes (Figure \ref{fig:coor}), then using Einstein notation and neglecting the gravitational force for simplicity, the Navier-Stokes equations for an incompressible flow are
\begin{equation}
u_j\frac{\partial u_i}{\partial x_j} + \frac{\partial u_i}{\partial t} = -\frac{1}{\rho}\frac{\partial p}{\partial x_i} + \nu \frac{\partial}{\partial x_j} \left( \frac{\partial u_i}{\partial x_j} \right) \, ,
\label{eq:NS}
\end{equation}
where $t$ denotes time, $p$ is pressure, and $\nu = \mu / \rho$ is the kinematic viscosity of the fluid where $\mu$ is the dynamic viscosity and $\rho$ is the fluid density. In this compact form, Eq. (\ref{eq:NS}) represents three component equations with four unknowns ($u_1$, $u_2$, $u_3$ and $p$). These are therefore supplemented with the continuity equation for an incompressible flow, namely,
\begin{equation}
\frac{\partial u_i}{\partial x_i}=0
\label{eq:continuity}
\end{equation}
If thermal or compositional buoyancy effects are involved, then Eq. (\ref{eq:NS}) and Eq. (\ref{eq:continuity}) must be further supplemented with the thermal energy equation or the compositional advection-diffusion equation, or both.

\begin{figure}[h]
	\includegraphics[width=0.5\textwidth]{Coordinate-System.jpg}
	\centering
	\caption{Graphical three-dimensional coordinate system with box showing movement directions for individual velocity components, where $u$, $v$ and $w$ are $u_1$, $u_2$ and $u_3$, respectively, for movement in the directions of $x$, $y$, and $z$, respectively.}
	\label{fig:coor}
\end{figure}

The three terms represented by $\partial u_i / \partial t$ are referred to as local accelerations. The nine terms represented by $u_j \partial u_i / \partial x_j$ are convective accelerations. These nonlinear terms are the source of instabilities in fluid motions giving rise to turbulence. The three terms involving $p$ are pressure terms that induce flow together with the unwritten gravitational terms. The nine terms involving $\nu$ are the viscous terms. These linear terms represent viscous friction, which tends to stabilize fluid motions. At sufficiently low Reynolds number $\mathit{Re}$ the viscous terms are much larger than the convective terms, and Eq. (\ref{eq:NS}) reduces to a diffusion equation with a source term due to pressure.

For simple, often idealized, flow configurations, simplified versions of Eq. (\ref{eq:NS}) and Eq. (\ref{eq:continuity}) can be solved analytically. For realistic flow configurations, notably involving flow around objects or over irregular surfaces, numerical treatments of these equations are required.  As described below, all fluid simulations involve solving Eq. (\ref{eq:NS}) and Eq. (\ref{eq:continuity}) or modified forms of these equations for specified initial and boundary conditions. Because solving these equations at each numerical grid point in the flow field at all times is computationally challenging, different numerical schemes are used. These include finite element (FEM) and finite volume (FVM) procedures, for which an in depth treatment is beyond the scope of this paper. Historically, FVM procedures have been favored for integrating these equations across the flow field. For a comprehensive treatment of the principles and details of these two methods and their differences, we suggest Blazek (2001) and Jeong \& Seong (2014).

\subsubsection{Reynolds-Averaged Navier-Stokes Equations}
Osborne Reynolds provided two of the most important contributions to the field of fluid mechanics in his systematic description of turbulent flows leading to what is now referred to as the Reynolds number, Eq. (\ref{eq:Re}), and in formulating a scheme of averaging of the Navier-Stokes equations. His descriptions came from experiments in which he introduced small jets of dyed water into the center of a large, glass conduit of flowing water. At low flow velocities, the dye remained visible as a coherent streak for the entire length of the conduit, but at higher velocities the dye became mixed throughout the cross-section of the conduit. This represented a transition from laminar to turbulent flow. He spent approximately twenty years developing and publishing the framework for understanding fluctuating motions of turbulence at large Reynolds numbers that is presented below.

Letting $\mathbf x = (x_1, x_2, x_3)$, we start by writing the three velocity components and the pressure as
\begin{equation}
u_i (\mathbf x,t) = \overline{u_i} (\mathbf x) + u_i^\prime (\mathbf x, t) \qquad \mathrm{and} \qquad p (\mathbf x, t) = \overline{p} (\mathbf x) + p^\prime (\mathbf x, t) \, ,
\label{eq:vp_components}
\end{equation}
where the overline represents an average and the prime denotes a fluctuation about the average, and we are assuming that the averages may vary with position $\mathbf x$ but not time $t$, that is, the velocity signal is stationary. By definition the averages of the fluctuations are zero, namely, $\overline{u_i^\prime} = 0$ and $\overline{p^\prime} = 0$. The averages in Eq. (\ref{eq:vp_components}) are formally ensemble averages as defined by Gibbs (1902). Namely, we are to imagine a great number (an ensemble) of nominally identical but independent systems, each evolving in time according to the laws of physics. An ensemble average at any geometrically similar position $\mathbf x$ within the member systems is then taken as the average over the ensemble of systems at any instant. If behavior is strictly ergodic, then the ensemble average is identical to a time average defined by
\begin{equation}
\overline{u_i} (\mathbf x) = \lim_{T \rightarrow \infty} \frac{1}{T} \int_{t_0}^{t_0 + T} u_i (\mathbf x,t) \, \mathrm d t \, ,
\end{equation}
for arbitrary starting time $t_0$. In practice the sampling interval $T$ is finite and we assume that the average is satisfactorily estimated as
\begin{equation}
\overline{u_i} (\mathbf x) = \frac{1}{T} \int_{t_0}^{t_0 + T} u_i (\mathbf x,t) \, \mathrm d t \, ,
\label{eq:time}
\end{equation}
for sufficient large interval $T$. If the continuous time series $u_i (\mathbf x,t)$ is discretely sampled, then Eq. (\ref{eq:time}) is replaced with the ordinary arithmetic average. Other similar averaging, including spatial averaging, can be applied to certain flow conditions, including nominally homogeneous turbulence and slowly varying (nonstationary) conditions.

Upon taking averages of Eq. (\ref{eq:NS}) and Eq. (\ref{eq:continuity}), the continuity equation becomes
\begin{equation}
\frac{\partial\overline{u_i}}{\partial x_i} = 0 \, ,
\end{equation}
yielding the additional result that $\partial u_i^\prime / \partial x_i = 0$ with $\overline{u_i^\prime} = 0$ by the definition of averaging. In turn, and again neglecting gravity, the Reynolds-averaged Navier-Stokes equations are
\begin{equation}
\rho \left( \overline{u_j}\frac{\partial\overline{u_i}}{\partial x_j} + \frac{\partial \overline{u_i}}{\partial t} \right) = -\frac{\partial \overline{p}}{\partial x_j} + \frac{\partial}{\partial x_j} \left( \mu \frac{\partial \overline{u_i}}{\partial x_j} - \rho \overline{u_i^\prime u_j^\prime} \right) \, .
\end{equation}
This has the same form as Eq. (\ref{eq:NS}) but with the addition of the nine terms defined by $\rho \overline{u_i^\prime u_j^\prime}$, which are the Reynolds stresses. Specifically, these define the Reynolds stress tensor,
\begin{equation}
\tau_{ij}^R = - \rho\overline{u_i^\prime u_j^\prime} = - \rho
\begin{bmatrix}
\overline{{u_1^\prime}^2} & \overline{u_1^\prime u_2^\prime} & \overline{u_1^\prime u_3^\prime}\\
\overline{u_2^\prime u_1^\prime} & \overline{{u_2^\prime}^2} & \overline{u_2^\prime u_3^\prime}\\
\overline{u_3^\prime u_1^\prime} & \overline{u_3^\prime u_2^\prime} & \overline{{u_3^\prime}^2}
\end{bmatrix}
\label{eq:RST}
\end{equation}
Each element $\rho \overline{u_i^\prime u_j^\prime}$ in Eq. (\ref{eq:RST}) represents a momentum flux associated with fluctuating motions.  For example, the product $\rho u_1^\prime u_3^\prime$ may be interpreted as an instantaneous flux of momentum $\rho u_1^\prime$ per unit volume associated with the $x_1$ direction at the rate $u_3^\prime$ in the transverse direction $x_3$.  Then $\rho \overline{u_1^\prime u_3^\prime}$ is the averaged momentum flux, and the negative sign in Eq. (12) makes this a stress resisting the mean motion parallel to $x_1$.  These stresses dominate the resistance to motion in fully turbulent flows except within the viscous sublayer next to a solid boundary.

\subsubsection{Turbulence Closures}
Solving the Reynolds-averaged equations requires expressing the elements of the Reynolds stress tensor in terms of other averaged quantities. A particularly important early effort on this closure problem was that of Boussinesq (1877, 1896), who assumed that momentum transfers associated with turbulence fluctuations are dominated by mixing of the largest eddies. In analogy with Stokes's theorem for the viscous stresses in laminar flows he further assumed that the Reynolds stresses can be expressed in terms of the mean rate of strain. The Boussinesq hypothesis is thus expressed as
\begin{equation}
\tau_{ij}^R = - \rho \overline{u_i^\prime u_j^\prime} = \rho \nu_t \left( \frac{\partial \overline{u_i}}{\partial x_j} + \frac{\partial \overline{u_j}}{\partial x_i} 	\right) - \frac{2}{3} \rho k \delta_{ij} \, .
\label{eq:Boussinesq}
\end{equation}
Here, $\nu_t$ denotes an eddy viscosity that is a function of local flow conditions and position rather than being a characteristic of the fluid as is the molecular viscosity, $\delta_{ij}$ denotes the Kronecker delta function, and $k = (1/2) \overline{u_i u_i}$ denotes the turbulence kinetic energy formed from the sum of the covariances in the principal diagonal of Eq. (\ref{eq:RST}), namely,
\begin{equation}
k = \frac{1}{2} \overline{u_i^\prime u_i^\prime} = \frac{1}{2} \left[ \, \overline{{u_i^\prime}^2} + \overline{{u_2^\prime}^2} + \overline{{u_3^\prime}^2} \, \right]. 
\end{equation}
This closure means that the momentum equations must be supplemented with the mechanical energy equations to obtain the kinetic energy $k$. Note also that Eq. (\ref{eq:Boussinesq}) sometimes is written more compactly as
\begin{equation}
\tau_{ij}^{R}=-\rho\overline{u_i^\prime u_j^\prime} = 2 \nu_t \overline{S_{ij}} - \frac{2}{3} \rho k \delta_{ij} \, .
\label{eq:compactBoussinesq}
\end{equation}
Here, $S_{ij}$ denotes the Reynolds-averaged strain-rate tensor, the elements of which are represented by the parenthetical part of Eq. (\ref{eq:RST}). This turbulence closure remains relevant in numerical modeling for Reynolds-Averaged Navier Stokes models such as $k-\varepsilon$ and $k-\omega$ (see below).

For the specific situation of a uniform, turbulent boundary-layer shear flow that is steady in the mean, a particularly important turbulence closure is provided by Prandtl's mixing length hypothesis.  In analogy with kinetic theory, Prandtl assumed that boundary-normal motions of fluid parcels (eddying motions) momentarily retained their streamwise momentum during transverse motions, thus inducing the velocity fluctuations in the boundary-parallel Reynolds stress.  With vertical axis $x_3 = z$ normal to the streamwise velocity $u_1 = u$ in the $x_1 = x$ direction, he proposed that the eddy viscosity (or eddy diffusivity) may be approximated as
\begin{equation}
\nu_t=l^2\bigg{|}\frac{\textrm{d}\overline{u}}{\textrm{d}z}\bigg{|}
\label{eq:eddy_visc}
\end{equation}
where $l$ denotes the mixing length, a measure of the transverse distance of eddying motion, which Prandtl assumed to increase linearly above the boundary.  Prandtl's development leads to the well-known logarithmic velocity law (or ``law of the wall'') describing the averaged streamwise velocity $\overline{u}(z)$ above the solid boundary, namely,
\begin{equation}
\overline{u} (z) = \frac{u_*}{\kappa} \ln \left( \frac{z}{z_0} \right)
\end{equation}
Here, $u_* = \sqrt{\tau_0 / \rho}$ is the friction (or shear) velocity where $\tau_0$ is the fluid stress at the boundary, $\kappa \approx 0.41$ is the von K\'{a}rm\'{a}n constant and $z_0$ is the roughness length at which $\overline u$ goes to zero.  For hydrodynamically smooth conditions the length $z_0$ is on the order of the thickness of the viscous sublayer and scales with $\nu/u_*$.  For hydrodynamically rough conditions this length scales with the height of the roughness (e.g., sand roughness). The logarithmic law, Eq. (17), stands as one of the most important results in the field of fluid mechanics. As described below, this result is an important if not essential benchmark for numerical simulations of flow next to a solid boundary.

Before turning to the topic of numerical modeling, we end this section with an important point. Consider a flow field for which solutions of the Reynolds-averaged velocity field $\overline{u_i} (\mathbf x,t)$ and the pressure field $\overline p (\mathbf x,t)$ are obtained either analytically or numerically. Recall that these formally involve ensemble averaging, or, assuming ergodic behavior, that time averaging suffices. For illustration let us then recall Prandtl's mixing-length hypothesis concerning fluctuating motions, leading to the logarithmic velocity law for uniform flow that is steady in the mean. At this juncture we have replaced the continuum description of fluid motion with a new scheme. Namely, in this new scheme the velocity field described by the logarithmic law \textit{does not exist in a physical sense at any instant anywhere in the flow}. It is a mathematical abstraction -- a continuously differentiable function describing the ensemble expected (average) velocity state. Although this law emerges from a description of fluctuating motions, it contains by itself no information regarding fluctuating motions. More generally, the Reynolds-averaged Navier-Stokes equations describe an imaginary fluid-like motion in which the velocity field represents statistically expected conditions, not actual conditions occurring in the continuum prototype. This point may be an important guide for choosing the numerical modeling approach. Specifically, we may choose to use such a time averaged approach when addressing a problem for which we only need to understand a system's basic flow patterns, or more specifically situations where we are less interested in details such as localized fluxes or force fluctuations.

\subsection{Numerical Reynolds-Averaged Navier-Stokes (RANS) Models} 
While there are several turbulence models, we focus on a subset that are used and applicable to paleontological studies. Unlike the previous section, we do not discuss in depth the underlying closures for these models, but we urge the reader to consult literature from the fluid mechanics field (such as Blazek, 2001). For a more robust comparison of turbulence models and their underlying mechanics, Barlinedina \textit{et al.} (1997) is an excellent resource.

In Eq. (\ref{eq:compactBoussinesq}), $\nu_T$ denotes the eddy viscosity that is a function of local flow conditions and not a physical characteristic of the fluid like the molecular dynamic viscosity is. Importantly, $\nu_T$ retains memory in that it is affected by the local history of flow. Once we know $\nu_T$, the Navier-Stokes equations can be used to address fluid flow questions using averaged flow variables. Implementing the eddy-viscosity approach, the dynamic viscosity $\mu$ in the viscous stress tensor embedded within the Navier-Stokes equations is replaced with individual components for laminar and turbulent such that $\mu = \mu_L+\nu_T$. Once the eddy viscosity $\nu_T$ is calculated, we can add it to the laminar viscosity and incorporate it into the averaged flow variables from before to simulate turbulent flow. 

\subsubsection{$k$--$\varepsilon$ model}
The $k$--$\varepsilon$ family of models is widely used in engineering and paleontological studies. These two-equation eddy viscosity models rely on the turbulent kinetic energy $k$ described previously and the turbulent dissipation rate $\varepsilon$. Because many of these models often require a dampening function to correctly calculate through the viscous sublayer, those with this function are frequently referred to as low Reynolds number models. Often these models have turbulence equations with stiff source terms requiring high grid resolution near walls to accurately model the viscous sublayer. To make this process more computationally feasible, many programs employ time-stepping schemes. Initialization of these models can require significant effort, but two approaches are to either 1) use freestream values for $k$ and $\varepsilon$, or 2) to prescribe profiles for these values near the walls. Depending on implementation, some software suites may without an increased mesh resolutions near the walls as they do not resolve these cells analytically (e.g. OpenFOAM; p. U-40).

\subsubsection{$k$--$\omega$ model}
The $k$--$\omega$ model (Wilcox, 1988; Wilcox 1993) work by solving for the turbulent kinetic energy $k$ and the dissipation per unit turbulent kinetic energy $\omega$ (i.e., a rate). It was developed because many of the convergence issues with $k$--$\varepsilon$ models were due to the modeling of the turbulent dissipation rate $\varepsilon$. Particularly near walls, the $\varepsilon$ equation is less accurate and difficult to solve due to local extrema.

\subsubsection{SST Model}
The $k$--$\omega$ Shear Stress Transport turbulence model (SST; Menter, 1994; Menter \& Rumsey 1994) combines a high Reynolds number version of the $k$--$\varepsilon$ model with a $k$--$\omega$ model (Wilcox, 1988; Wilcox 1993) providing the positive features of both.  Within the SST model, the $k$--$\omega$ model is applied to sublayers near any walls because it needs no dampening function. Further up in the logarithmic velocity profile near the walls, the $k$--$\omega$ is also exploited to avoid $k$--$\omega$ numerical issues from adverse pressure flows. The $k$--$\varepsilon$ model is then heavily relied up on in the turbulent wakes downstream where the $k$--$\omega$ is often too sensitive to the freestream $\omega$ values. Of important note is that the SST turbulence model has a modified turbulent eddy-viscosity function to improve performance in flows characterized by strong pressure gradients or pressure-induced boundary separation.

\subsection{Numerical Turbulence Models}
\subsubsection{Direct Numerical Simulations}
Direct Numerical Simulations (DNS) are numerically complicated models that compute the entire range of turbulent length scales at all locations, potentially down to the Komolgorov microscales where turbulent kinetic energy is dissipated into heat; these are thus approaches that can overcome the limitations of RANS simulations by solving all equations in simulations, without using simplified, averaged quantities. However, they are extremely computationally intensive and never used in paleontological studies. While such accuracy is desired, even with cluster computing the computational requirements often limit the applicability of these models for most experiments.

\subsubsection{Large Eddy Simulations}
Between the two end-members of RANS and DNS exists another family of models that solves turbulent scales above the Komolgorov scale. Large Eddy Simulations (LES) employ a time and/or spatial convolution
\begin{equation}
\overline{\phi(x,t)}=\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\phi(r,t)G(x-r,t-\tau)\,\mathrm{d}\tau\,\mathrm{d}r\, ,
\end{equation}
where $\overline{\phi(x,t)}$ is the filtered field, $G$ is the convolution kernel that has associated length and time cutoff scales, and $r$ and $\tau$ are length and time quantities, respectively. When applied to the incompressible flow Navier-Stokes equations, the LES governing equations become the filtered incompressible continuity equation
\begin{equation}
\frac{\partial\overline{u_i}}{\partial x_i}=0
\end{equation}
and the filtered Navier-Stokes equations
\begin{equation}
\frac{\partial\overline{u_i}}{\partial t}+\frac{\partial}{\partial x_j}(\overline{u_iu_j})=-\frac{1}{\rho}\frac{\partial\overline{p}}{\partial x_i}+\nu\frac{\partial}{\partial x_j}\bigg{(}\frac{\partial\overline{u_i}}{\partial x_j}+\frac{\partial\overline{u_j}}{\partial x_i}\bigg{)}=-\frac{1}{\rho}\frac{\partial\overline{p}}{\partial x_i}+2\nu\frac{\partial}{\partial x_j}S_{ij}\, .
\label{eq:filtered}
\end{equation}					
Through the use of substitution and some algebra, the governing LES equations become
\begin{equation}
\frac{\partial\overline{u_i}}{\partial t}+\overline{u_j}\frac{\partial\overline{u_i}}{\partial x_j}=-\frac{1}{\rho}\frac{\partial \overline{p}}{\partial x_i}+\nu\frac{\partial^2\overline{u_i}}{\partial x_j\partial x_j}-\frac{\partial\tau_{ij}}{\partial x_j}\, .
\label{eq:LES}
\end{equation}
In these equations the overbars no longer represent time or ensemble averages, but instead represent spatially filtered quantities. While LES resolves vector fields to much finer scales than RANS, there are still unresolved scales that can be broken into resolved sub-filter scales and sub-grid scales. The resolved sub-filter scales are those with wave numbers above a specified cutoff $k_c$, which are thus dampened by the filter. Sub-grid scales are all the scales smaller than the cutoff spatial filter of width $\Delta$. These are solved for through a variety of methods each specific to the individual LES model that is being used, such as the eddy-viscosity models, the Smagorinsky classic model, or the Germano dynamic models. While RANS have been the most widely used turbulence models applied to paleontological studies, LES presents great opportunity for more accurately modeling the turbulent flows in which organisms typically live, and it allows one to examine fluctuations and force impulses that the fluid imparts on a structure or organism (Furbish \& Parker, 1992). LES were originally exploited for meteorological studies in the 1960's (Smagorinsky, 1963) but have been increasingly adapted for a range of fluid flow studies (Wu \textit{et al.}, 1998; Cook, 1999). In engineering, they are often employed when RANS solutions are unacceptable due to solution failure, or in such cases where the mean flow frequencies are of the same order of magnitude as their associated fluctuations. The greatest obstacle to these studies has been the required computational abilities. These arise for several reasons. LES models are time-dependent 3D solutions to the governing Navier-Stokes equations, and they require high resolution grids in both the streamwise and cross-sectional directions of flow. While the increased computational requirements have been a drawback, the increased accuracy in modeling turbulence over a range of spatial scales sets this method apart from RANS models. Furthermore, improvements in workstation capabilities and easier access to cluster computing makes these approaches more feasible. See Piomelli (1998textit{a}) for a current overview of LES, while Ferziger (1998), Piomelli (1998\textit{b}), and Mossi (1958) provide in-depth treatments of these models.

\section{Fluid dynamics and the latest Neoproterozoic `Ediacara biota'}\label{Section heading 4}
\subsection{Case Studies}
\subsubsection{Physical Experiments}
The earliest fluid studies to address Ediacaran paleobiology were conducted using physical flume tanks. Schopf \& Baumiller (1998) used recirculating tanks to analyze the effects of tissue density on the flow dynamics of \textit{Dickinsonia} (Figure \ref{fig:EPanel}). Their results provided the first quantitative constraints on the range of plausible tissue densities required to permit \textit{Dickinsonia} to remain in association with the seafloor without being unwillingly transported.

Singer \textit{et al.} (2012) used a similar approach to test between hypothesized methods for feeding in frondose taxa, specifically how the leaf-like morphology and hypothesized tissue rigidity affected macroscopic flow around the organism and how fine-scale flow over the frond surface differed between two species of \textit{Charniodiscus} fronds. The authors demonstrated that more textured frond surfaces lowered drag while increasing entrainment, and also that models oscillated in flow -- potentially increasing gas and/or nutrient exchange in the living organisms. Although they tackled very different questions, these two studies illustrate the beginnings of a new research avenue in Ediacaran paleobiology focused on mechanics and functional morphology, using the characteristics of fluid flow as a means for hypothesis testing. It's also worth noting that the three aspects of fluid and organism mechanics investigated in these studies -- drag force calculations, tissue properties (i.e. rigidity and density), and fluid flow patterns around organisms -- have been repeatedly targeted in subsequent studies, and thus have had an out-sized influence on the field. Other properties such as the individual velocity components ($u$, $v$, $w$), turbulent kinetic energy magnitude $k$, viscous stresses, spatial distribution of pressure magnitudes, and more may be equally or more important for a given question. While these aspects have historically been `go to' aspects, others also offer opportunity with minimal exploration.

\subsubsection{Computational Fluid Dynamics Simulations} 	
While the bizarre body plans of Ediacaran organisms have proved to be a point of contention among paleontologists, fluid mechanics offers the opportunity to discern paleobiological information about the individual organisms while remaining agnostic about total group phylogeny. This information can then be used in a careful, targeted fashion to inform evolutionary history (see Rahman \textit{et al.}, 2015\textit{b}). Laflamme \textit{et al.} (2009) proposed that some Ediacaran groups could have used their overall high surface-area to volume ratios (SA/V) to feed via direct osmosis (osmotrophy). Life relying \textit{solely} on osmotrophy is constrained to a small subset of modern organisms (e.g. megasulfur bacteria; Schulz \textit{et al.}, 1999); however, in the absence of any preserved feeding appendages, guts, or orifices preserved, and their occurrence below the photic zone, there remain few testable hypotheses. One prediction of osmotrophy that can readily be tested using CFD is the distribution of flow; macroscopic osmotrophs would be expected to adopt a morphology and/or position in the water column that distributes flow over their entire absorptive surface (see for example, the distribution of water flow over \textit{Charniodiscus} fronds in Singer \textit{et al.}, 2012), thus maximizing the potential for nutrient absorption. In contrast, sessile organisms utilizing suspension mechanisms  adopt life positions whereby feeding appendages are repositioned in flow, such as crinoids repositioning their fans into flow (see Baumiller, 1997; Byrne \& Fontaine, 1988), or they develop morphologies that redirect flow to certain locations of feeding, such as in stalked crinoids (Dynowski \textit{et al.}, 2016), upside-down jellyfish (Santhanakrishan \textit{et al.}, 2012), and black fly larvae (Lacoursi\`{e}re \& Craig, 1993). However, while these flow patterns can be used to infer locations of nutrient acquisition in Ediacaran organisms, they say little about actual mechanisms for moving nutrients across body tissues (Liu \textit{et al.}, 2015). 

Amongst Ediacaran organisms, this logic structure involving the distribution of flow has been applied to the enigmatic fossil \textit{Tribrachidium} by Rahman \textit{et al.} (2015\textit{a}; see also Figure \ref{fig:EPanel}b). \textit{Tribrachidium} is a small ($2-4$ cm diameter) and approximately hemispherical organism with three-fold symmetry produced by three raised primary ``arms" that spiral anti-clockwise outward from the apex towards the margin, and that possesses three equally-spaced circular depressions near the center of the organism's apex termed `apical pits'. Field studies reveal that \textit{Tribrachidium} is commonly found in a variety of shallow-water facies alongside sedimentological evidence for currents (Gehling \& Droser, 2013; Hall \textit{et al.}, 2015), thus providing initial hints that living \textit{Tribrachidium}, like many taxa in present-day nearshore environments, was likely adapted to a life in variable water flow. In CFD simulations, Rahman \textit{et al.} (2015\textit{a}) demonstrated that \textit{Tribrachidium}'s three primary arms re-directed flow toward the organism's center, where slow-velocity recirculation developed inside what they termed `apical pits' (three depressions near the center of the organism's apex). This pattern of flow was interpreted as much more characteristic of suspension feeding than osmotrophy, and specifically a passive suspension feeding strategy whereby larger food particles fall out of suspension in apical pits under the influence of gravity, and which is thought to be an important mechanism of food acquisition in some extant bivalves and zooanthids (Koehl, 1977; Vogel, 1994). Crucially, CFD simulations showed that these flow patterns were consistent regardless of the organism's orientation to current, potentially revealing that the shape of \textit{Tribrachidium} itself represents an adaptation to environments where current directions were variable.  These results establish \textit{Tribrachidium} as potentially the oldest macroscopic suspension feeder known from the fossil record.  %%heraldicum

Similarly, Darroch \textit{et al.} (2017) tested between hypothesized feeding modes in the enigmatic Ediacaran fossil \textit{Parvancorina} -- a small, bilaterally symmetrical fossil with a shield-like base and a dorsal anchor-shaped ridge, principally known from shallow-marine sediments in Australia and Russia (Naimark \& Ivantsov, 2009; Gehling \& Droser, 2013). CFD analysis of \textit{Parvancorina} illustrated consistent redirection of fluid to specific regions of the organism (again refuting a solely osmotrophic feeding model), but in contrast to \textit{Tribrachidium}, that these flow patterns were highly dependent on fossil orientation with respect to current direction (Figure \ref{fig:EP}). In addition, drag forces extracted from CFD experiments of \textit{Parvancorina} resting on the seafloor demonstrated that \textit{Parvancorina} was likely able to re-orient itself with respect to current direction to reduce drag (Darroch \textit{et al.}, 2017), despite the lack of associated trace fossils or limbs. Interestingly, Patterson \textit{et al.} (2017) independently described evidence for mobility in \textit{Parvancorina} on the basis of rheotactic behavior evident in preserved fossil surfaces from South Australia. %Note that \textit{Parvancorina} has yet to be found associated with any form of trace fossil, and as such, showcases the power of this approach applied to relatively enigmatic organisms. 

\begin{figure}[h!]
	\includegraphics[width=16cm]{Erni-Parv.jpg}
	\centering
	\caption{Digital models and Computational Fluid Dynamics experiment results of \textit{Ernietta} (top) and \textit{Parvancorina} (bottom). a) Fossil \textit{Ernietta}. b) Digital model. c) CFD results. a-c) from Gibson \textit{et al.}, 2019). d) Fossil \textit{Parvancorina}. e) Digital model. f) CFD results. d-f) from Darroch \textit{et al.} 2017. c,f) All flow is from left to right, where velocity scales from blue (slow) to red (fast).}
	\label{fig:EP}
\end{figure}

Most recently, these techniques have been used to shed light on the functioning of entire populations, specifically of the late Ediacaran taxon \textit{Ernietta} (Gibson \textit{et al.}, 2019). Like many Ediacaran fossils, \textit{Ernietta} possesses no unambiguous metazoan synapomorphies (being a broadly bag-shaped organism constructed from repeated tube-shaped modules, lacking a mouth, gut, or any discernible feeding structures), and so occupies an uncertain position on the eukaryotic tree of life (Elliott \textit{et al.}, 2016; Ivantsov \textit{et al.}, 2016; Crimes \& Fedonkin, 1996; Dzik, 1999; Seilacher, 1992). Furthermore, field investigations reveal that individual \textit{Ernietta} are typically found in aggregated patches, and when found in life position are shown to have lived at least partially buried in the sediment, with open cavities facing upwards into the water column (Ivantsov \textit{et al.}, 2016). These observations prompted two questions: 1) how was \textit{Ernietta} feeding? and 2) why were these organisms living gregariously? Addressing the first question, Gibson \textit{et al.} (2019) used CFD simulation to demonstrate the consistent generation of fluid recirculation within organism cavities (Figure \ref{fig:EP}) that is suggestive of suspension feeding, and reminiscent of flow patterns seen within (for example) brachiopods (Shiino \textit{et al.}, 2009; Shiino \& Kuwazuru, 2010). On the basis of these results, the authors hypothesized that low velocity recirculation within the cavities would have allowed food particles as well as transported sediment to fall out of suspension and settle within the cavities (further providing an explanation for the laminated sediment found inside \textit{Ernietta} cavities by Ivantsov \textit{et al.}, 2016). CFD also offers a means for addressing the second question; when multiple models were placed together in simulations, enhanced recirculation was observed in downstream individuals (Figure \ref{fig:EP}). Furthermore, visualizing simulations in terms of turbulent kinetic energy $k$ instead of velocity magnitudes revealed a thickening of the turbulent mixing layer above the aggregated ``populations" of \textit{Ernietta}. These results illustrate that living gregariously would likely have provided a mechanism for enhancing nutrient delivery (and availability) to the broader population while also reducing waste water being funneled into downstream neighbors. These hydrodynamic patterns have been well described in modern benthic invertebrates that live in aggregated patches, where they are understood to form an important facilitatory behavior. For example, early flume studies and models conducted by Butman \textit{et al.} (1994) demonstrated that mussel hummocks act to redistributed food supply by manipulating boundary layer flow. They note that with increasing free stream velocity, momentum fluxes increase towards hummocks living along a bed, which actively redistributes food supply towards the individuals within the hummock. 

In summary, Ediacaran fluid mechanics analyses provided first order tissue density values for Ediacaran tissues. More recent studies have affirmed feeding ecologies only previously speculated, and demonstrated Ediacaran mobility for taxa that otherwise lacked physical traces. They have even demonstrated complex behavioral interactions not yet documented within the Ediacaran, but that are known to have persisted into the Modern marine biosphere. Each of these examples demonstrates the value of this approach, and emphasize that careful model and hypothesis construction can be crucial in shedding new light on ancient fossils. Next, we provide an example experiment where we document two approaches for simulating fluid flow over an Ediacaran organism. 

\subsection{Example analysis: \textit{Ernietta} feeding}
\subsubsection{Introduction} Fluid dynamics experiments have provided rich insights into the character of fluid-organism interactions in the paleontological record; however, the applications of these techniques in paleobiology continue to grow, and necessitates in-depth examples that include specifics of experimental design and interpretation. Whereas Rahman (2017) presents a pragmatic approach to conducting CFD experiments (and reviews a breadth of paleontological CFD studies), in this section we present a more theory-based approach to CFD focused on the underlying physics. Moreover, we provide a specific demonstration of an alternative, more robust application of CFD than has so far been used in paleontology. The specifics of any CFD simulation will vary with the question at hand, and we stress that there is no standard ``pipeline" that can be used for all instances. Instead we emphasize a few steps that occur in a relatively consistent order but often require multiple iterations as an analysis progresses. Figure \ref{fig:pipeline} shows a general outline for our specific case study presented here. %As a general guide, there are key points that must be satisfied for all CFD studies:

Gibson \textit{et al.} (2019) previously tested whether \textit{Ernietta} may have fed via the hypothesized feeding modes of osmotrophy or suspension feeding as using the logic structure outlined in Section 4.5.1.2. Further examination of their results demonstrates an unexpected high velocity jet near the no-slip seafloor boundary condition (Figure \ref{fig:vprofiles}), which should be described by the law of the log when time-averaged, but Gibson \textit{et al.}'s results show a developed jet near the no-slip seafloor boundary condition. Here, we perform a set of experiments detailing this phenomenon while simultaneously providing a more sophisticated and accurate experimental design for future paleontology CFD studies.

\begin{figure}[h]
	\includegraphics[width=0.75\textwidth]{FlowChart.jpg}
	\centering
	\caption{Flow chart of CFD experimental setup for \textit{Ernietta} case study.}
	\label{fig:pipeline}
\end{figure}

Broadly following Gibson \textit{et al.} (2019) as an example, we conduct a series of CFD experiments to test between two plausible feeding ecologies for \textit{Ernietta}, osmotrophy and suspension feeding. If fluid flow is evenly dispersed over exposed tissue surfaces, then this would suggest that \textit{Ernietta} was primarily osmotrophic. Alternatively, if fluid flow is redirected to specific anatomical regions, we interpret these regions as the primary locations of nutrient acquisition, and suggest \textit{Ernietta} was more likely suspension feeder. Because surface area to volume (SA/V) ratios do not rely on CFD, we will \textit{a priori} assume that \textit{Ernietta} exhibits lower SA/V ratios than those required for osmotrophy (see Gibson \textit{et al.}, 2019) and instead focus on CFD as a means for hypothesis testing.


\begin{figure}[h!]
	\includegraphics[width=0.75\textwidth]{velocity-profiles.jpg}
	\centering
	\caption{Streamwise $u$ velocity profiles near the upstream face of the fluid domain. Left shows original Gibson \textit{et al.} (2019) study with anomalous jet near the no-slip condition. Right shows current study with characteristic law of the log profile.}
	\label{fig:vprofiles}
\end{figure}

\subsubsection{Methods} On the basis of field evidence, \textit{Ernietta} was a semi-infaunal, sack-like organism that lived in shallow marine environments (Ivantsov \textit{et al.}, 2016; Elliott \textit{et al.}, 2017). To represent this lifestyle, we set the sediment-water interface at the midline of the digital model (Gibson \textit{et al}., 2019\textit{b}). Coupling grain-size fluid flow experiments (Paphitis, 2001) with sedimentological descriptions of Ediacaran deposits in which \textit{Ernietta} fossils are found (Ivantsov \textit{et al.}, 2016; Maloney \textit{et al.}, in review), we reconstruct paleoenvironmental flow velocity ranges of 0.01 m/s -- 0.5 m/s, noting they fall within the velocity range of modern shallow marine environments (Valle-Levinson \& Matsuno, 2003). For reasons related to the geometrical similitude of systems discussed above (Section 4.1 :: Basic Elements), we choose to use a 3-D hexahedron that is scaled larger than our fossil model as the flow domain. Our domain is sufficiently long that the flow field is capable of fully developing the boundary layer. We use an arbitrary but sufficient starting point for hexahedron dimensions (to adjust after the prototype CFD run) of $\sim10x$ the width, $\sim20x$ the depth, and $\sim6x$ the height of the digital model. The flow domain size is then increased if flow does not match theory, or it is decreased to reduce computational resources while still ensuring it correctly reflects theory. After these sensitivity tests, our final setup is $\sim5x$ the width, $\sim40x$ the depth, and $\sim3x$ the exposed model height; this allows the use of multiple turbulence closures (see below), and is required for geometric similitude (Figure \ref{fig:setup}). 

Making use of Eq (\ref{eq:Re}), we calculate a systems $\mathit{Re_S}=4988.46$ based off our depth of 0.25 m and using maximum fluid velocity of 0.05 m/s, which falls within the range of velocities reconstructed from the field. This $\mathit{Re_S}$ represents our maximum systems Reynolds number $\mathit{Re_S}$, and can be used to inform us that we are likely in a laminar or turbulent flow regime. Given such a low systems Reynolds number (i.e. $\mathit{Re}<\sim 20,000$), our system could feasibly be modeled with a simplified turbulence model, but for the illustrative purposes mentioned above, we instead use SST RANS (as used in Gibson \textit{et al.}, 2019) and LES turbulence closures to demonstrate an example methodology compatible with a greater number of experimental questions and to compare the fidelity of data between them. For fully turbulent flow, we advocate using a turbulence model from the LES family, which allows us to observe turbulent structures that would typically be smoothed over in RANS studies. While LES has thus far not been applied to paleontological questions, it promises great fidelity in pushing the field forward. LES allows us to  so construct temporal averages that would then reduce in essence to RANS results. Finally, to demonstrate information that is present or absent in each of these turbulence models, we also conduct particle imaging velocimetry (PIV) analyses for comparison between physical experiments and CFD. 

For our CFD analyses we prescribe the boundary conditions outlined in Figure \ref{fig:setup}. Due to \textit{Ernietta}'s semi-infaunal lifestyle, the base of the hexahedron must accurately approximate the solid boundary of the seafloor and is therefore prescribed a no-slip condition. We also apply a no-slip condition to the ``exhumed" portion of the \textit{Ernietta} model, and apply a slip condition to the top surface of our hexahedron whereby velocity will not approach 0 m/s due to decreased fluid momentum. In Gibson \textit{et al.} (2019) the authors applied slip conditions to the two opposing walls of the hexahedron that ran parallel with flow. They then prescribed inlet and outlet conditions to the remaining two walls. In their study the inlet face has a uniform velocity profile initiating from the seafloor to the top slip condition. In the ocean, the seafloor does not experience uniform velocity profiles, but instead follows the Law of the Log in a time-averaged sense. Due to conservation of mass (Eq. \ref{eq:continuity}) and the placement of these slip conditions, the velocity profiles from Gibson \textit{et al.} (2019; Figure \ref{fig:vprofiles}) actually do not approximate the law of the log, but instead develop an acceleration near the fluid-seafloor intersection (i.e. a `jet'; Figure \ref{fig:vprofiles}). To resolve this issue in our example here, we may take either of two approaches: 1) we may prescribe that our inlet velocity is ``fully developed" flow or at least non-uniform in profile (i.e. we \textit{a priori} prescribe the correct time-averaged velocity profile at inlet), or 2) we may use periodic boundary conditions where fluid that is sourced from the outlet is immediately delivered back to the inlet, which in essence creates a recirculating flow but requires a specified pressure to drive flow. Using either of these approaches circumvents inconsistencies regarding conservation of mass/volume (Eq. \ref{eq:continuity}) leading to the flow anomalies observed in Gibson \textit{et al.} (2019; Figure \ref{fig:vprofiles}). To fully demonstrate this, we use the first approach for our SST RANS experiment, and use the second approach for our LES experiment as it is the standard in LES literature. 

For our SST RANS experiment, we will use the same general setup that Gibson \textit{et al.} used, with opposing inlet/outlet faces, a no-slip seafloor, and slip walls on the remaining faces. Our inlet is provided a fully developed flow (e.g. not ``uniform velocity"), and our outlet suppresses backflow pressure. We then vary this setup for our LES setup. For the hexahedron walls that correspond to Gibson \textit{et al.}'s slip walls and inlet/outlet walls, we will use opposing periodic boundary conditions. The walls parallel to our desired flow direction (e.g. the long axis) have a periodic condition with no additional pressure differential $\Delta p$ which permits turbulent flow to laterally approach the model as we might expect in a realistic seafloor environment. We prescribe a pressure difference $\Delta p$ between the periodic conditions for upstream and downstream to drive the flow at a desired velocity, namely,
\begin{equation}
\mathrm \Delta p = u_*^2\rho\frac{B}{A}\, ,
\label{eq:p}
\end{equation}
where $\rho$ is the density of the fluid, $B$ is the surface area of the floor in the flow domain, $A$ is the cross-sectional area of the outflow face, and $u_*$ is the shear velocity. In turn we estimate the shear velocity from the specified desired velocity for which we still need to calculate based off our desired depth-averaged flow velocity. From a pragmatic view, this pressure differential is often first estimated and subsequently determined through trial and error. RANS experiments, such as SST models, can also make use of Eq (\ref{eq:p}) and may additionally incorporate a surface roughness at no-slip conditions which will change boundary layer development (see also Appendix \ref{ap:ustar}, which expands on this). We use a pressure differential of 0.05 Pa that corresponds to an average velocity of $\sim 0.05$ m/s. Important to note is that for this approach to satisfy the law of the log in a time-averaged sense, the flow domain length parallel to flow must be sufficiently long that free-stream velocity perturbations caused by the pressure of the model dissipate before they reach the upstream face of the model again. Depending on which turbulence model is being used (e.g. LES), we must also provide a pressure point constraint on a no-slip condition to inform the software of a known absolute pressure. Importantly, this should not be a point along periodic boundaries, so we instead choose an arbitrary point along the no-slip ``seafloor" that is far from both our organism and any slip/periodic boundary conditions. This minimizes programmatic or ``ill-posed problem" issues. For a summary of the boundary conditions that we have prescribed, see Figure \ref{fig:setup}.

\begin{figure}[h!]
	\includegraphics[width=0.75\textwidth]{ExampleSetup.jpg}
	\centering
	\caption{LES experiment setup pre-meshing. Periodic boundary A has a pressure differential of 0.05 Pa that yields a depth-averaged velocity of 0.05 m/s.}
	\label{fig:setup}
\end{figure}

We mesh the flow domain to provide a discretized field for which the fluid equations will be solved. In practice, we iteratively solve and re-mesh at higher grid resolution (i.e., increasing number of mesh elements) to assess the dependence of our solutions on the grid resolution. Smaller grid cells, or finer resolution, yield more resolved flow fields, but come at the cost of increased computational time and resources. For our experiment, we use COMSOL's unstructured meshing routines using free-tetrahedral elements and structured boundary layer elements, the latter of which are necessary to accurately compute the velocity gradient from the no-slip boundary conditions to fully turbulent flow in an approximate the law of the log profile from a time-averaged sense. To verify this, we plot time-averaged velocity profiles of streamwise velocity magnitude at several free-stream locations within our flow domain (for example see Figure \ref{fig:vprofiles}). We further compare the time-averaged drag coefficients on the upstream face of our \textit{Ernietta} model to see when these values converge (i.e. not a significant difference in computed values as mesh resolution changes), which informs us of our solutions dependence on grid resolution.

We run the same experiment using both LES Residual-Based Variational Multiscale (RBVM) and SST RANS turbulence models. To ensure these two experiments' results are directly comparable, we calculate the Reynolds number of a cut plane on the same slice upstream from the digital model in both experiments (Figure \ref{fig:Eresults}). LES experiments are time-dependent simulations run for 60 seconds `real world' time with data recorded at 0.01 second intervals. Time averages were always calculated using the final 40 second data to ensure proper formation of the boundary layer had occurred. SST experiments are allowed to reach a stationary relaxation state.

Lastly, we also conduct particle imaging velocimetry (PIV) to observe fine scale flow features that may be too small to be captured by our grid resolution. We 3D printed our model using a Lulzbot TAZ6 with 3 mm ABS filament. The model was then attached to flume floor using double-sided tape. We used irregularly shaped microplastic particles ($\sim$8 $\mu$m) as tracers in the flow. A 1.5 Watt, 1.4 nm laser was directed incident from above to allow the camera to pickup the plastic particles. We used a Redlake MotionPro PCI capturing at 200 fps and shutter speed of 1/800 seconds with combined Nikon Nikkor 85 mm 1:1.4 244914 lens and additional Canon 72 mm close up 500 D running at 2.8 f-stop. The camera was positioned $\sim$90$\degree$ from flow at organism level. To capture the images, we used RedLake MIDAS Software. We collected PIV data at the position of the model as well as downstream to acquire the reattachment of flow and mixing. We then calculated pressure and velocity fields using OpenPIV (Taylor \textit{et al}., 2010).

\subsubsection{Results/Discussion} 
In all experiments (PIV and CFD), the viscous sublayer (e.g. see Figure \ref{fig:Re}) developed and transitioned to fully turbulent flow above the no-slip seafloor (Figure \ref{fig:Eresults}). Time-averaged velocity profiles confirm that the jet near the no-slip from Gibson \textit{et al.}'s data (2019) did not develop in either SST or LES experiments, and the velocity profiles of our time averaged results match the law of the log (Figure \ref{fig:vprofiles}). All three experiments exhibit a decrease in average velocity along the upstream face of the model, and develop recirculation within the cavity of the \textit{Ernietta} model. Pressure magnitude maps show the upstream face of the model creates a region of backflow pressure that accelerates flow over and around the model organism, which is to be expected from analytical solutions such as flow around a sphere. 

\begin{figure}[h!]
	\includegraphics[width=\textwidth]{Ernietta-Results-linked.jpg}
	\centering
	\caption{a) Particle imaging velocimetry (PIV) of 3D printed \textit{Ernietta}. Flow is from right to left, and arrows are averaged over $\sim30$ s and scaled to velocity magnitude. b) Shear Surface Transport Reynolds Averaged Navier-Stokes (SST RANS) stationary solution with flow from right to left. c) Temporally averaged Large Eddy Simulation (LES) over last 40 s of experiment with flow from right to left.}
	\label{fig:Eresults}
\end{figure}

In the PIV and CFD experiments, small eddies are shed from the top upstream face of the \textit{Ernietta} model in the form of K\'{a}rm\'{a}n vortex streets. In the SST RANS experiment, this is observed as a zig-zagged trail of almost 0 m/s flow; however, the time-averaged LES experiment resolved this eddy trail with more detail exhibiting the classic pattern of swirling vortices. We also note that in all physical and digital experiments, there are consistent recirculation features where fluid flow downstream of the model is redirected towards the backwards face of the model. Not so easily captured in the time averaged PIV and CFD results, there is an ephemeral recirculation vortex on the upstream face of the model near the no-slip seafloor (\textcolor{red}{EMS Movies 1--2}). Consistently observable in all results is the flow separation initiating at the upstream face of the model with reattachment several model-lengths downstream. Lastly, all three experiments demonstrated varying patterns of recirculation within the cavity of the \textit{Ernietta} model. This recirculation region in the PIV as well as both CFD results develops repeated turbulent mixing, but stagnation zones are also apparent in the SST with some stagnation less apparent in the LES results. This is likely a result of the turbulence closure and its reliance on turbulent kinetic energy $k$. The LES and PIV time-dependent solutions (\textcolor{red}{ESM Movies 1--2}) both demonstrate that these zones of low velocity magnitude fluid are not permanent features within the flow. Instead the time-averaged low magnitude velocity reflects areas that on average receive slower velocity flow than at other flow locations. Interestingly, PIV and LES results were broadly comparable in quality of information. Perhaps the biggest advantage to PIV data over LES is the ability to observe even higher resolution details in flow features such as with the K\'{a}rm\'{a}n vortex streets, but the necessity of such detail will obviously be question specific. In our case, both provided benefits over stationary SST by resolving smaller eddy scales, showing time-dependent and time-averaged behaviors, and not over-estimating the effects of low velocity regions. 

These results represent the first LES CFD analysis performed on reconstructed fossils, and they confirm the fidelity of CFD in comparison to PIV experiments. While both LES and SST RANS turbulence closures show the consistent recirculation within the cavity of \textit{Ernietta} as also noted by Gibson \textit{et al.} (2019), more detail is observed in the time averaged results of the LES experiment than SST. Furthermore, the development of flow patterns through time (ESM Movie 1) demonstrate that regions of stagnant flow in the SST model are ephemeral. Taken together, these results emphasize the importance and prevalence of recirculation within the cavity, but also provide additional information informing us that stagnation zones are over-represented in the SST stationary solution. These ephemeral, low-magnitude recirculating velocities within the cavity are likely what is responsible for depositing the laminated sediments described in fossil material (Ivantsov \textit{et al.}, 2016). Furthermore, fine-scale features such as the K\'{a}rm\'{a}n vortex streets were more resolved in LES using the same resolution as the SST experiment. While not as important for the specific question of \textit{Ernietta} feeding, these results do emphasize the importance of resolving higher resolution patterns when focusing on smaller anatomical regions for other questions or smaller spatial scales. Our SST RANS simulations are unlikely to resolve such patterns without increased mesh resolution.

Using the same logic structure as outlined in other studies that anatomical regions receiving consistent redirection of fluid are likely locations of feeding (Rahman \textit{et al.}, 2015), our results support the interpretation that \textit{Ernietta} central cavities were likely the location of nutrient acquisition which in turn suggests \textit{Ernietta} was more likely to primarily be a suspension feeder than an osmotroph (though we note that some organisms supplement suspension feeding with osmotrophy, for example in. corals -- de Goeij \& van Duyl, 2007; and mussels -- Baines \textit{et al.}, 2005). This interpretation of suspension feeding is further supported by the SA/V ratios calculated in Gibson \textit{et al.} (2019), which are orders of magnitude lower than extant organisms using osmotrophy as their primary feeding mode. %While we come to similar conclusions to Gibson \textit{et al.}'s interpretations, the possibility existed that we would not have concluded the same interpretations if \textit{Ernietta} size been on the same scale as the turbulent boundary layer.  In such a case, the boundary and viscous sublayer flow patterns from the Gibson \textit{et al.} jet would likely result in patterns and could permit us to develop alternative conclusions about \textit{Ernietta}'s feeding ecology.

\subsection{Future Directions}
\subsubsection{Techniques}
Though CFD is increasingly being used in paleontological studies (Shiino \textit{et al.}, 2009; 2012; Shiino \& Kuwazuru, 2010; Rahman \textit{et al.}, 2015\textit{b}; Rigby \& Taylor, 2006; Dynowski \textit{et al.} 2016), there are concurrent opportunities for more sophisticated and detailed experiments. With advancement in computational resources, paleontologists may now take advantage of more complex and accurate turbulence models, such as the LES example presented above. LES and DNS experiments permit the description of turbulent structures at finer resolutions than previously possible, and provide the ability to make time-averaged comparisons to the currently widely used RANS stationary experiments. Using LES/DNS and time-dependent analyses, we may address time-dependent and turbulence-dependent behaviors for which we previously were unable to address. Better still, averaging LES solutions allows us to observe both the instantaneous flow structures (LES solution), as well as persistent emergent flow phenomena (averaged LES), associated with fluid flow around organisms.

Another advantage of recent increases in computing power is the ability to more easily conduct fully-coupled multiphysics analyses. Structural mechanics is a powerful tool that can be used in conjunction with CFD to assess how fluid flow may deform the bodies of organisms (ex. Sponaugle \& LaBarbera, 1991). Using fluid-structure interaction (FSI) CFD studies, we can assess the role of tissue rigidity on flow patterns (Gibson \textit{et al.}, 2019) or gain insight into the spatial competition among organisms such as rangeomophs and arboreomorphs (Figure \ref{fig:FSI}). FSI experiments are not meant to accurately constrain the exact tissue rigidity of ancient Ediacaran organisms, but they permit limits on labilities and possible behaviors. Coupled with moving meshes, FSI CFD studies may allow us to begin to test tiering and spatial competition models such as for Ediacaran fronds (e.g., compare Clapham \textit{et al.}, 2003, and Kenchington \textit{et al}., 2018). Importantly, such coupled experiments require careful treatment of turbulence model choice and boundary conditions, else there is the very real possibility of solving nonsensical problems, such as incorrectly using averaged turbulence quantities to assess time-specific turbulence induced phenomenon.

Ediacaran and paleontological CFD studies have used streamlines and arrows to infer movement of nutrient particles via fluid parcels, but we also have the capability to use individual particle tracing with CFD to simulate nutrient particle capture via one-way or fully coupled mass-balanced experiments. Such techniques could also be used to inform gamete dispersal experiments for individual Ediacaran organisms, or could be used to quantify sediment mixing and migration in the vicinity of organisms like \textit{Ernietta}. Similar to the FSI CFD experiments, these types of experiments are not meant to exactly replicate Ediacaran reproduction, but instead would be aimed at providing limitations on individual reproductive behavior.

Furthermore, we are nearing the point where we may combine several of these approaches such as particle tracing, FSI, and time dependent LES to assess methods for gamete release and dispersal from individual fronds, or mechanisms for waste export from any number of taxa. It is also worth noting that while advances in computing have opened these doors, such complex experiments are still limited to cluster computing, particularly when performed using complex 3D geometries. Furthermore, with increasing complexity we must explicitly understand and make transparent any assumptions that are inherently built into our experiments. We stress that all of these techniques do not accurately reflect real flow but are instead ideal techniques for testing specifically tailored hypotheses for well-defined questions.


\begin{figure}[h]
	\includegraphics[width=0.75\textwidth]{FSI.jpg}
	\centering
	\caption{Example fluid-structure interaction experiment of a 3D rangeomorph oriented with largest surface area perpendicular to flow. Numbers represent timesteps normalized to final timestep, and velocity increases from blue to red with inflow on the left face. Flow is from left to right.}
	\label{fig:FSI}
\end{figure}

Ultimately, with access to advanced workstations and cluster computing capabilities, more comprehensive community models are also now possible. While recent analyses have focused on individuals or small idealized populations of individuals, we are reaching a point where we will soon be computationally capable of running experiments on entire bedding surfaces of benthic organisms. These studies will be highly informative for understanding Ediacaran gamete dispersal, larval recruitment, spatial competition, and much more. However, with the inclusion of additional individuals, we must think carefully about research questions and hypotheses, and experimental designs (including meshing). We reiterate that the information CFD provides is dependent on the turbulence closure implemented. RANS provides a description of an idealized (i.e. non-real) fluid that is informative for emergent phenomenon like consistent locations of recirculation. LES more accurately approximates a fluid but must rely on approximations at small mesh scales. As such, no CFD result is providing an exact reconstruction of Ediacaran organisms in flow, but instead indirectly provides details that can then inform us about individual taxa or Ediacaran ecosystems.

Lastly, much like other methodologies used in digital paleontology (e.g. $\mu$CT), now is also the time to create proper data management and research method transparency practices. As with any data analysis, CFD code and files should be reposited where others can access and reproduce the experiments. Fortunately, these datasets are typically smaller than other digital datasets allowing us to more easily share data. While file sizes are smaller, there is not currently an accepted protocol for which data to make available for future paleontological CFD studies. We propose that any $\mu$CT scan or organism model, all simulation codes or files, and even vector field exports of pressure and velocity magnitudes (if using proprietary software) should be reposited. With increasing model complexity and the addition of multiphysics approaches, more data exports likely will need to be made available. While the application of this and related techniques is still fairly young within the field, we recommend erring on the side of repositing too much rather than too little data and description of methods.
\subsubsection{Research Questions}
Even more than the appearance of new techniques, fluid mechanics studies have the opportunity to target key questions surrounding the Ediacaran-Cambrian transition. For example, shallow marine microbial mats were ubiquitous  during the Ediacaran (Gehling \& Droser, 2009; Gehling \textit{et al.}, 2005), but their effects on vertical velocity profiles have not been formally described. Low tiering organisms on the scale of the viscous sublayer and turbulent transition layer would be particularly affected by flow differences due to textured organic surfaces, as these flow patterns dictate nutrient particle delivery. At the larger community scale, it is still currently unknown how Ediacaran tiering from White Sea and Nama intervals may have been affected by patterns of canopy flow (see e.g. Ghisalberti \textit{et al.}, 2014), and moreso how this interaction may have evolved with the changing structure of Ediacaran communities through time. Additionally, in this context of ecological escalation during the latest Ediacaran, the proliferation of benthic suspension feeding is thought to have been particularly crucial (Wood \& Curtis, 2014); suspension feeding has several important geobiological impacts, including influencing the structure of food webs, filtering and oxygenating the water column, creating unique habitats, and delivering waste organics to the substrate, thus providing a direct link between pelagic and benthic ecosystems (Hentschel \& Shimeta, 2008; Wood \& Curtis, 2014; Erwin \& Tweedt, 2012; Schiffbauer \textit{et al.}, 2016). CFD has the potential to examine how many Ediacaran taxa were suspension feeders, and how their unusual morphologies may represent sophisticated adaptations to interact with moving fluids in a way that aids particle capture.

On a broader scale, the application of fluid physics studies may even help to contribute to debates surrounding end-Ediacaran extinction, and the character of the Ediacaran-Cambrian transition. After $\sim$30 million years as the dominant components of benthic ecosystems, the Ediacara biota disappeared, broadly coincident with the beginning of the Cambrian. Recent analyses (Darroch \textit{et al.}, 2018\textit{b}; Muscente \textit{et al.}, 2019) reveal that this apparent extinction event occurred in two pulses -- one at the White Sea-Nama boundary $\sim$548 Ma, and a second at the Ediacaran-Cambrian boundary ($\sim$539 Ma) itself. An open question surrounding these two extinction pulses (especially given the uncertainties surrounding Ediacaran paleobiology and -ecology) is: to what extent were these extinction pulses selective? Patterns of selectivity in extinction can offer clues as to what the proximal extinction drivers were in any given event (see e.g., Knoll \textit{et al.}, 1996). As demonstrated above, studies using CFD have begun to establish feeding modes and the potential for mobility among a variety of Ediacaran taxa. By expanding these experiments to include additional taxa, we can ascertain if individual Ediacaran extinction pulses targeted specific ecological groups. As a specific example, the `biotic replacement' model hypothesizes that the appearance of metazoan ecosystem engineering drove the extinction of the Ediacara biota. However, paleobiologists have yet to identify a plausible extinction drivers and/or sources of ecological stress; thus far, three models have been proposed: 1) a change in the character of bioavailable carbon from labile dissolved organic carbon to coarser particulate matter (with the appearance of metazoan zooplankton); 2) the removal of microbial mats with the evolution of grazing and burrowing strategies (favoring groups less reliant on matgrounds for nutrients or as a firm substrate for attachment); and 3) the evolution of predation (Laflamme \textit{et al.}, 2013; Darroch \textit{et al.}, 2018\textit{b}). These three models carry with them specific predictions regarding the ecology of victims and survivors over late Ediacaran extinction pulses -- the first predicts the extinction of osmotrophs at the expense of suspension feeding strategies; the second predicts the extinction of sessile taxa,  as well as motile taxa such as \textit{Dickinsonia} which feed on mats via a ventral sole, and (potentially) low-tier suspension feeders such as \textit{Tribrachidium}; while the third predicts the survival of motile over sessile taxa. Alternatively, the `catastrophe' model hypothesizes an abiotic (rather than biotic) driver of extinction; among the many possible abiotic sources of ecological stress, anoxia has been supported by recent geochemical studies in the Ediacaran (Wood \textit{et al.}, 2018; Zhang \textit{et al.}, 2018), and is also implicit in several Phanerozoic extinction events (Hull \& Darroch, 2013). A `catastrophe' and anoxia-driven model would instead predict random extinction among all groups, or (plausibly) the survival of motile over sessile taxa (see e.g., Zhang \textit{et al.}, 2018). By more widely applying CFD to successive ‘assemblages' of Ediacaran fossils and reconstructing their paleobiology, many of these hypotheses may become testable, thus shedding valuable new light on a critical interval in Earth history.

%In summary, describing behaviors apparent within the Ediacara biota is key to informing our understanding of the Ediacaran-Cambrian transition, which is a crucial interval representing the origins of the modern animal-dominated biosphere. CFD and related fluid mechanics analyses can offer insight into such behaviors even though direct physical evidence may no long be present. Such studies will be particularly informative for addressing uncertainties about the proliferation of complex feeding ecologies just before the Cambrian as well as the end Ediacaran extinctions.

\section{Conclusions}\label{Section heading 4}
\begin{itemize}
	\item Studies in experimental biology have shown that organisms in aquatic environments have evolved a spectacular array of adaptations to aid life in moving fluids (Denny, 1988; Vogel, 1996). As well as shedding light on the processes of evolution and adaptation in extant organisms, this observation offers a valuable window into reconstructing the paleobiology and -ecology of ancient and enigmatic fossils, allowing us to pose the question: how might the unusual morphologies seen in extinct organisms have aided feeding, movement, or reproduction in the fluid environment? 
	\item As a result, the number of paleobiological studies employing fluid physics, and specifically CFD, is rapidly increasing. This is particularly true for the Ediacara biota, where studies using CFD are demonstrating that Neoproterozoic ecosystems were surprisingly dynamic and ecologically complex, with a larger diversity of feeding modes and inter-/intraspecific ecological interactions than previously suspected. 
	\item Moreover, CFD offers an innovative new means for addressing broader questions in Ediacaran paleobiology, including those surrounding the evolution of new community structures, the appearance of new behaviors, and (potentially) the drivers of Ediacaran-Cambrian biotic turnover.
	\item In this paper we describe the underlying theory on which studies in CFD are based, and at the same time dispel common misunderstandings frequently observed in the literature. We provide a sophisticated and robust worked example for performing CFD analysis of fossil organisms, involving (for the first time) large eddy simulations, as well as a combined CFD/PIV approach to examining flow patterns. 
	\item Lastly, we attempt to establish a starting set of guidelines for data reproducibility and transparency in CFD and related studies. This field will inevitably continue to evolve and expand, as it does so, it is important that we continue to evaluate best practices for data storage and methods reporting (as is happening in many other paleobiological fields, see, for example Parham et al., 2012). We emphasize, however, that experiments in fluid physics represent an exciting frontier in paleontology and evolutionary biology, and one which promises to shed new light on key intervals in the history of life.
\end{itemize}
	\section{Acknowledgments} \label{Section heading 4}
BMG was supported by two Alberstadt-Reesman-Stearns Research grants. We thank Craig Turner and Madeline Kelley for 3D printing flume models, Sarah Williams for assistance in flume studies, and Chris Tasich for programming discussions. DJF acknowledges NSF EAR-1735992. SAFD acknowledges National Geographic Grant No. 9968-16, and a Paleontological Society Arthur Boucot Award, both of which supported Ediacaran fieldwork in Namibia. %\textcolor{red}{MWS acknowledges support from XXX (flume tank costs?).} 
\clearpage
	\begin{thebibliography}{100}\label{Section heading 4}
\bibitem{Amthor2003} Amthor, J.E., Grotzinger, J.P., Schr\"{o}der, S., Bowring, S.A., Ramezani, J., Martin, M.W., \& Matter, A. (2003). Extinction of \textit{Cloudina} and \textit{Namacalathus} at the Precambrian-Cambrian boundary in Oman. \emph{Geology} \textbf{31}, 431-434.
\bibitem{Anderson1997} Anderson, E.J., MacGillivray, P.S., \& DeMont, M.E. (1997). Scallop shells exhibit optimization of riblet dimensions for drag reduction. \emph{Biological Bulletin} \textbf{192}, 341-344.
\bibitem{Arkema2009} Arkema, K.K. (2009). Flow-mediated feeding in the field: consequences for the performance and abundance of a sessile marine invertebrate. \emph{Marine Ecology Progress Series} \textbf{388}, 207-220.
\bibitem{Baines2005} Baines, S.B., Fisher, N.S., \& Cole, J.J. (2005). Uptake of dissolved organic matter (DOM) and its importance to metabolic requirements of the zebra mussel, \textit{Dreissena polymorpha}. \emph{Limnology and oceanography} \textbf{50}, 36-47.
\bibitem{Bardina1997} Bardina, J.E., Huang, P.G., \& Coakley, T.J. (1997). Turbulence modeling validation, testing, and development. \emph{NASA TM-110446}.
\bibitem{Baumiller1997} Baumiller, T.K. (1997). Crinoid functional morphology. \emph{The Paleontological Society Papers: Geobiology of Echinoderms} \textbf{3}, 45-68.
\bibitem{Bidder1923} Bidder, G.P. (1923). The relationship of the form of a sponge to its currents. \emph{Quarterly Journal of Microscopical Society} \textbf{67}, 292-323.
\bibitem{Blake2004} Blake, R.W. (2004). Fish functional design and swimming performance. \emph{Journal of Fish Biology} \textbf{65}, 119.
\bibitem{Bobrovskiy2018} Bobrovskiy, I., Hope, J.M., Ivantsov, A., Nettersheim, B.J., Hallmann, C., \& Brocks, J.J. (2018). Ancient steroids establish the Ediacaran fossil Dickinsonia as one of the earliest animals. \emph{Science} \textbf{361}, 1246 – 1249.
\bibitem{Boussinesq1877} Boussinesq, J. (1877). Essai sur la théorie des eaux courantes. \emph{Mem. Press. Acad. Scie.}, \textbf{XXIII} 46.
\bibitem{Boussinesq1896} Boussinesq, J. (1896). Theorie de l' \'{e}coulement tourbillonant et tumulteur des liquids dans les lits rectiligues. \emph{Comptes Rendus de l'Acad. Des Sciences}, \textbf{CXXII}, 1294.
\bibitem{Bowerbank1864} Bowerbank, J.S. (1864). \emph{A Monograph of the British Spongiadae} \textbf{1} London: The Ray Society.
\bibitem{Budd2000} Budd, G.E., \& Jensen, S. (2000). A critical reappraisal of the fossil record of the bilaterian phyla. \emph{Biological Reviews} \textbf{75}, 253-295.
\bibitem{Budd2017} Budd, G. E. \& Jensen, S. (2017). The origin of the animals and a `Savannah' hypothesis for early bilaterian evolution. \emph{Biological Reviews} \textbf{92}(1), 446 – 473.
\bibitem{Byrne1981} Byrne, M., \& Fontaine, A.R. (1981). The feeding behavior or \textit{Florometra serratissima} (Echinodermata: Crinoidea). \emph{Canadian Journal of Zoology} \textbf{59}, 11-18.
\bibitem{Chance1986} [16]	Chance, M.M., \& Craig, D.A. (1986) Hydrodynamics and behaviour of Simuliddae larvae (Diptera). \emph{Canadian Journal of Zoology} \textbf{64}, 1295-1309.
\bibitem{Cheer1993} Cheer, A.Y., \& van Dam, C.P. (1993). \emph{Fluid Dynamics in Biology}. Providence, RI. American Mathematical Society. p. 586.
\bibitem{Chia1984} Chia, F.S., Buckland-Nicks, J., \& Young, C.M. (1984). Locomotion of marine invertebrate larvae: a review. \emph{Canadian Journal of Zoology} \textbf{62}, 1205-1222.
\bibitem{Choi1989} Choi, K.S. (1989). Near-wall structure of a turbulent boundary layer with riblets. \emph{Journal of Fluid Mechanics} \textbf{208}, 417-458.
\bibitem{Choi2013} Choi, K.S. (2013). Smart flow control with riblets. \emph{Trans Tech Publications: Advanced Materials Research} \textbf{745}, 27-40.
\bibitem{Constaninescu2013} Constantinescu, G., Miyawaki, S., \& Liao, Q. (2013). Flow and turbulence structure past a cluster of freshwater mussels. \emph{Journal of Hydraulic Engineering ASCE.} \textbf{139}(4), 347-358.
\bibitem{Cook1999} Cook, A.W. (1999). A consistent approach to large eddy simulation using adaptive mesh refinement. \emph{Journal of Computational Physics} \textbf{154}, 117-133.
\bibitem{Crimes1996} Crimes, T.P., \& Fedonkin, M.A. (1996). Biotic changes in platform communities across the Precambrian – Phanerozoic boundary. \emph{Rivista Italiana di Paleontologia e Stratigrafia} \textbf{102}(3), 317-332.
\bibitem{Dadswell1990} Dadswell, M.J., \& Weihs, D. (1990). Size-related hydrodynamics characteristics of the giant scallop \textit{Placopecten magellanicus} (Bivalvia: Pectinidae). \emph{Canadian Journal of Zoology} \textbf{68}, 778-785.
\bibitem{Darroch2018a} Darroch, S.A.F., Laflamme, M., \& Wagner, P.J. (2018\textit{a}). High ecological complexity in benthic Ediacaran communities. \emph{Nature Ecology \& Evolution} \textbf{2}, 1541 – 1547.
\bibitem{Darroch2018b} Darroch, S.A.F., Smith, E., Laflamme, M., \& Erwin, D.H. (2018\textit{b}). Ediacaran extinction and Cambrian explosion. \emph{Trends in Ecology \& Evolution} \textbf{33}, 653-663.
\bibitem{Darroch2017} Darroch, S.A.F., Rahman, I.A., Gibson, B., Racicot, R.A., \& Laflamme, M. (2017). Inference of facultative mobility in th enigmatic Ediacaran organism \textit{Parvancorina}. \emph{Biology Letters} \textbf{13}, 20170033.
\bibitem{Darroch2015} Darroch, S.A.F., Sperling, E.A., Boag, T., Racicot, R.A., Mason, S.J., Morgan, A.S., Tweedt, S., Myrow, P., Erwin, D.H., \& Laflamme, M. (2015). Biotic replacement and mass extinction of the Ediacara biota. \emph{Proceedings of the Royal Society B} \textbf{282}, 20151003.
\bibitem{} de Goeij, J.M., \& van Duyl, F.C. (2007). Coral cavities are sinks of dissolved organic carbon (DOC). \emph{Limnology and Oceanography} \textbf{52}, 2608–2617.
\bibitem{Dececchi2017} Dececchi, T.A., Narbonne, G.M., Greentree, C., \& Laflamme, M. (2017). Relating Ediacaran fronds. \emph{Paleobiology} \textbf{43}, 171 – 180.
\bibitem{Denny1988} Denny, M. (1988). Biology and the mechanics of the wave-swept environment. Princeton University Press, p.917.
\bibitem{Drescher2011} Drescher, K., Dunkel, J., Cisneros, L.H., Ganguly, S., \& Goldstein, R.E. (2011). Fluid dynamics and noise in bacterial cell-cell and cell-surface scattering. \emph{Proceedings National Academy of Sciences of the United States} \textbf{108}, 10940-10945.
\bibitem{Droser2005} Droser, M.L., Gehling, J.G., \& Jensen, S. (2005). Ediacaran trace fossils: true or false. In D.E.G. Briggs (ed.) \emph{Evolving Form and Function: Fossil Development}. Peabody Museum of Natural History, New Haven.
\bibitem{Droser2017} Droser, M.L., Tarhan, L.G., \& Gehling, J.G. (2017). The rise of animals in a changing environment: global and ecological innovation in the Late Ediacaran. \emph{Annual Review of Earth and Planetary Sciences} \textbf{45}, 593-617.
\bibitem{Droser2019} Droser, M.L., Gehling, J.G., Tarhan, L.G., Evans, S.D., Hall, C.M.S., Hughes, I.V., Hughes, E.B., Dzaugis, M.E., Dzaugis, M.P., Dzaugis, P.W., \& Rice, D. (2019). Piecing together the puzzle of the Ediacara Biota: excavation and reconstruction at the Ediacara National Heritage site Nilpena (South Australia). \emph{Palaeogeography, Palaeoclimatology, Palaeoecology}, \textbf{513}, 132-145.
\bibitem{Dufour2017} Dufour, S.C., \& McIlroy, D. (2017). Ediacaran pre-placazoan diploblasts in the Avalonian biota: the role of chemosynthesis in the evolution of early animal life. \emph{Earth System Evolution and Early Life: A Celebration of the Work of Martin Brasier}. Brasier, A.T., McIlroy, D., and McLoughlin, N. (eds.). Geological Society, London, Special Publications \textbf{448}, 211-219.
\bibitem{Dunn2017} Dunn, F.S., Liu, A.G., \& Donoghue, P.C.J. (2017). Ediacaran developmental biology. \emph{Biological Reviews} \textbf{93}(2), 914 – 932.
\bibitem{Dynowski2016} Dynowski, J.F., Nebelsick, J.H., Klein, A., \& Roth-Nebelsick, A. (2016). Computational fluid dynamics analysis of the fossil cronoid \textit{Encrinus liliiformis} (Echinodermata: Crinoidea). \emph{PLOS One} \textbf{11}, e0156408.
\bibitem{Dzik1999} Dzik, J. (1999). Organic membranous skeleton of the Precambrian metazoans from Namibia. \emph{Geology} \textbf{27}, 519-522.
\bibitem{Elliott2106} Elliott, D.A., Trusler, P.W., Narbonne, G.M., Vickers-Rich, P., Morton, N., Hall, M., Hoffmann, K.H., \& Schneider, G.I.C. (2016). Ernietta from the late Ediacaran Nama Group, Namibia. \emph{Journal of Paleontology} \textbf{90}, 540-554.
\bibitem{Erwin2011} Erwin, D.H, Laflamme, M., Tweedt, S.M., Sperling, E.A., Pisani, D., \& Peterson, K.J. (2011). The Cambrian conundrum: Early divergence and later ecological success in the early history of animals. \emph{Science} \textbf{334}(6059),1091–1097. 
\bibitem{Erwin2012} Erwin, D.H., \& Tweedt, S. (2012). Ecological drivers of the Ediacaran-Cambrian diversification of Metazoa. \emph{Evolutionary Ecology} \textbf{26}, 417-433.
\bibitem{Evans2015} Evans, S.D., Droser, M.L., \& Gehling, J.G. (2015). \textit{Dickinsonia} liftoff: evidence of current derived morphologies. \emph{Palaeogeography, Palaeoclimatology, Palaeoecology} \textbf{434}, 28-33.
\bibitem{Evans2019} Evans, S.D., Huang, W., Gehling, J.G., Kisailus, D., \& Droser, M.L. (2019). Stretched, mangled, and torn: responses of Edaicaran fossil \textit{Dickinsonia} to variable forces. \emph{Geology} \textbf{47}, 1049-1053.
\bibitem{Evans2018} Evans, S.D., Diamond, C.W., Droser, M.L., \& Lyons, T.W. (2018). Dynamic oxygen and coupled biological and ecological innovation during the second wave of the Ediacara biota. \emph{Emerging Topics in Life Sciences} \textbf{2}, 223-233.
\bibitem{Fedonkin1997} Fedonkin, M.A., \& Waggoner, B.M. (1997). The Late Precambrian fossil \textit{Kimberella} is a mollusk-like bilaterian organism. \emph{Nature} \textbf{388}, 868-871.
\bibitem{Fedonkin2007} Fedonkin, M.A., Simonetta, A., \& Ivantsov, A.Y. (2007). New data on Kimberella, the Vendian mollusc-like organism (White Sea region; Russia): palaeoecological and evolutionary implications. \emph{Geological Society, London, Special Publications} \textbf{286}, 157-179.
\bibitem{Ferziger1998} Ferziger, J.H. (1998). Direct and large eddy simulation of turbulence. In \emph{Numerical Methods in Fluid Mechanics}. A. Vincent (ed).), Centre de Recherches Mathématiques Université de Montréal, \emph{Proceedings and Lecture Notes} \textbf{16}, 53-97.
\bibitem{Full2010} Full, R.J. (2010). Invertebrate locomotor systems. \emph{Comprehensive Physiology}, 853-930.
\bibitem{Furbish1997} Furbish, D.J. (1997) Fluid Physics in Geology: An Introduction to Fluid Motions on Earth's Surface and Within Its Crust. Oxford University Press, p. 476. 
\bibitem{Furbish1997b} Furbish, D.J., \& Arnold, A.J. (1997). Hydrodynamic strategies in the morphological evolution of spinose planktonic foraminifera. \emph{GSA Bulletin} \textbf{109}, 1055-1072.
\bibitem{Furbish1992} Furbish, D.J. \& Parker, W.C. (1992). On the lengths of crossing excursions: the case of a discrete normal process with underlying exponential autocovariance. \emph{Stochastic Hydrology and Hydraulics} \textbf{6}, 167-182.
\bibitem{Gazzola2014} Gazzola, M., Argentina, M., \& Mahadevan, L. (2014). Scaling macroscopic aquatic locomotion. \emph{Nature} \textbf{10}, 758-761.
\bibitem{Gehling2009} Gehling, J.G., \& Droser, M.L. (2009). Textured organic surfaces associated with the Ediacara biota in South Australia. \emph{Earth Science Reviews} \textbf{93}, 196-206.
\bibitem{Gehling2005} Geling, J.G., Droser, M.L., \& Runnegar, B.N. (2005). Ediacaran organisms: relating form to function. In D.E.G. Briggs (ed.) \emph{Evolving form and function. Fossils and development, Proceedings of a Symposium Honoring Adolf Seilacher for his contributions to palaeontology in celebration o fhis 80th Birthday} (pp. 43-66). new Haven, CT: Peabody Museum of Natural History. 
\bibitem{Gehling2014} Gehling, J.G., Runnegar, B.N., \& Droser, M.L. (2014). Scratch traces of large Ediacaran bilaterian animals. \emph{Journal of Paleontology} \textbf{88}, 284-298.
\bibitem{Ghisalberti2014} Ghisalberti, M., Gold, D.A., Laflamme, M., Clapham, M.E., Narbonne, G.M., Summons, R.E., Johnston, D.T., Jacobs, D.T. (2014). Canopy flow analysis reveals the advantage of size in the oldest communities of multicellular eukaryotes. \emph{Current Biology} \textbf{24}, 305-309 
\bibitem{Gibbs1902} Gibbs, J.W. (1902). Elementary principles in statistical mechanics: developed with especial reference to the rational foundation of thermodynamics. C. Scribner's sons.
\bibitem{Gibson2019a} Gibson, B.M., Rahman, I.A., Maloney, K.M., Racicot, R.A., Mocke, H., Laflamme, M., \& Darroch, S.A.F. (2019). Gregarious suspension feeding in a modular Ediacaran organism. \emph{Science Advances}\textbf{5}, eaaw0260.
\bibitem{Gibson2019b} Gibson, B.M., Rahman, I.A., Maloney, K.M., Racicot, R.A., Mocke, H., Laflamme, M., \& Darroch, S.A.F. (2019\textit{b}). Gregarious suspension feeding in a modular Ediacaran organism. \emph{Dryad Dataset}, doi: 10.5061/dryad.v9s0hk5.
\bibitem{Gibson2018} Gibson, B.M., Schiffbauer, J.G., \& Darroch, S.A.F. (2018). Ediacaran-style decay experiments using mollusks and sea anemones. \emph{PALAOIS} \textbf{33}, 185-203.
\bibitem{Gold2015} Gold, D.A., Runnegar, B., Gehling, J.G., \& Jacobs, D.K. (2015). Ancestral state reconstruction of ontogeny supports bilaterian affinity for \textit{Dickinsonia}. \emph{Evolution \& Development} \textbf{17}, 315-324.
\bibitem{Goldstein2015} Goldstein, R.E. (2015). Green algae as model organisms for biological fluid dynamics. \emph{Annual Review of Fluid Mechanics} \textbf{47}, 343-375.
\bibitem{Grant1825}Grant, R.E. (1825). Observations of the structure and function of the sponge. \emph{Edinburgh Philosophical Journal} \textbf{13}, 192-199.
\bibitem{Grazhdankin2014} Grazhdankin, D.V. (2014). Patterns of evolution of the Ediacaran soft-bodied biota. \emph{Journal of Paleontology} \textbf{88}(2), 269 – 283.
\bibitem{Grotzinger1995} Grotzinger, J.P., Bowring, S.A., Saylor, B.Z., \& Kaufman, A.J. (1995). Biostratigraphic and geochronologic constraints on early animal evolution. \emph{Science} \textbf{270}, 598-604.
\bibitem{Hentschel2008} Hentschel, B.T., \& Shimeta, J. (2008). \emph{Suspension Feeders}, 3437-3442.
\bibitem{Hoyal-Cuthill2018} Hoyal Cuthill, J.F., \& Han,J. (2018). Cambrian petalonamid \textit{Stromatoveris} phylogenetically links Ediacaran biota to later animals. \emph{Palaeontology} \textbf{61}, 813-823.
\bibitem{Ivantsov2011} Ivantsov, A.Y. (2011). Feeding traces of Proarticulata -- the Vendian Metazoa. \emph{Paleontological Journal} \textbf{45}, 237-248.
\bibitem{Ivantsov2002} Ivantsov, A.Y., \& Malakhovskaya, Y.E. (2002). Giant feeding traces of Vendian animals. \emph{Doklady Earth Science} English Transactions \textbf{385A}, 618-622.
\bibitem{Ivantsov2016} Ivantsov, A.Y., Narbonne, G.M., Trusler, P.W., Greentree, C., \& Vickers-Rich, P. (2016). Elucidating Ernietta: New insights from exceptionally preserved specimens in the Ediacaran of Namibia. \emph{Lethaia} \textbf{49}, 540-554.
\bibitem{Jenkins1978} Jenkins, R.J.F., \& Gehling, J.G. (1978). A review of frond-like fossils of the Ediacara assemblage. \emph{Records of the South Australia Museum} \textbf{17}, 347-359.
\bibitem{Jensen2003} Jensen, S. (2003). The Proterozoic and earliest Cambrian trace fossil re-cord; patterns, problems and perspectives. \emph{Integrative and Comparative Biology} \textbf{43}, 219–228.
\bibitem{Jensen2006} Jensen, S., Droser, M.L., \& Gehling, J.G. (2006). A critical look at the Ediacaran trace fossil record. In S. Xiao \& A.J. Kaufman (eds.) \emph{Neoproterozoic Geobiology and Paleobiology}. Springer, Netherlands.
\bibitem{Jeong2014} Jeong, W. \& Seong, J. (2014). Comparison of effects on technical variances of computational fluid dynamics (CFD) software based on finite element and finite volume methods. \emph{International Journal of Mechanical Sciences} \textbf{78}, 19-26.
\bibitem{Koehl1977} Koehl, M.A.R. (1977). Effects of sea anemones on the flow forces they encounter. \emph{Journal of Experimental Biology} \textbf{69}, 87-105.
\bibitem{Laflamme2013} Laflamme, M., Darroch, S.A.F., Tweedt, S.M., Peterson, K.J., \& Erwin, D.H. (2013). The end of the Ediacara biota: Extinction, biotic replacement, or Cheshire Cat? \emph{Gondwana Research} \textbf{23}, 558-573.
\bibitem{Lac1993} Lacoursi\'{e}re, J.O., \& Craig, D.A. (1993). Fluid transmission and filtration efficiency of the labral fans of black fly larvae (Diptera: Simullidae): hydrodynamic, morphological, and behavioural aspects. \emph{Canadian Journal of Zoology} \textbf{71}, 148-162.
\bibitem{Laflamme2009} Laflamme, M., Xiao, S., \& Kowalewski, M. (2009). Osmotrophy in modular Ediacara organisms. \emph{Proceedings Royal Society B} \textbf{106}, 13328-14443.
bibitem{Laflamme2013} Laflamme, M., Darroch, S.A.F., Tweedt, S.M., Peterson, K.J., \& Erwin, D.H. (2013). The end of the Ediacara biota: extinction, biotic replacement, or Cheshire Cat? \emph{Gondwana Research} \textbf{23}, 558-573.
\bibitem{Lin2006} Lin, J.P., Gon, S.M., Gehling, J.G., Babcock, L.E., Zhao, Y.L., Zhang, X.L., Hu, S.X., Yuan, J.L., Yu, M.Y., \& Peng, J. (2006). A \textit{Parvancorina}-like arthropod from the Cambrian of South China. \emph{Historical Biology} \textbf{18}(1), 33-45.
\bibitem{Linnemann2019} Linnemann, U., Ovtcharova, M., Schaltegger, U., G\"{a}rtner, Hautmann, M., Geyer, G., Vickers-Rich, P., Rich, T., Plessen, B., Hofmann, M., Zieger, J., Krause, R., Friesfeld, L., \& Smith, L. (2019). New high-resolution age data from the Ediacaran-Cambrian boundary indicate rapid, ecologically driven onset of the Cambrian explosion. \emph{Terra Nova} \textbf{31}, 49-58. 
\bibitem{Liu2011} Liu, A.G., McIlroy, D., Antcliffe, J.B., \& Brasier, M.D. (2011). Effaced preservation in the Ediacara biota and its implications for the early macrofossil record. \emph{Palaeontology} \textbf{54}, 607-360.
\bibitem{Liu2015} Liu, A.G., Kenchington, C.G., \& Mitchell, E.G. (2015). Remarkable insights into the paleoecology of the Avalonian Ediacaran macrobiota. \emph{Gondwana Research} \textbf{27}, 1355-1380.
\bibitem{Martin2000} Martin, M.W., Grazhadankin, D.V., Bowring, S.A., Evands, D.A.D., Fedonkin, M.A., \& Kirschvink, J.L. (2000). Age of Neoproterozoic bilaterian body and trace fossils, White Sea, Russia: implications for metazoan evolution. \emph{Science} \textbf{288}, 841-845.
\bibitem{McMenamin1986} McMenamin, M.A.S. (1986). The Garden of Ediacara. \emph{PALAIOS} \textbf{1}, 178-182.
\bibitem{McMenamin1990} McMenamin, M.A.S., \& McMenamin, D.L.S. (1990). The Emergence of Animals: The Cambrian Breakthrough. Columbia University Press, New York.
\bibitem{McMenamin1993} McMenamin, M.A.S. (1993). Osmotrophy in fossil protoctists and early animals. \emph{Invertebrate Reproduction and Development} \textbf{23}, 165-169.
\bibitem{Menter1993} Menter, F.R. (1993). Two-equation eddy-viscosity turbulence models for engineering applications. \emph{AIIA Paper} \textbf{93-2906}.
\bibitem{Menter1994} Menter, F.R., \& Rumsey, L.C. (1994). Assessment of two-equation turbulence models for transonic flows. \emph{AIIA Paper} \textbf{94}-2343.
\bibitem{Meyer1973} Meyer, D.L. (1973). Feeding behavior and ecology of shallow-water unstalked crinoids (Echinodermata) in the Caribbean Sea. \emph{Marine Biology} \textbf{22}, 105-129.
\bibitem{Mossi} Mossi, M. (1999). Simulation of benchmark and industrial unsteady compressible turbulent fluid flows. PhD Thesis, No 1958, École Polytechnique Fédérale de Lausanne, Départment de Génie Méchanique, Switzerland.
\bibitem{Muscente2018} Muscente, A.D., Bykova, N., Boag, T.H., Buatois, L.A., M\'{a}ngano, M.G., Eleish, A., Prabhu, A., Pan, F., Meyer, M.B., Schiffbauer, J.D., Fox, P., Hazen, R.M., \& Knoll, A.H. (2019). Ediacaran biozones identified with network analysis provide evidence for pulsed extinctions of early complex life. \emph{Nature Communications} \textbf{10}, 911.
\bibitem{Nakamura1994} Nakamura, R. (1994). Lift and drag on inclined sand dollars. \emph{Journal of Experimental Marine Biology and Ecology} \textbf{178}, 275--285.
\bibitem{Narbonne1997} Narbonne, G.M., Saylor, B.Z., \& Grotzinger, J.P. (1997). The youngest Ediacaran fossils from southern Africa. \emph{Journal of Paleontology} \textbf{71}, 953-967.
\bibitem{Narbonne2014} Narbonne, G.M., Laflamme, M., Trusler, P.W., Dalrymple, R.W., \& Greentree, C. (2014). Deep-water Ediacaran fossils from northwestern Canada: taphonomy, ecology, and evolution. \emph{Journal of Paleontology} \textbf{88}, 207-223.
\bibitem{Norris1989} Norris, R.D. (1989). Cnidarian taphonomy and affinities of the Ediacara biota. \emph{Lethaia} \textbf{22}, 381-393.
\bibitem{Parham2012} Parham, J.F., Donoghue, P.C.J., Bell, C.J., Calway, T.D., Head, J.J., Holroyd, P.A., Inoue, J.G., Irmis, R.B., Joyce, W.G., Ksepka, D.T., Patan\'{e}, J.L., Smith, N.D., Tarver, J.E., van Tuinen, M., Yang, Z., Angielczyk, K.D., Greenwood, J.M., Hipsley, C.A., Jacobs, J., Makovicky, P.J., M\"{u}ller, J., Smith, K.T., Theodor, J.M., Warnock, R.C.M., \& Benton, M.J. (2012). Best practices for justifying fossil calibrations. \emph{Systematic Biology} \textbf{61}, 346-359.
\bibitem{Paphitis2001} Paphitis, D. (2001). Sediment movement under unidirectional flows: an assessment of empirical threshold curves. \emph{Coastal Engineering} \textbf{43}, 227-245.
\bibitem{Paterson2017} Paterson, J.R., Gehling J.G., Droser, M.L., \& Bicknell, R.D.C. (2017). Rheotaxis in the Ediacaran epibenthic organism Parvancorina from South Australia. \emph{Scientific Reports} \textbf{7}, 45539.
\bibitem{Piomelli1988a} Piomelli, U. (1998A). Large-eddy simulation: present state and future directions. \emph{AIAA Paper} \textbf{98}-0534.
\bibitem{Piomelli1988b} Piomelli, U. (1998B). Large-eddy simulation of turbulent flows. VKI Lecture Series 1998-05.
\bibitem{Pu2027} Pu,J.P., Bowring, S.A., Ramezani, J., Myrow, P., Raub, T.D., Landing, E., Mills, A., Hodgin, E., \& Macdonald, F.A. (2016). Dodging snowballs: geochronology of the Gaskiers glaciation and the first appearance of the Ediacaran biota. \emph{Geology} \textbf{44}, 955-958.
\bibitem{Rahman2017} Rahman, I.A. (2017). Computational fluid dynamics as a tool for testing functional and ecological hypotheses in fossil taxa. \emph{Palaeontology} \textbf{60}, 451-459.
\bibitem{Rahman2015a} Rahman, I.A., Darroch, S.A.F., Racicot, R.A., \& Laflamme, M. (2015\textit{a}). Suspension feeding in the enigmatic Ediacaran organism \textit{Tribrachidium} demonstrates complexity of Neoproterozoic ecosystems. \emph{Science Advances} \textbf{1}, e1500800.
\bibitem{Rahman2015b} Rahman,I.A., Zamora, S., Falkingham, P.L., \& Phillips, J.C. (2015\textit{b}). Cambrian cinctan echinoderms shed light on feeding in the ancestral deuterostome. \emph{Proceedings Royal Society B} \textbf{282}, 20151964.
\bibitem{Regnard1893} Regnard, P. (1893). Sur un dispositif qui permet de mesurer la vitesse de translation d'un poisson se mouvant dans l'eau.\emph{C.R. Soc. Biol. Paris Ser. 9} \textbf{5}, 81-83.
\bibitem{Rigby2006} Rigby, S., \& Tabor, G. (2006). The use of computational fluid dynamics in reconstructing the hydrodynamic properties of graptolites. \emph{GFF} \textbf{128}, 189-194.
\bibitem{Rothman2003} Rothman, D.h., Hayes, J.M., \& Summons, R.E. (2003). Dynamics of the Neoproterozoic carbon cycle. \emph{Proceedings National Academy of Sciences of the United States of America} \textbf{100}, 8124-8129.
\bibitem{Rubenstein1977} Rubenstein, D.I., \& Koehl, M.A.R. (1977). The mechanisms of filter feeding: some theoretical cosiderations. \emph{The American Naturalist} \textbf{111}, 981-994.
\bibitem{Santhanakrishan2012} Santhanakrishnan, A., Dollinger, M., Hamlet, C.L., Colin, S.P., \& Miller, L.A. (2012). Flow structure transported characteristics of feeding and exchange currents generated by upside-down \textit{Cassiopea} jellyfish. \emph{The Journal of Experimental Biology} \textbf{215}, 2369-2381.
\bibitem{Sappenfield2011} Sappenfield, A., Droser, M.L., \& Gehling, J.G. (2011). Problematica, trace fossils, and tubes within the Ediacara Member (South Australia): redefining the Edaicaran trace fossil record one tube at a time. \emph{Journal of Paleontology} \textbf{85}, 256-265.
\bibitem{Schiffbauer2016} Schiffbauer, J.D., Huntley, J.W., O'Neil, G.R., Darroch, S.A.F, Laflamme, M., \& Cai, Y. (2016). The latest Ediacaran wormworld fauna: setting the ecological stage for the Cambrian Explosion. \emph{GSA Today} \textbf{26}(11), 4 – 11.
\bibitem{Schopf1998} Schopf, K.M., \& Baumiller, T.K. (1998). A biomechanical approach to the Ediacaran hypotheses: how to weed the Garden of Ediacara. \emph{Lethaia} \textbf{31}, 89-97.
\bibitem{Schulz1999} Schulz, H.N., Brinkhoff, T., Ferdelman, T.G., Hern\'andez Marin\'e, M., Teske, A., \& J{\o}rgensen, B.B. (1999) Dense populations of a giant sulfur bacterium in Namibian shelf sediments. \emph{Science} \textbf{284}, 493-495.
\bibitem{Seilacher1989} Seilacher, A. (1989). Vendozoa: organismic construction in the Proterozoic biosphere. \emph{Lethaia} \textbf{22}, 229-239.
\bibitem{Seilacher1992} Seilacher, A. (1992). Vendobionta and Psammocorallia: Lost constructions of Precambrian evolution. \emph{Journal of the Geological Society} \textbf{149}, 607-613.
\bibitem{Shiino2009} Shiino, Y., Kowazuru, O., \& Yoshikawa, N. (2009). Computational fluid dynamics on a Devonian spiriferid \textit{Paraspirifer bownockeri} (Brachiopoda): generating mechanism of passive feeding flows. \emph{Journal of Theoretical Biology} \textbf{259}, 132-141.
\bibitem{Shiino2010} Shiino, Y., \& Kuwazuru, O. (2010). Functional adaptation of spiriferide brachiopod morphology. \emph{Journal of Evolutionary Biology} \textbf{23}, 1547-1557.
\bibitem{Shiino2012} Shiino, Y., Kuwazuru, Suzuki, Y., \& Ono, S. (2012). Swimming capability of the remopleuridid trilobite \textit{Hypodicranotus striatus}: hydrodynamic functions of the exoskeleton and the long, forked hypostome. \emph{Journal of Theoretical Biology} \textbf{300}, 29-38.
\bibitem{Singer2012} Singer, A., Plotnick, R., \& Laflamme, M. (2012). Experimental fluid mechanics of an Ediacaran frond. \emph{Paleontologia Electronica} \textbf{15}, 19A.
\bibitem{Smagorinsky1963} Smagorinsky, J. (1963). General circulation experiments with the primitive equations. \emph{Monthly Weather Review} \textbf{91}, 99-165.
\bibitem{Smith2016} Smith, E.F., Nelson, L.L., Strange, M., Eyster, A.E., Rowland, S., Schrag, D.P., \& Macdonald, F.A. (2016). The end of the Ediacaran: two new exceptionally preserved body fossil assemblages from Mount Dunfee, Nevada, USA. \emph{Geology} \textbf{44}, 911-914.
\bibitem{Smith2017} Smith, E.F., Nelson, L.L., Tweedt, S.M., Zeng, H., \& Workman, J.B. (2017). A cosmopolitan late Ediacaran biotic assemblage: new fossils from Nevada and Namibia support a global biostratigraphic link. \emph{Proceedings Royal Society B} \textbf{284}, 20170934.
\bibitem{Sperling2007} Sperling, E.A., Pisani, D., \& Peterson, K.J. (2007). Poriferan paraphyly and its implications for Precambrian paleobiology. In P. Vickers-Rich and P. Komarower (eds.) \emph{The Rise and Fall of the Ediacara biota} Special Publications Geological Society, London, \textbf{286}, 355-368.
\bibitem{Sperling2010} Sperling, E.A., \& Vinther, J. (2010). A placazoan affinity for \textit{Dickinsonia} and the evolution of Proterozoic metazoan feeding modes. \emph{} \textbf{}, .
\bibitem{Sponaugle1991} Sponaugle, S., \& LaBarbera, M. (1991). Drag-induced deformation: a functional feeding strategy in two species of gorgonians. \emph{Journal of Experimental Marine Biology and Ecology} \textbf{148}, 121-134.
\bibitem{Tarhan2018} Tarhan, L.G., Droser, M.L., Cole, D.B., \& Gehling, J.G. (2018). Ecological expansion and extinction in the Late Ediacaran: weighing the evidence for environmental and biotic drivers. \emph{Integrative and Comparative Biology} \textbf{58}, 688-702.
\bibitem{Taylor2010} Taylor, Z.J., Gurka, R., Kopp, G.A., \& Liberzon, A. (2010). Long-duration time-resolved PIV to study unsteady aerodynamics. \emph{IEEE Transactions on Instrumentation and Measurements} \textbf{59}, 3262-3269.
\bibitem{Telford1983} Telford, M. (1983). An experimental analysis of lunule function in the sand dollar \textit{Mellita quinquesperforata}. \emph{Marine Biology} \textbf{76}, 125--134.
\bibitem{Telford1987} Telford, M., \& Mooi, R. (1987). The art of standing still. \emph{New Scientist} \textbf{April 16}, 30--35.
\bibitem{Valle-Levinson2003} Valle-Levinson, A., \& Matsuno, T. (2003). Tidal and subtitdal flow along a cross-shelf transect on the East China Sea. \emph{Journal of Oceanography} \textbf{59}, 573-584.
\bibitem{Verhagen2019} Verhagen, G., Hendrik, H., Korsch, K., Kerth, G., Brede, M., \& Haase, M. (2019). Testing the adaptive vealue of gastropod shell morphology to flow: a multidisciplinary approach based on morphometrics, computational fluid dynamics, and a flow tank experiment. \emph{Zoological Letters} \textbf{5}, 5.
\bibitem{Vo2018} Vo, M., Mehrabian, S., Villalpando, F., Etienne, S., Pelletier, D., \& Cameron, C.B. (2018). The fluid dynamics of \textit{Balanus glandula} barnacles: adaptations to sheltered and exposed habitats. \emph{Journal of Biomechanics} \textbf{71}, 225-235.
\bibitem{Vogel1993} Vogel, St. (1996). Life in moving fluids: the physical biology of flow. Princeton University Press, p. 484.
\bibitem{Wade1968} Wade, M. (1968). Preservation of soft-bodied animals in Precambrian sandstones at Ediacara, South Australia. \emph{Lethaia} \textbf{1}, 238-267.
\bibitem{Wardle1977} Wardle, C.S. (1977). Effects of size on the swimming speeds of fish. In \emph{Scale Effects in Animal Locomotion} (ed. T. Pedley), p. 299-313. London Academic Press. 
\bibitem{Wilcox1988} Wilcox, D.C. (1988). Reassessment of the scale-determing equation for advanced turbulence models. \emph{AIAA Journal} \textbf{26}, 1299-1310.
\bibitem{Wilcox1993} Wilcox, D.C. (1993). Turbulence modeling for CFD. DCW Industries, Inc. La Cañada, California, USA.
\bibitem{Wood2015} Wood, R.A., \& Curtis, A. (2015). Extensive metazoan reefs from the Ediacaran Nama Group, Namibia: the rise of benthic suspension feeding. \emph{Geobiology} \textbf{13}, 112-122.
\bibitem{Wu1998} Wu, Y., Cao, S., Yang, J., Ge, L., Guilbaud, M., \& Soula, V. (1998). Turbulent flow calculation through a water turbine draft tube by using the Smagorinsky model. \emph{ASME Fluids Engineering Division Summer Meeting (FEDSM), Washington D.C.}, \textbf{Paper No. FEDSM98-4564}.
\bibitem{Xiao2009} Xiao, S., \& Laflamme, M. (2009). On the eve of animal radiation: phylogeny, ecology and evolution of the Ediacara biota. \emph{Trends in Ecology \& Evolution} \textbf{24}(1), 31 – 40.
\bibitem{Zhang2018} Zhang, F., Xiao, S., Kendall, B., Romaniello, S.J., Cui, H., Meyer, M., Gilleaudeau, G.J., Kaufman, A.J., \& Anbar, A.D. (2018). Extensive marine anoxia during the terminal Ediacaran Period. \emph{Science Advances} \textbf{4}, eaan8983.
\end{thebibliography}
\clearpage
\section{Appendix}\label{Section heading 4}
\subsection{Derivation of Eq. (\ref{eq:p})}
To calculate the pressure difference for a laminar flow, we start by choosing our desired Reynolds number. Then we calculated our associated velocity using \ref{eq:Re}, which in this case would be our depth-averaged velocity $U$ for a parabolic velocity profile as 
\begin{equation}
U=\frac{h^2}{3\mu}\frac{\Delta p}{L}\, ,
\end{equation} 
where $h$ is the height from the seafloor to the maximum height of the hexahedron flow domain, $\mu$ is the dynamic viscosity, $L$ is the characteristic length of (depth) of the flow domain parallel to flow, and $\Delta p$ is the change in pressure. Rearranging we get,
\begin{equation}
\Delta p = UL\frac{3\mu}{h^2},
\label{eq:lp}
\end{equation}
which provides the pressure differential for our periodic boundary conditions to drive laminar flow. Alternatively, not every problem can be treated with laminar flow, such that we must derive Eq.(\ref{eq:lp}) for a transitional or fully turbulent flow following law of the log. We begin with the time averaged velocity $\overline{u_t}$ defined as
\begin{equation}
\overline{u}_t(z)=\frac{u_*}{\kappa}\ln\frac{z}{z_0}\, ,
\label{eq:ut}
\end{equation}
where $u_*$ is the shear velocity, $\kappa$ is the von K\'{a}rm\'{a}n constant equal 0.41, $z$ is the height of surface, and $z_0$ is the roughness height of the seafloor. and solving for the depth-averaged velocity. To get the depth-averaged velocity, we solve
\begin{equation}
U=\frac{1}{h-z_0}\int_{z_0}^{h}\overline{u_t}\,\mathrm{d}z\, ,
\label{eq:U1}
\end{equation}
where we can substitute Eq. (\ref{eq:ut}) into (\ref{eq:U1}) as
\begin{equation}
U=\frac{1}{h-z_0}\int_{z_0}^{h}\overline{u_t}\,\mathrm{d}z\, ,=\frac{1}{h-z_0}\frac{u_*}{\kappa}\bigg{|}z\ln\frac{z}{z_0}-z\bigg{|}_{z_0}^{h}=\frac{1}{h-z_0}\frac{u_*}{\kappa}h\ln\frac{h}{z_0}-\frac{1}{h-z_0}h\frac{u_*}{\kappa}+\frac{z_0}{h-z_0}\frac{u_*}{\kappa}\, ,
\end{equation} 
which due to scaling can reduce to 
\begin{equation}
U\approx \frac{u_*}{\kappa}\ln\frac{h}{z_0}-\frac{u_*}{\kappa}.
\end{equation}
With some rearranging and solving for $u_{*}$ we see,
\begin{equation}
u_*=\frac{U\kappa}{\ln\frac{h}{z_0}-1}\,.
\end{equation}
Using the definition $u_*=\sqrt{\frac{\tau_0}{\rho}}$, we may substitute and rearrange as 
\begin{equation}
\tau_{0}=u_*^2\rho\, ,
\end{equation}
and plug this into Eq. (\ref{eq:lp}) as 
\begin{equation}
\Delta p = \frac{\tau_0 B}{A}\, ,
\end{equation}
where $A$ is the cross sectional area of the periodic boundary, and $B$ is area of the digital seafloor. Of note is that this will lead to the pressure difference for our flow domain if there is no fossil organism in the domain. The actual pressure difference will be lower when the fossil is incorporated because the organism will extract momentum from the flow through drag. Through substitution this leads to 
\begin{equation}
\Delta p = \bigg{(}\frac{U\kappa}{\ln(h/z_0)-1}\bigg{)}^2\rho \frac{B}{A}\, .
\end{equation}

\subsection{Surface roughness $\mathit{u_s}$}
\label{ap:ustar}
This can be calculated as
\begin{equation}
u_*\approx \frac{U\kappa}{\ln\frac{0.37h}{z_0}}\, ,
\end{equation}
where $h$ is the height of the flow domain, $z_0$ is an effective height that incorporates an experimentally determined surface roughness of the substrate $k_s$ and a coefficient $k_1$ which is 1/30th the diameter of the grain size for a sand grain, and $\kappa$ is the von K\'{a}rm\'{a}n constant typically $0.41$. Fortunately, in many CFD software suites (i.e. see fvOptions in OpenFOAM), this calculation is not necessary as there are under-the-hood algorithms that will assert this differential based off the depth-averaged velocity that we prescribe.


%---------------------------------------------------------------------------------------------------------------%
%------------------------------------------------SECTION------------------------------------------------%
%---------------------------------------------------------------------------------------------------------------%
\chapter{Summary}\label{Chapter5 title}
\vspace{-7mm}
%\section{Introduction}\label{Section heading 5}
While many uncertainties still surround the latest Neoproterozoic Ediacara biota and their role in the origins of the modern marine biosphere, the work presented in this dissertation joins a larger body of research demonstrating that we are increasingly addressing these unknowns. The research presented here focuses on constraining Ediacaran three-dimensional preservation and using fluid physics to reconstruct individual Ediacaran paleobiologies and -ecologies. These two disparate approaches combine to provide much needed insight into what these organisms were like in life and what information is likely lost due to taphonomic processes. 

In chapter 2, I specifically focus on replicating pyritic death mask preservational processes using a range of initial porewater iron concentrations to define the role iron plays in Ediacaran fossilization. My results demonstrate that iron and sulfide associations occur with minimal concentrations of bioavailable iron, but necessitate the availability of organic nucleation sites from either microbial mat or carcass material. These experiments represent the first iron sulfide veneers produced under laboratory conditions to replicate Ediacaran death mask preservation. They further demonstrate the fidelity of this preservational pathway by suggesting that this preservation need not occur under a narrow range of sediment and seawater chemistries, but instead can occur under a range of paleoenvironmental conditions. 

In chapter 3, I use computational fluid dynamics (CFD) experiments to reconstruct the feeding ecology of the key Ediacaran taxon \textit{Ernietta} that lived right up to the Precambrian-Cambrian transition. My CFD results demonstrate that \textit{Ernietta} likely acquired nutrients via suspension feeding, another example of conserved Ediacaran-Phanerozoic behaviors. Furthermore, when combining multiple individuals within my experiments, I demonstrate that the aggregated populations of these organisms was likely beneficial to feeding by enhancing recirculation in downstream individuals and increasing turbulent mixing above the group. This represents one of the oldest examples of facilitation yet described in the fossil record. 

Lastly, in chapter 4, I provide a detailed review of important fluid physics concepts while simultaneously addressing common misconceptions reported in the literature. I then review pivotal insights regarding Ediacaran paleoecology that have been informed by fluid physics experiments, and provide a detailed case study for conducting Ediacaran CFD analyses that relies on a more realistic and sophisticated approach than what is currently presented in the literature. Finally, I present future directions for Ediacaran CFD research, and provide guidelines for best practices. 

Each of these chapters represents targeted approach for tackling key Ediacaran questions. Importantly, each study presented within this dissertation also represents a starting point for future research. While chapter 2 has contributed to our understanding of the role of iron within Ediacaran preservation, the complimentary study experimentally assessing the role of sulfur compounds still needs to be performed. Chapters 3 and 4 provide a detailed guide for how to perform and interpret the results of Ediacaran CFD analyses, but the range of organisms that have been assessed is still limited. Furthermore, chapter 3 presents two new approaches, fluid-structure interaction analyses and multi-individual populations CFD analyses, that may now be used to address a number of Ediacaran taxa and preserved ecosystems. While chapter 3 assessed an idealized and geometrically structured population, future analyses will focus on replicating flow through preserved snapshots of Ediacaran communities. Of primary interest is using these techniques to understand how populations of these organisms affect nutrient partitioning through the interference of individuals' boundary layers such as for fronds at Mistaken Point. 

This dissertation has focused on using two novel methodologies to constrain Earth's earliest complex lifeforms and the ecosystems in which they lived. While these studies and the larger literature base they join make significant strides in characterizing life during this pivotal period, future studies will undoubtedly build on this work to further elucidate these organisms and how they helped shape the modern oceans.
\end{document} 


