A simple probabilistic, biologically informed model of the population dynamics of desert shrubs

Abstract

In arid environments, spatiotemporal variations in the processes of erosion and deposition are strongly coupled with the structure and dynamics of plant communities as well as the specific life behavior of individual plants. Understanding how physical transport processes affect the evolution of the land surface on geomorphic time-scales therefore requires considering how long-term changes in plant dynamics may in turn impact such processes. The development of this desert shrub population dynamics model is therefore motivated by the need to link rain-splash induced mound building at the shrub-scale with the unfolding ‘biological play’ occurring on a hillslope. Using the Master Equation to conserve shrub age, probabilistic and biologically informed statements for recruitment and mortality are formulated to function as source and sink terms respectively. This simple accounting framework, by tracking the number of individuals entering and leaving a population, captures the changes in shrub count that can be expected in time as the key variables driving the dynamics of these plant communities (i.e. precipitation) also change in time. The result is a tool through which it is possible to statistically describe the aggregate spatiotemporal behavior of different shrub populations, with their own characteristic life-cycles and physical dimensions, under different external forcing scenarios. This model features inputs that have a solid biophysical basis and insofar as it has the capacity to mimic key features of real processes, leads to outputs which appear consistent with findings reported in the literature.