The combined effects of demographic and environmental stochasticity yield predictable transient and long-term extinction effects in grasslands

Lauren Shoemaker, Department of Botany, University of Wyoming, Laramie, WY, Lauren L. Sullivan, Division of Biological Sciences, University of Missouri, Columbia, MO, Katharine N. Suding, Institute of Arctic and Alpine Research, University of Colorado, Boulder, CO and Brett Melbourne, Department of Ecology & Evolutionary Biology, University of Colorado, Boulder, CO

Background/Question/Methods
Persistence of local populations, and their corresponding extinction dynamics, have played a central role in population ecology with profound implications for community dynamics and species richness. Classic theoretical models show that both demographic stochasticity and environmental perturbations can alter species’ extinction risk, but the functional form of this effect depends on population size. The coefficient of variation decreases exponentially with a species' population size due to demographic stochasticity, but is independent of population size when environmental perturbations affect a population. The relative importance of these stochastic processes, and their role in jointly contributing to observed extinction dynamics through time remains an open question. Here, we present a framework that describes how different forms of stochasticity (notably demographic and environmental stochasticity) combine to provide predictable structure of extinction dynamics in diverse communities through time. We couple our framework with a stochastic model of competitive community dynamics and an empirical test from the Nutrient Network, calculating extinction risk for grassland species from sites across the globe over 9 years, comparing plots with background demographic and environmental stochasticity (control plots) to those with imposed environmental perturbations (nutrient addition or herbivore removal).
Results/Conclusions
In control plots, short-term extinction risk decreases exponentially with initial local population size, as estimated by pre-treatment (year 0) percent cover; this result closely matches theoretical predictions. However, longer-term extinction risk depends less on population size, showing a more linear relationship with percent cover. This is likely the integration of both demographic and environmental processes acting on populations, closely matching model results. In particular, we find that grassland sites with higher environmental variability (CV of annual precipitation) experience similar short-term extinction dynamics to those with low environmental variability, but have heightened extinction risk in the long-term. Compared to control plots, the added perturbations of nutrient addition or herbivore removal yield an increased probability of longer-term extinction especially at moderate and large initial population sizes, but have minimal effects over the short-term. Similar to other studies, we find nutrient additions increases extinction dynamics, especially for legumes. These results highlight the importance of jointly incorporating both demographic and environmental sources of variability in analyses of population extinction risk as well as considering their combined effects over longer timescales.