Speaker: Dr. Sebastian Schreiber
Professor
Department of Evolution and Ecology
One Shields Avenue
University of California
Davis, CA 95616

Title: Persistence of structured populations in random environments

Abstract: Environmental fluctuations often have different impacts on individuals that differ in size, age, or spatial location. To understand how population structure, environmental fluctuations, and density-dependent interactions influence population dynamics, I will discuss a general theory developed in collaboration with Michel Benaim for persistence for density-dependent matrix models in random environments. For populations with compensating density dependence, exhibiting "bounded" dynamics, and living in a stationary environment, persistence is proven to be determined by the stochastic growth rate (alternatively, dominant Lypaunov exponent) when the population is rare. If this stochastic growth rate is negative, then the total population abundance goes to zero with probability one. If this stochastic growth rate is positive, there is a unique positive stationary distribution. Provided there are initially some individuals in the population, the population dynamics converge in distribution to this stationary distribution and the empirical measures almost surely converge to the distribution of the stationary distribution. For models with overcompensating density-dependence or non-stationary environmental noise, weaker results can be proven. Methods to estimate stochastic growth rates will be discussed. To illustrate the utility of these results, I will discuss applications to unstructured, spatially structured, and stage-structured population models. For instance, analytical approximations for the stationary distributions of unstructured models show that 1) red noise results in a highly skewed, bimodal stationary distribution which inflates mean population abundance but also increases extinction risk and 2) blue noise results in a unimodal stationary distribution with lower extinction risk and less of an inflationary effect on mean abundance. Alternatively, diffusively coupled sink populations can persist provided that within patch fitness is sufficiently variable in time but not strongly correlated across space.