Persistence in fluctuating environments for interacting structured populations

TL;DR

This paper develops a general theoretical framework for understanding how structured, interacting species can persist in fluctuating environments, emphasizing the role of stochastic growth rates and environmental autocorrelations.

Contribution

It introduces a novel coexistence criterion based on long-term growth rates and Lyapunov exponents for multi-species matrix models in stochastic environments.

Findings

Positive autocorrelations can disrupt predator-prey coexistence.

Fluctuations in log-fecundity can promote persistence.

Sedentary populations are likely to coexist in heterogeneous environments.

Abstract

Individuals within any species exhibit differences in size, developmental state, or spatial location. These differences coupled with environmental fluctuations in demographic rates can have subtle effects on population persistence and species coexistence. To understand these effects, we provide a general theory for coexistence of structured, interacting species living in a stochastic environment. The theory is applicable to nonlinear, multi species matrix models with stochastically varying parameters. The theory relies on long-term growth rates of species corresponding to the dominant Lyapunov exponents of random matrix products. Our coexistence criterion requires that a convex combination of these long-term growth rates is positive with probability one whenever one or more species are at low density. When this condition holds, the community is stochastically persistent: the fraction of time that a species density goes below $\delta>0$ approaches zero as $\delta$ approaches zero. Applications to predator-prey interactions in an autocorrelated environment, a stochastic LPA model, and spatial lottery models are provided. These applications demonstrate that positive autocorrelations in temporal fluctuations can disrupt predator-prey coexistence, fluctuations in log-fecundity can facilitate persistence in structured populations, and long-lived, relatively sedentary competing populations are likely to coexist in spatially and temporally heterogenous environments.