The Critical Domain Size of Stochastic Population Models

TL;DR

This paper investigates the critical habitat size needed for populations to survive under stochastic influences, comparing traditional deterministic models with stochastic approaches like branching processes to gain better insights.

Contribution

It introduces novel stochastic modeling approaches, including scaled branching processes, to better understand population persistence in variable environments.

Findings

Branching process models closely approximate individual-based models.

Stochastic models provide insights into critical domain size under environmental variability.

Comparison of deterministic and stochastic models highlights the importance of stochasticity in population persistence.

Abstract

Identifying the critical domain size necessary for a population to persist is an important question in ecology. Both demographic and environmental stochasticity impact a population's ability to persist. Here we explore ways of including this variability. We study populations which have traditionally been modelled using a deterministic integrodifference equation (IDE) framework, with distinct dispersal and sedentary stages. Individual based models (IBMs) are the most intuitive stochastic analogues to IDEs but yield few analytic insights. We explore two alternate approaches; one is a scaling up to the population level using the Central Limit Theorem, and the other a variation on both Galton-Watson branching processes and branching processes in random environments. These branching process models closely approximate the IBM and yield insight into the factors determining the critical domain size for a given population subject to stochasticity.