Extinction dynamics of a discrete population in an oasis

TL;DR

This paper introduces an individual-based model to study extinction dynamics of populations in finite patches, accounting for demographic stochasticity, and compares it with classical reaction-diffusion models to understand persistence thresholds.

Contribution

It develops a discrete, stochastic analogue of the KiSS model to analyze extinction times and population persistence in finite habitats, extending classical deterministic results.

Findings

Extinction times increase with patch size above the critical threshold.

Demographic stochasticity significantly affects population persistence.

Quasi-stationary distributions provide insights into population stability.

Abstract

Understanding the conditions ensuring the persistence of a population is an issue of primary importance in population biology. The first theoretical approach to the problem dates back to the 50's with the KiSS (after Kierstead, Slobodkin and Skellam) model, namely a continuous reaction-diffusion equation for a population growing on a patch of finite size $L$ surrounded by a deadly environment with infinite mortality -- i.e. an oasis in a desert. The main outcome of the model is that only patches above a critical size allow for population persistence. Here, we introduce an individual-based analogue of the KiSS model to investigate the effects of discreteness and demographic stochasticity. In particular, we study the average time to extinction both above and below the critical patch size of the continuous model and investigate the quasi-stationary distribution of the number of individuals for patch sizes above the critical threshold.