Extinction threshold of a population in spatial and stochastic model

TL;DR

This paper investigates how spatial scales influence the extinction threshold in a stochastic population model, comparing simulations and analytical approximations to understand their accuracy near critical points.

Contribution

It provides new insights into the dependence of extinction thresholds on spatial parameters and evaluates the validity of mathematical approximations in stochastic spatial models.

Findings

Critical parameter values depend on spatial scales of competition and dispersal.

Analytical approximations break down near the extinction threshold.

Higher-order terms improve the convergence of naive approximations.

Abstract

In this study, spatial stochastic and logistic model (SSLM) describing dynamics of a population of a certain species was analysed. The behaviour of the extinction threshold as a function of model parameters was studied. More specifically, we studied how the critical values for the model parameters that separate the cases of extinction and persistence depend on the spatial scales of the competition and dispersal kernels. We compared the simulations and analytical results to examine if and how the mathematical approximations break down at the vicinity of the extinction threshold, and found a functional form of the naive approximation for which higher-order term of analytical approximation converges.