Finite size scaling of survival statistics in metapopulation models

TL;DR

This paper extends classical metapopulation models to include finite population sizes, analyzing how stochastic effects influence species survival and extinction probabilities near critical thresholds.

Contribution

It introduces analytical expressions for finite-size scaling of survival probability, highlighting the role of deterministic metapopulation capacity in stochastic dynamics.

Findings

Finite populations significantly affect survival probabilities.

Deterministic metapopulation capacity influences stochastic extinction times.

Analytical formulas for survival probability near critical points.

Abstract

Spatial metapopulation models are fundamental to theoretical ecology, enabling to study how landscape structure influences global species dynamics. Traditional models, including recent generalizations, often rely on the deterministic limit of stochastic processes, assuming large population sizes. However, stochasticity - arising from dispersal events and population fluctuations - profoundly shapes ecological dynamics. In this work, we extend the classical metapopulation framework to account for finite populations, examining the impact of stochasticity on species persistence and dynamics. Specifically, we analyze how the limited capacity of local habitats influences survival, deriving analytical expressions for the finite-size scaling of the survival probability near the critical transition between survival and extinction. Crucially, we demonstrate that the deterministic metapopulation capacity plays a fundamental role in the statistics of survival probability and extinction time moments. These results provide a robust foundation for integrating demographic stochasticity into classical metapopulation models and their extensions.