Analytical Solution of Metapopulation Dynamics in Stochastic Environment

TL;DR

This paper provides an analytical solution to the distribution of populations in a stochastic metapopulation model, revealing a complex self-similar structure and log-normal distributions at individual habitats.

Contribution

It introduces an analytical approach to understanding metapopulation dynamics under stochastic environments, highlighting the distribution patterns across habitats.

Findings

Populations follow a log-normal distribution at each habitat.

The overall population distribution exhibits a self-similar structure.

Analytical expressions for stable distributions are derived.

Abstract

We study a stochastic linear discrete metapolulation model to understand the effect of risk spreading by dispersion. We calculate analytically the stable distribution of populations that live in different habitats. The result shows that the simultaneous distribution of the populations has a complicated self-similar structure, but a population at each habitat follows a log-normal distribution.