The effect of dispersal area on the extinction threshold

TL;DR

This study examines how the size of dispersal area influences the extinction threshold in spatial population models, revealing universal scaling laws and implications for dispersal evolution.

Contribution

It introduces a detailed analysis of the relationship between dispersal area and extinction threshold using a lattice model, highlighting universal scaling behaviors.

Findings

Extinction threshold $(A)$ is largely independent of lattice geometry.

Universal scaling laws govern the relationship between dispersal area and extinction threshold.

Selection pressures vary with dispersal area, especially at low values.

Abstract

The survival of populations hinges on their ability to offset local extinctions through new colonizations. The dispersal area ($A$) plays a crucial role in this process, as it determines the probability of finding colonizable vacant sites. We investigated the spatial colonization-extinction dynamics in a lattice model (a contact process), exploring various finite dispersal areas and estimating the extinction threshold $\lambda_E(A)$. Our results revealed a consistent $\lambda_E(A)$ relationship, largely independent of lattice geometry (except for the smallest $A$). This $\lambda_E(A)$ relationship obeyed universal scaling laws within two broad ranges of $A$. The scaling relations suggest considerable selection upon the increase of dispersal area, particularly at low $A$ values. We discuss these findings in the broader context of the evolution of dispersal area.