The effect of dispersal area on the extinction threshold

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.