How Levins' dynamics emerges from a Ricker metapopulation model on the brink of extinction

TL;DR

This paper derives a connection between Levins' metapopulation models and Ricker local dynamics, providing analytical expressions for colonisation and extinction rates near extinction, enhancing model parameterization.

Contribution

It introduces a stochastic Ricker-based metapopulation model and analytically links local demographic parameters to Levins' colonisation and extinction rates.

Findings

Metapopulation dynamics align with Levins' model at low dispersal rates.

Analytical formulas for colonisation and extinction rates derived.

Numerical tools provided for practical parameter estimation.

Abstract

Understanding the dynamics of metapopulations close to extinction is of vital importance for management. Levins-like models, in which local patches are treated as either occupied or empty, have been used extensively for this purpose, but they ignore the important role of local population dynamics. In this paper, we consider a stochastic metapopulation model where local populations follow a Ricker dynamics, and use this framework to investigate the behaviour of the metapopulation at the brink of extinction. As long as dispersal rates are not too large, the system is shown to have a time evolution consistent with Levins' dynamics. We derive analytical expressions for the colonisation and extinction rates (c and e) in Levins-type models in terms of reproduction, survival, and dispersal parameters of the local populations, providing an avenue to parameterising Levins-like models from the type of information on local demography that is available for a number of species. To facilitate applying our results, we provide a numerical implementation for computing c and e.