Dynamics of Metapopulations with Demographic Stochasticity and Environmental Catastrophes

Abstract

In the first part of the paper, a method is developed for computing extinction properties of populations that are subject to demographic and environmental noise (catastrophes). The theory requires estimation of demographic birth and death rates, rates of catastrophes, and distribution of deaths when catastrophes occur. The colonization probability (chance of successful immigration), mean extinction time, and the long time conditional distribution of population size are predicted. The results can be put into algorithmic form so that workers can concentrate on developing parameters from empirical data. In the second part, the results are compared to the exact solution of a model (due to MacArthur and Wilson) without catastrophes and shown to be extremely accurate. The MacArthur-Wilson model is then extended to include environmental catastrophes. Finally, a metapopulation model with linear birth and death rates, immigration, catastrophes occurring at a rate independent of population size, and individuals dying independently is proposed.