A metapopulation model with population jumps of varying sizes

A model is developed for a single species composed of a metapopulation consisting of many patches. It incorporates the processes of local growth and stochastic disasters or sudden jumps of varying sizes within a patch, combined with the colonization of empty patches. It is shown that this model includes many other metapopulation models as special cases. This reduction to simpler cases allows for the demonstration of a variety of behaviors in the full model. In the case when there is no immigration into existing patches, an iterative method is developed for finding the unique equilibrium distribution of numbers of individuals within patches using techniques for analyzing linear Fredholm integral equations.