Fast Dispersal in Semelparous Populations

Abstract

We consider a model for the dynamics of a semelparous age-structured population where individuals move among different sites. The model consists of a system of difference equations with two time scales. Individual movements are considered to be fast in comparison to demographic processes. We propose a general model with m + 1 age classes and n different sites. Demography is described locally by a general density dependent Leslie matrix. Dispersal for each age-class is defined by a stochastic matrix depending on the total numbers of individuals in each class. The (m + 1) × n dimensional two time scales system is approximately reduced to an m + 1 dimensional semelparous Leslie model. In the case of 2 age-classes and 2 sites with constant dispersal rates we consider the bifurcation that occurs at the trivial equilibrium using the inherent net reproductive number as the bifurcation parameter. We find that different dispersal strategies can change at the global level the local demographic outcome. This modeling framework can be further used to correctly embed different fast processes in population-level models.