Spatial Patterns in Stage-Structured Populations with Density Dependent Dispersal

Abstract

Spatial segregation among life cycle stages has been observed in many stage-structured species, including species of the flour beetle Tribolium. Patterns have been observed both in homogeneous and heterogeneous environments. We investigate density dependent dispersal of life cycle stages as a mechanism responsible for this separation. By means of mathematical analysis and numerical simulations, we explore this hypothesis using stage-structured, integrodifference equation (IDE) models that incorporate density dependent dispersal kernels.In Chapter 2 we develop a bifurcation theory approach to the existence and stability of (non-extinction) equilibria for a general class of structured integrodifference equation models on finite spatial domains with density dependent kernels. We show that a continuum of such equilibria bifurcates from the extinction equilibrium when it loses stability as the net reproductive number n increases through 1. We give several examples to illustrate the theory.In Chapter 3 we investigate mechanisms that can lead to spatial patterns in two dimensional Juvenile-Adult IDE models. The bifurcation theory shows that such patterns do not arise for n near 1. For larger values of n we show, via numerical simulation, that density dependent dispersal can lead to the segregation of life cycle stages in the sense that each stage peaks in a different spatial location.Finally, in Chapter 4, we construct spatial models to describe the population dynamics of T. castaneum, T. confusum and T. brevicornis and use them to assess density dependent dispersal mechanisms that are able to explain spatial patterns that have been observed in these species.