10 - Extinction Models for Local Populations

Abstract

This chapter reviews stochastic models of extinction within a local population. The main thread of the chapter is an analytic model of environmental stochasticity, in which populations fluctuate between a ceiling and extinction. A diffusion analysis of environmental and demographic stochasticity is complemented by analytic and numerical investigations into the robustness of the analysis. The environmental stochasticity model presented in this chapter generates simple analytic predictions of extinction rates and population densities. These can be used in metapopulation models to improve analysis of the fundamental processes of extinction and colonization. The environmental stochasticity model has many largely unexplored implications for metapopulation dynamics. Emigration rates are influenced by local fluctuations; extinction rates become correlated across populations; and the time scales of local growth and extinction may overlap. Simulations in discrete time, used in the study, show that the diffusion analysis works. The robustness investigations show that the model can be extended to deal with many biological details.