The founder and allee effects in the patch occupancy metapopulation model

Abstract

The problem of ever-increasing habitat fragmentation due to human land use calls for a theoretical framework to study the potential dangers and to find ways of combating these dangers. The metapopulation approach, with the Levins model as its patriarch, provides such a framework. A metapopulation is a collection of populations that live in habitat fragments (called patches). These populations can become extinct, but new populations can be established by dispersing individuals from extant populations. If these colonizations can balance these extinctions, metapopulation persistence is possible. In theoretical literature surprisingly little attention has been paid to the colonization term in the Levins model and its extensions. Specifically, the Allee effect (i.e. reduced probability of colonization due to, e.g., reduced probability of finding a mate, or reduced defence against predators) may play a major role although it has not received appropriate attention. In this paper, we study the colonization term in the Levins model and conclude that it describes the founder effect (i.e. stochastic fluctuations in births and deaths of an establishing population causing colonization to fail). We then incorporate the Allee effect in the colonization term and conclude that previous attempts to do so were erroneous because they ignored some difficulties in the model formulation and interpretation. We devise a phenomenological model for the Allee effect that is consistent in both discrete and continuous time. Although the model with Allee effect shows a fold bifurcation in its deterministic formulation (both in discrete and continuous time), suggesting the possibility of sudden metapopulation extinction when the bifurcation parameter is only changed slightly, the model in its stochastic formulation does not fully support this: the expected occupancy and the expected metapopulation extinction time decrease gradually when the number of patches is moderate. © 2005 Springer.