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| Component Allee effects are low density positive feedback mechanisms that affect individual fitness. They can, under certain circumstances, lead to a strong Allee effect, that is, the simultaneously occurrence of an extinction attractor and a non-extinction (or positive) attractor. Motivated by issues concerning endangered species, especially in the light of climate change, there is a rapidly growing interest in strong Allee effects and the resulting extinction thresholds. I will discuss strong Allee effects in matrix models that describe the discrete time dynamics of a structured population. From a bifurcation theory point of view, I will give some general criteria under which strong Allee effects occur in nonlinear matrix models. One key is a backward bifurcation of positive equilibria. I will also apply this approach to evolutionary versions of matrix models. I will give a specific application arising from my collaborative research with field ecologists who study marine birds at the US National Wildlife Refuge on Protection Island, Washington State, USA. The model, with its strong Allee effect, offers an hypothesis that explains certain life history strategy changes recently observed in breeding colonies that relate to climate change during the last half century (specifically, a mean sea surface temperature increase). |
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