Distribution patterns of metapopulation determined by Allee effects

The Allee effect, the social dysfunction and failure to mate successfully when population density falls below a certain threshold, is one of the most important phenomena in ecology that can profoundly affect metapopulation persistence. We have developed a continuous dynamic model by pair approximation and two derived spatial lattice models to describe the influences of Allee effects on the distribution and dynamics of metapopulation. Analytical results of pair approximation show that the initial global stable equilibrium of metapopulation size turns into a local stable equilibrium with Allee effects and sensitivity to the initial situations that can incur a threshold phenomenon in dynamics. When the intensity of the Allee effect varies within a certain range, a new positive local stable equilibrium appears. This new equilibrium has the same local intensity as the initial one and a smaller metapopulation size. However, a metapopulation with a too strong Allee effect is doomed. Simulation results from the lattice models reinforce these findings and show that the new equilibrium forms a static distribution border in space. Hence, an Allee effect with moderate intensity can incur three distribution patterns that are sensitive to the initial metapopulation size and the spatial configuration of local populations: aggregation, circumscription and extinction. The pattern of circumscription may be a new explanation for the species' current distributional range. The relationships between distribution patterns (such as random, uniform, aggregation, circumscription and extinction) and other factors (such as mean-field assumption, local interaction, demographic stochasticity and Allee effect) are also discussed.