The Impact of the Allee Effect in Dispersal and Patch-Occupancy Age on the Dynamics of Metapopulations

In this paper, we introduce a Levins-type metapopulation model with empty and occupied patches, and dispersing population. We structure the proportion of occupied patches according to the patch-occupancy age. We observe that patch-occupancy age may destabilize the metapopulation, leading to persistent oscillations. We also allow for the dispersal rate to vary with the proportion of empty patches in a monotone or unimodal way. The unimodal dependence leads to multiple non-trivial equilibria and bistability when the reproduction number of the metapopulation R <1 but greater than a lower critical value R* . We show that the metapopulation will persist independently of its initial status if R > 1.