A Metapopulation Model with Discrete Size Structure

We consider a discrete size-structured metapopulation model with the proportions of patches occupied by n individuals as dependent variables. Adults are territorial and stay on a certain patch. The juveniles may emigrate to enter a dispersers’ pool from which they can settle on another patch and become adults. Absence of colonization and absence of emigration lead to extinction of the metapopulation. We define the basic reproduction number R0 of the metapopulation as a measure for its strength of persistence. The metapopulation is uniformly weakly persistent if R0 > 1. We identify subcritical bifurcation of persistence equilibria from the extinction equilibrium as a source of multiple persistence equilibria: it occurs, e.g., when the immigration rate (into occupied pathes) exceeds the colonization rate (of empty patches). We determine that the persistence-optimal dispersal strategy which maximizes the basic reproduction number is of bang-bang type: If the number of adults on a patch is below carrying capacity all the juveniles should stay, if it is above the carrying capacity all the juveniles should leave.