Problem SE12

Colonization rate c in metapopulations is generally a decreasing function of the average distance between patches that constitute the metapopulation habitat. Therefore, a further impact of habitat destruction is the increase of the average distance between patches, which implies the decrease of the colonization rate. Include this further effect into the Levins model with habitat destruction that has been illustrated in class. Assume that the metapopulation you are studying is characterized by an extinction rate e = 0.2 year$^{-1}$, that $1/4$ of the original habitat is being destroyed and that this destruction implies an increase of the average distance d from 1 km to 1.3 km. You have estimated that c [year$^{-1}$] = 0.4$/d^2$. Explain whether the metapopulation can persist in the long term after the habitat has been destroyed. If it can persist, estimate the fraction of occupied patches at equilibrium.