Connecting the parameters of local extinction and metapopulation dynamics

This paper explores the correspondence between the parameters of an extinction model analysed by Lande, Foley and Middleton et al. and the parameters of the incidence function model of metapopulation dynamics. The parameters of the extinction model, the intrinsic rate of population increase (r), its variance (v) and the population ceiling (K), can be mapped to the parameters of the incidence function model describing the scaling of the probability of local extinction (E) with patch area (A), E = e/A(x), via the equations s = x and r = eD(s)/s, where s = 2r/v, D is population density and K = DA. I explore this correspondence with two empirical examples, a mainland- island metapopulation of the European common shrew (Sorex araneus) on islands in lakes and a classical metapopulation of the American pika (Ochotona princeps). The most robust result is the correspondence x = 2r/v, which value decreases with increasing strength of environmental stochasticity. Thus the impact of environmental stochasticity on population dynamics can, in principle, be inferred from the pattern of habitat patch occupancy in a metapopulation.