Spatially discrete metapopulation models with directional dispersal.

We use an age-structured discrete-time metapopulation model linking two sub-populations through larval transport and directed movements of adults to study the implications of linkages among subpopulations for the stability and resilience of exploited species. Our two-habitat model, a generalization of Fogarty's inshore-offshore lobster population model, includes isolated habitats under compensatory (monotone) or overcompensatory (oscillatory) dynamics [M.J. Fogarty, Implications of migration and larval interchange in American lobster (Homarus americanus) stocks: spatial structure and resilience, in: G.S. Jamieson, A. Campbell (Eds.), Proc. of North Pacific Symposium on Invertebrate Stock Assessment and Management, Can. Spec. Publ. Fish. Aquat. Sci. 125 (1998) 273]. Pre-migration local dynamics are selected from general classes of functions that capture the effects of competition for resources via contest (compensatory) and scramble (overcompensatory) intraspecific competitions. We explore the implications of these mechanisms on the long-term survival of exploited species. In particular, we use threshold parameters R(d)1 for Habitat 1 and R(d)2 for Habitat 2 together with precise mathematical definitions to prove that species persistence is possible at high levels of fishing in one habitat and low to moderate levels of fishing in the other. Our results support Fogarty's conclusion that conservative management of larval source populations could contribute to the resilience of exploited species.