STABILIZATION THROUGH SPATIAL PATTERN-FORMATION IN METAPOPULATIONS WITH LONG-RANGE DISPERSAL

Many studies of metapopulation models assume that spatially extended p opulations occupy a network of identical habitat patches, each coupled to its nearest neighbouring patches by density-independent dispersal. Much previous work has focused on the temporal stability of spatially homogeneous equilibrium states of the metapopulation, and one of the main predictions of such models is that the stability of equilibrium s tates in the local patches in the absence of migration determines the stability of spatially homogeneous equilibrium states of the whole met apopulation when migration is added. Here, we present classes of examp les in which deviations from the usual assumptions lead to different p redictions. In particular, heterogeneity in local habitat quality in c ombination with long-range dispersal can induce a stable equilibrium f or the metapopulation dynamics, even when within-patch processes would produce very complex behaviour in each patch in the absence of migrat ion. Thus, when spatially homogeneous equilibria become unstable, the system can often shift to a different, spatially inhomogeneous steady state. This new global equilibrium is characterized by a standing spat ial wave of population abundances. Such standing spatial waves can als o be observed in metapopulations consisting of identical habitat patch es, i.e. without heterogeneity in patch quality, provided that dispers al is density dependent. Spatial pattern formation after destabilizati on of spatially homogeneous equilibrium states is well known in reacti on-diffusion systems and has been observed in various ecological model s. However, these models typically require the presence of at least tw o species, e.g. a predator and a prey. Our results imply that stabiliz ation through spatial pattern formation can also occur in single-speci es models. However, the opposite effect of destabilization can also oc cur: if dispersal is short rang e, and if there is heterogeneity in pa tch quality, then the metapopulation dynamics can be chaotic despite t he patches having stable equilibrium dynamics when isolated. We conclu de that more general metapopulation models than those commonly studied are necessary to fully understand how spatial structure can affect sp atial and temporal variation in population abundance.