Metapopulation dynamics in a complex ecological landscape.

We propose a general model to study the interplay between spatial dispersal and environment spatiotemporal fluctuations in metapopulation dynamics. An ecological landscape of favorable patches is generated like a Lévy dust, which allows to build a range of patterns, from dispersed to clustered ones. Locally, the dynamics is driven by a canonical model for the time evolution of the population density, consisting of a logistic expression plus multiplicative noises. Spatial coupling is introduced by means of two spreading mechanisms: diffusion and selective dispersal driven by patch suitability. We focus on the long-time population size as a function of habitat configurations, environment fluctuations, and coupling schemes. We obtain the conditions, that the spatial distribution of favorable patches and the coupling mechanisms must fulfill, to grant population survival. The fundamental phenomenon that we observe is the positive feedback between environment fluctuations and spatial spread preventing extinction.