Extinctions in a Metapopulation with Nonlinear Dispersal Coupling

Major threats to biodiversity are climate change, habitat fragmentation (in particular, habitat loss), pollution, invasive species, over-exploitation, and epidemics. Over the last decades habitat fragmentation has been given special attention. Many factors are causing biological systems to extinct; therefore, many issues remain poorly understood. In particular, we would like to know more about the effect of the strength of inter-site coupling (e.g., it can represent the speed with which species migrate) on species extinction or persistence in a fragmented habitat consisting of sites with randomly varying properties. To address this problem we use theoretical methods from mathematical analysis, functional analysis, and numerical methods to study a conceptual single-species spatially-discrete system. We state some simple necessary conditions for persistence, prove that this dynamical system is monotone and we prove convergence to a steady-state. For a multi-patch system, we show that the increase of inter-site coupling leads to the formation of clusters—groups of populations whose sizes tend to align as coupling increases. We also introduce a simple one-parameter sufficient condition for a metapopulation to persist.