Separability of Local and Regional Dynamics in Metapopulations

Many models of metapopulations describe the regional dynamics of local extinction and recolonization separately from the local dynamics within the habitat patches. A strict justification of this approach has not been given yet. In this work we systematically derive the processes of extinction and colonization from the local dynamics and the dispersal of the individuals. We show that local and regional dynamics can be described separately only if the variances of environmental fluctuations and the rates of dispersal (emigration and immigration) are below particular bounds. If environmental fluctuations and dispersal satisfy these conditions the local dynamics have a much faster time scale than the regional dynamics and extinction and recolonization can each be described by a single rate which depends on the parameters of the local dynamics and dispersal.