Dispersal and Metapopulation Viability in a Heterogeneous Landscape

Conditions of persistence or extinction of a metapopulation of a colonizing annual species are studied in a heterogeneous landscape, a mixture of two elementary landscapes. An elementary landscape is a landscape whose age-structure is described by only one transition matrix, giving the probability for a site to be disturbed, or to follow the process of succession. We first provide an analytical study of the range of dispersal rates that allow metapopulation persistence in an elementary landscape. Second, conditions for metapopulation persistence in a heterogeneous landscape are derived from results obtained in each elementary landscape. Three cases are distinguished. If the two ranges of dispersal rates defined in each elementary landscape overlap, the metapopulation persists in any mixture of the elementary landscapes. If these two dispersal rates ranges are non-overlapping, either the metapopulation goes extinct for some values of the proportion of the elementary landscapes, or two discontinuous ranges of dispersal rates allow the metapopulation persistence. The consequences of these results are discussed in terms of landscape management. In particular, it is shown that under some conditions, a rapid change in environment (from one elementary landscape to another one) might less often lead to metapopulation extinction than a slower change.