The metapopulation capacity of a fragmented landscape

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Abstract
Ecologists and conservation biologists have used many measures of landscape structure1,2,3,4,5 to predict the population dynamic consequences of habitat loss and fragmentation6,7,8, but these measures are not well justified by population dynamic theory. Here we introduce a new measure for highly fragmented landscapes, termed the metapopulation capacity, which is rigorously derived from metapopulation theory and can easily be applied to real networks of habitat fragments with known areas and connectivities. Technically, metapopulation capacity is the leading eigenvalue of an appropriate ‘landscape’ matrix. A species is predicted to persist in a landscape if the metapopulation capacity of that landscape is greater than a threshold value determined by the properties of the species. Therefore, metapopulation capacity can conveniently be used to rank different landscapes in terms of their capacity to support viable metapopulations. We present an empirical example on multiple networks occupied by an endangered species of butterfly. Using this theory, we may also calculate how the metapopulation capacity is changed by removing habitat fragments from or adding new ones into specific spatial locations, or by changing their areas. The metapopulation capacity should find many applications in metapopulation ecology, landscape ecology and conservation biology.