Merging Spatial and Temporal Structure within a Metapopulation Model

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Abstract
Current research recognizes that both the spatial and temporal structure of the landscape influence species persistence. Patch models that incorporate the spatial structure of the landscape have been used to investigate static habitat destruction by comparing persistence results within nested landscapes. Other researchers have incorporated temporal structure into their models by making habitat suitability a dynamic feature of the landscape. In this article, we present a spatially realistic patch model that allows patches to be in one of three states: uninhabitable, habitable, or occupied. The model is analytically tractable and allows us to explore the interactions between the spatial and temporal structure of the landscape as perceived by the target species. Extinction thresholds are derived that depend on habitat suitability, mean lifetime of a patch, and metapopulation capacity. We find that a species is able to tolerate more ephemeral destruction, provided that the rate of the destruction does not exceed the scale of its own metapopulation dynamics, which is dictated by natural history characteristics and the spatial structure of the landscape. This model allows for an expansion of the classic definition of a patch and should prove useful when considering species inhabiting complex dynamic landscapes, for example, agricultural landscapes.