Journal
APPLICABLE ANALYSIS
Volume 89, Issue 7, Pages 1091-1108Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00036811003735816
Keywords
nonlocal dispersal; averaging; invasion speed; persistence condition
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While reaction-diffusion equations are the standard modelling framework for many questions in spatial ecology, their nonlocal analogues, integrodifferential equations, have gained in popularity recently. Here we consider integrodifferential equations for population spread and persistence in heterogeneous landscapes, and we develop appropriate averaging methods for these models. We average over landscape and patch scales. While averaging methods for reaction-diffusion equations lead to relatively simple expressions of persistence conditions and invasion speeds, we find that the results are much richer and more complicated for integro-differential equations. We illustrate our results with two dispersal mechanisms: (1) individuals are mobile throughout their lifetime and (2) only offspring move.
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