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Linking animal movement to site fidelity. (English) Zbl 1252.92054

Summary: Site fidelity, the recurrent visit of an animal to a previously occupied area, is a wide-spread behavior in the animal kingdom. The relevance of site fidelity to territoriality, successful breeding, social associations, optimal foraging and other ecological processes, demands accurate quantification. We generalize previous theory that connects site fidelity patterns to random walk parameters within the framework of the space-time fractional diffusion equation. In particular, we describe the site fidelity function in terms of animal movement characteristics via the Lévy exponent, which controls the step-length distribution of the random steps at each turning point, and the waiting time exponent that controls for how long an animal awaits before actually moving. The analytical results obtained will provide a rigorous benchmark for empirically driven studies of animal site fidelity.

MSC:

92D40 Ecology
92D50 Animal behavior
60G50 Sums of independent random variables; random walks
60G22 Fractional processes, including fractional Brownian motion
60G51 Processes with independent increments; Lévy processes
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