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Lévy Processes,Saltatory Foraging, and Superdiffusion

Published online by Cambridge University Press:  07 November 2008

J. F. Burrow
Affiliation:
Department of Mathematics and York Centre for Complex Systems Analysis, University of York, York, UK
P. D. Baxter
Affiliation:
Department of Statistics, University of Leeds, Leeds, UK
J. W. Pitchford*
Affiliation:
Department of Mathematics and York Centre for Complex Systems Analysis, University of York, York, UK Department of Biology, University of York, York, UK
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Abstract

It is well established that resource variability generated by spatial patchiness and turbulence is an importantinfluence on the growth and recruitment of planktonic fish larvae. Empirical data show fractal-like prey distributions, and simulationsindicate that scale-invariant foraging strategies may be optimal. Here we show how larval growth and recruitment in a turbulent environment canbe formulated as a hitting time problem for a jump-diffusion process. We present two theoretical results. Firstly, if jumps are of a fixed sizeand occur as a Poisson process (embedded within a drift-diffusion), recruitment is effectively described by a diffusion process alone.Secondly, in the absence of diffusion, and for “patchy” jumps (of negative binomial size with Pareto inter-arrivals), the encounter processbecomes superdiffusive. To synthesise these results we conduct a strategic simulation study where “patchy” jumps are embedded in adrift-diffusion process. We conclude that increasingly Lévy-like predator foraging strategies can have a significantly positive effect onrecruitment at the population level.

Type
Research Article
Copyright
© EDP Sciences, 2008

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