Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-22T17:12:36.627Z Has data issue: false hasContentIssue false

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)