Lévy Processes, Saltatory Foraging, and Superdiffusion

Burrow, J. F., Baxter, P. D., and Pitchford, J. W.. "Lévy Processes, Saltatory Foraging, and Superdiffusion." Mathematical Modelling of Natural Phenomena 3.3 (2008): 115-130. <http://eudml.org/doc/222239>.

@article{Burrow2008,
abstract = { It is well established that resource variability generated by spatial patchiness and turbulence is an important influence on the growth and recruitment of planktonic fish larvae. Empirical data show fractal-like prey distributions, and simulations indicate that scale-invariant foraging strategies may be optimal. Here we show how larval growth and recruitment in a turbulent environment can be formulated as a hitting time problem for a jump-diffusion process. We present two theoretical results. Firstly, if jumps are of a fixed size and 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 process becomes superdiffusive. To synthesise these results we conduct a strategic simulation study where “patchy” jumps are embedded in a drift-diffusion process. We conclude that increasingly Lévy-like predator foraging strategies can have a significantly positive effect on recruitment at the population level. },
author = {Burrow, J. F., Baxter, P. D., Pitchford, J. W.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {fish larvae; power law; Pareto distribution; hitting time; jump-diffusion; Lévy walk},
language = {eng},
month = {11},
number = {3},
pages = {115-130},
publisher = {EDP Sciences},
title = {Lévy Processes, Saltatory Foraging, and Superdiffusion},
url = {http://eudml.org/doc/222239},
volume = {3},
year = {2008},
}

TY - JOUR
AU - Burrow, J. F.
AU - Baxter, P. D.
AU - Pitchford, J. W.
TI - Lévy Processes, Saltatory Foraging, and Superdiffusion
JO - Mathematical Modelling of Natural Phenomena
DA - 2008/11//
PB - EDP Sciences
VL - 3
IS - 3
SP - 115
EP - 130
AB - It is well established that resource variability generated by spatial patchiness and turbulence is an important influence on the growth and recruitment of planktonic fish larvae. Empirical data show fractal-like prey distributions, and simulations indicate that scale-invariant foraging strategies may be optimal. Here we show how larval growth and recruitment in a turbulent environment can be formulated as a hitting time problem for a jump-diffusion process. We present two theoretical results. Firstly, if jumps are of a fixed size and 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 process becomes superdiffusive. To synthesise these results we conduct a strategic simulation study where “patchy” jumps are embedded in a drift-diffusion process. We conclude that increasingly Lévy-like predator foraging strategies can have a significantly positive effect on recruitment at the population level.
LA - eng
KW - fish larvae; power law; Pareto distribution; hitting time; jump-diffusion; Lévy walk
UR - http://eudml.org/doc/222239
ER -