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Efficiency functionals for the Lévy flight foraging hypothesis.

Serena Dipierro1, Giovanni Giacomin2, Enrico Valdinoci2

  • 1Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley, WA6009, Australia. serena.dipierro@uwa.edu.au.

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|September 17, 2022
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Summary

This study explores optimal foraging strategies using fractional heat equations. It reveals a switch between Lévy and Brownian motion patterns, impacting foraging efficiency.

Keywords:
Anomalous diffusionForaging strategiesFractional LaplacianLévy flights

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Area of Science:

  • Mathematical Biology
  • Theoretical Ecology
  • Statistical Physics

Background:

  • Foraging behavior is crucial for species survival and resource acquisition.
  • Lévy flights and Brownian motion are established models for animal movement.
  • Understanding optimal foraging strategies in diverse environments remains a key challenge.

Purpose of the Study:

  • To analyze optimal foraging strategies for a forager modeled by a fractional heat equation.
  • To investigate the influence of the Lévy exponent on foraging efficiency across various biological scenarios.
  • To identify conditions under which Lévy or Brownian motion strategies are optimal.

Main Methods:

  • Utilizing fractional heat equations to model forager diffusion.
  • Introducing and analyzing efficiency functionals.
  • Examining specific scenarios: single close target, sparse environment, single distant target, and two targets.
  • Employing special functions for explicit analysis.

Main Results:

  • Optimal strategies were derived for different foraging configurations.
  • Bifurcation phenomena were observed, showing a switch between Lévy (inverse square law) and Brownian motion strategies.
  • Lévy strategies can be optimal even when Brownian motion appears to be a less efficient choice.
  • Optimal strategies near Brownian motion were identified even when it's suboptimal.

Conclusions:

  • The study provides a theoretical framework for understanding optimal foraging under fractional diffusion.
  • Bifurcation phenomena highlight the complex trade-offs between strategy reliability and efficiency.
  • Results offer insights into the adaptability of foraging patterns in response to environmental conditions and target characteristics.