{"title":"Lévy flights, optimal foraging strategies, and foragers with a finite lifespan","authors":"S. Dipierro, Giovanni Giacomin, Enrico Valdinoci","doi":"10.1051/mmnp/2024015","DOIUrl":null,"url":null,"abstract":"In some recent work, we have introduced some efficiency functionals to account for optimal dispersal strategies of predators in search of food.\nThe optimization parameter in this framework is given by the L\\'evy exponent of the dispersal of the predators.\nIn this paper,\nwe apply our model to the case of foragers with finite lifetime (i.e., foragers which need to eat a certain amount of food in a given time, otherwise they die).\nSpecifically, we consider the case in which the initial distribution of the forager coincides with a stationary distribution of the targets and we determine the optimal L\\'evy exponent for the associated efficiency functional.\nNamely, we show that if the Fourier transform of the prey distribution is supported in a sufficiently small ball, then the optimizer is given by a Gaussian dispersal, and if instead the Fourier transform of the prey distribution is supported in the complement of a suitable ball, then\nthe ballistic diffusion provides an optimizer\n(precise conditions for the uniqueness of these optimizers are also given).","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":"100 12","pages":""},"PeriodicalIF":4.6000,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1051/mmnp/2024015","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
Abstract
In some recent work, we have introduced some efficiency functionals to account for optimal dispersal strategies of predators in search of food.
The optimization parameter in this framework is given by the L\'evy exponent of the dispersal of the predators.
In this paper,
we apply our model to the case of foragers with finite lifetime (i.e., foragers which need to eat a certain amount of food in a given time, otherwise they die).
Specifically, we consider the case in which the initial distribution of the forager coincides with a stationary distribution of the targets and we determine the optimal L\'evy exponent for the associated efficiency functional.
Namely, we show that if the Fourier transform of the prey distribution is supported in a sufficiently small ball, then the optimizer is given by a Gaussian dispersal, and if instead the Fourier transform of the prey distribution is supported in the complement of a suitable ball, then
the ballistic diffusion provides an optimizer
(precise conditions for the uniqueness of these optimizers are also given).
期刊介绍:
ACS Applied Bio Materials is an interdisciplinary journal publishing original research covering all aspects of biomaterials and biointerfaces including and beyond the traditional biosensing, biomedical and therapeutic applications.
The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrates knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important bio applications. The journal is specifically interested in work that addresses the relationship between structure and function and assesses the stability and degradation of materials under relevant environmental and biological conditions.