Ideal free distribution in a system of multiple predator and prey species.

IF 2.7 4区数学 Q2 BIOLOGY

Journal of Mathematical Biology Pub Date : 2026-08-01 DOI:10.1007/s00285-026-02428-9

Robert Stephen Cantrell, Chris Cosner, King-Yeung Lam, Hua Zhang

{"title":"Ideal free distribution in a system of multiple predator and prey species.","authors":"Robert Stephen Cantrell, Chris Cosner, King-Yeung Lam, Hua Zhang","doi":"10.1007/s00285-026-02428-9","DOIUrl":null,"url":null,"abstract":"<p><p>We study mechanisms and effects of ideal free distributions (IFDs) on an ecological community consisting of n prey and m predator species, for any positive integers n and m, by considering the corresponding diffusive Lotka-Volterra system with time-periodic coefficients. We define a notion of joint IFD in a time-periodic environment, and give necessary and sufficient conditions for it to be achieved by a subcollection of prey and predator species with suitable dispersal strategies. Next, we show, via construction of a Lyapunov functional, that such dispersal strategies are evolutionarily stable, in the sense that if a subcollection of prey and predator species adopts an ideal free dispersal strategy, then the total community must converge to an IFD for large time; if a unique combination of prey-predator species adopts an ideal free strategy, then it can drive all other species to extinction. Conversely, if a combination of prey-predator species adopts a non-ideal free dispersal strategy, then it can be invaded by some suitable mutant strategies. Our results provide insight into the evolution of spatial distribution of ecological communities with predator-prey interactions.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 2","pages":""},"PeriodicalIF":2.7000,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Biology","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00285-026-02428-9","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"BIOLOGY","Score":null,"Total":0}

引用次数: 0

Abstract

We study mechanisms and effects of ideal free distributions (IFDs) on an ecological community consisting of n prey and m predator species, for any positive integers n and m, by considering the corresponding diffusive Lotka-Volterra system with time-periodic coefficients. We define a notion of joint IFD in a time-periodic environment, and give necessary and sufficient conditions for it to be achieved by a subcollection of prey and predator species with suitable dispersal strategies. Next, we show, via construction of a Lyapunov functional, that such dispersal strategies are evolutionarily stable, in the sense that if a subcollection of prey and predator species adopts an ideal free dispersal strategy, then the total community must converge to an IFD for large time; if a unique combination of prey-predator species adopts an ideal free strategy, then it can drive all other species to extinction. Conversely, if a combination of prey-predator species adopts a non-ideal free dispersal strategy, then it can be invaded by some suitable mutant strategies. Our results provide insight into the evolution of spatial distribution of ecological communities with predator-prey interactions.

查看原文本刊更多论文

多捕食者和猎物物种系统中的理想自由分布。

本文通过考虑具有时间周期系数的扩散Lotka-Volterra系统，研究了理想自由分布（IFDs）对n个被捕食物种和m个捕食物种组成的生态群落的作用机制和影响。我们定义了一个时间周期环境下的联合IFD的概念，并给出了在合适的分散策略下，由一个猎物和捕食者的子集合来实现联合IFD的充分必要条件。接下来，我们通过Lyapunov函数的构造证明了这种扩散策略是进化稳定的，也就是说，如果一个猎物和捕食者物种的子集采用理想的自由扩散策略，那么整个群落必须在很长一段时间内收敛于一个IFD；如果一个独特的猎物-捕食者物种组合采用了一种理想的自由策略，那么它可以驱使所有其他物种灭绝。相反，如果一个捕食者-猎物物种的组合采用了非理想的自由扩散策略，那么它可能会被一些合适的突变策略入侵。我们的研究结果揭示了捕食者-猎物相互作用下生态群落空间分布的演变。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Mathematical Biology 生物-生物学

CiteScore

3.30

自引率

5.30%

发文量

120

审稿时长

6 months

期刊介绍： The Journal of Mathematical Biology focuses on mathematical biology - work that uses mathematical approaches to gain biological understanding or explain biological phenomena. Areas of biology covered include, but are not restricted to, cell biology, physiology, development, neurobiology, genetics and population genetics, population biology, ecology, behavioural biology, evolution, epidemiology, immunology, molecular biology, biofluids, DNA and protein structure and function. All mathematical approaches including computational and visualization approaches are appropriate.