{"title":"具有强Allee效应和超补偿的积分-差分模型的非展开解和斑块形成","authors":"Garrett Otto, W. Fagan, Bingtuan Li","doi":"10.21203/rs.3.rs-953137/v1","DOIUrl":null,"url":null,"abstract":"\n Previous work involving integro-difference equations of a single species in a homogenous environment has emphasized spreading behaviour in unbounded habitats. We show that under suitable conditions, a simple scalar integro-difference equation incorporating a strong Allee effect and overcompensation can produce solutions where the population persists in an essentially bounded domain without spread despite the homogeneity of the environment. These solutions are robust in that they occupy a region of full measure in the parameter space. We develop bifurcation diagrams showing various patterns of nonspreading solutions from stable equilibria, period two, to chaos. We show that from a relatively uniform initial density with small stochastic perturbations a population consisting of multiple isolated patches can emerge. In ecological terms this work suggests a novel endogenous mechanism for the creation of patch boundaries.AMS subject classification. 92D40, 92D25","PeriodicalId":51198,"journal":{"name":"Theoretical Ecology","volume":"1 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2021-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Nonspreading Solutions and Patch Formation in An Integro-Difference Model With a Strong Allee Effect and Overcompensation\",\"authors\":\"Garrett Otto, W. Fagan, Bingtuan Li\",\"doi\":\"10.21203/rs.3.rs-953137/v1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n Previous work involving integro-difference equations of a single species in a homogenous environment has emphasized spreading behaviour in unbounded habitats. We show that under suitable conditions, a simple scalar integro-difference equation incorporating a strong Allee effect and overcompensation can produce solutions where the population persists in an essentially bounded domain without spread despite the homogeneity of the environment. These solutions are robust in that they occupy a region of full measure in the parameter space. We develop bifurcation diagrams showing various patterns of nonspreading solutions from stable equilibria, period two, to chaos. We show that from a relatively uniform initial density with small stochastic perturbations a population consisting of multiple isolated patches can emerge. In ecological terms this work suggests a novel endogenous mechanism for the creation of patch boundaries.AMS subject classification. 92D40, 92D25\",\"PeriodicalId\":51198,\"journal\":{\"name\":\"Theoretical Ecology\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2021-10-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theoretical Ecology\",\"FirstCategoryId\":\"93\",\"ListUrlMain\":\"https://doi.org/10.21203/rs.3.rs-953137/v1\",\"RegionNum\":4,\"RegionCategory\":\"环境科学与生态学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"ECOLOGY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical Ecology","FirstCategoryId":"93","ListUrlMain":"https://doi.org/10.21203/rs.3.rs-953137/v1","RegionNum":4,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ECOLOGY","Score":null,"Total":0}
Nonspreading Solutions and Patch Formation in An Integro-Difference Model With a Strong Allee Effect and Overcompensation
Previous work involving integro-difference equations of a single species in a homogenous environment has emphasized spreading behaviour in unbounded habitats. We show that under suitable conditions, a simple scalar integro-difference equation incorporating a strong Allee effect and overcompensation can produce solutions where the population persists in an essentially bounded domain without spread despite the homogeneity of the environment. These solutions are robust in that they occupy a region of full measure in the parameter space. We develop bifurcation diagrams showing various patterns of nonspreading solutions from stable equilibria, period two, to chaos. We show that from a relatively uniform initial density with small stochastic perturbations a population consisting of multiple isolated patches can emerge. In ecological terms this work suggests a novel endogenous mechanism for the creation of patch boundaries.AMS subject classification. 92D40, 92D25
期刊介绍:
Theoretical Ecology publishes innovative research in theoretical ecology, broadly defined. Papers should use theoretical approaches to answer questions of ecological interest and appeal to and be readable by a broad audience of ecologists. Work that uses mathematical, statistical, computational, or conceptual approaches is all welcomed, provided that the goal is to increase ecological understanding. Papers that only use existing approaches to analyze data, or are only mathematical analyses that do not further ecological understanding, are not appropriate. Work that bridges disciplinary boundaries, such as the intersection between quantitative social sciences and ecology, or physical influences on ecological processes, will also be particularly welcome.
All areas of theoretical ecology, including ecophysiology, population ecology, behavioral ecology, evolutionary ecology, ecosystem ecology, community ecology, and ecosystem and landscape ecology are all appropriate. Theoretical papers that focus on applied ecological questions are also of particular interest.