Nonspreading Solutions and Patch Formation in An Integro-Difference Model With a Strong Allee Effect and Overcompensation

IF 1.2 4区环境科学与生态学 Q4 ECOLOGY Theoretical Ecology Pub Date : 2021-10-26 DOI:10.21203/rs.3.rs-953137/v1

Garrett Otto, W. Fagan, Bingtuan Li

引用次数: 0

Abstract

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

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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

先前涉及单一物种在同质环境中的积分-差分方程的工作强调了无边界栖息地中的传播行为。我们证明，在适当的条件下，一个简单的标量积分差分方程结合了强Allee效应和过补偿，可以产生这样的解，即尽管环境是均匀的，但种群仍然存在于基本有界的域中而没有扩散。这些解决方案是稳健的，因为它们在参数空间中占据了完全度量的区域。我们发展了分叉图，显示了从稳定平衡，周期二到混沌的各种非扩展解模式。我们证明，在具有较小随机扰动的相对均匀的初始密度中，可以出现由多个孤立斑块组成的种群。从生态学的角度来看，这项工作为斑块边界的形成提出了一种新的内生机制。AMS受试者分类。92D40、92D25

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来源期刊

Theoretical Ecology 环境科学-生态学

CiteScore

3.30

自引率

6.20%

发文量

审稿时长

>12 weeks

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.