Nonspreading solutions and patch formation in an integro-difference model with a strong Allee effect and overcompensation
Nonspreading solutions and patch formation in an integro-difference model with a strong Allee effect and overcompensation
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DOI：
10.1007/s12080-022-00544-y
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发表时间：
2021-10
影响因子：
1.6
通讯作者：
Garrett Otto;W. Fagan;Bingtuan Li
中科院分区：
文献类型：
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作者：
Garrett Otto;W. Fagan;Bingtuan Li
以往的工作涉及一个单一的物种在一个均匀的环境中的积分差分方程强调在无界栖息地的传播行为。我们表明，在适当的条件下，一个简单的标量积分差分方程，结合了强大的Allee效应和过度补偿可以产生的解决方案，人口持续在一个基本上有界的域没有蔓延，尽管同质的环境。这些解决方案是强大的，因为它们占据了参数空间中的满测度区域。我们开发的轨道图显示了各种模式的非扩展解决方案，从稳定的平衡，周期2，更高的周期性。我们发现，从一个相对均匀的初始密度与小的随机扰动，人口组成的多个孤立的补丁可以出现。在生态学方面，这项工作提出了一种新的内源性机制的斑块边界的创建。
Previous work involving integro-difference equations of a single species in a homogenous environment has emphasized spreading behavior 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 parameter space. We develop orbit diagrams showing various patterns of nonspreading solutions from stable equilibria, period-two, to higher periodicity. 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.