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Simple discrete‐time metapopulation models of patch occupancy
Oikos ( IF 3.1 ) Pub Date : 2021-01-29 , DOI: 10.1111/oik.07716
Nathan G. Marculis 1 , Alan Hastings 1
Affiliation  

Simple models in theoretical ecology have a long‐standing history of being used to understand how specific processes influence population dynamics as well as providing a foundation for future endeavors. The Levins model is the seminal example of this for continuous‐time metapopulation dynamics. However, many natural populations have a distinct separation between processes and data is not collected continuously leading to the need for using a discrete‐time model. Our goal is to develop a simple discrete‐time metapopulation model of patch occupancy using difference equations. In our formulation, we consider the two fundamental processes of colonization and extinction that will be treated as sequential events and will only consider patch occupancy. To achieve this, we use a composition of two functions where one will reflect the extinction process and the other for the colonization process. Under some mild assumptions, we are able determine the dynamic behavior of the metapopulation. In addition, we provide numerous examples for the functions used to emulate the colonization and extinction processes. Our results illustrate that the dynamics of the model are tied to properties such as convexity and monotonicity of the colonization and extinction functions. In particular, if the model is non‐monotone, then complex dynamics can arise such as cyclic and even chaotic behavior. Overall, our approach shows how certain properties of the colonization and extinction functions can influence metapopulation dynamics.

中文翻译:

斑块占用的简单离散时间元种群模型

理论生态学中的简单模型已有很长的历史,可用于了解特定过程如何影响种群动态以及为将来的工作奠定基础。Levins模型是连续时间种群动态的开创性例子。但是,许多自然种群在流程之间存在明显的分离,并且无法连续收集数据,因此需要使用离散时间模型。我们的目标是使用差异方程式开发一个简单的离散时间斑块占用人群种群模型。在我们的表述中,我们考虑了定殖和灭绝的两个基本过程,它们将被视为连续事件,并且只会考虑斑块的占用。为了达成这个,我们使用了两个函数的组合,其中一个函数将反映灭绝过程,另一个函数用于定植过程。在一些温和的假设下,我们能够确定亚群的动态行为。此外,我们提供了许多用于模拟定殖和灭绝过程的功能的示例。我们的结果表明,模型的动力学与定殖和消光函数的凸性和单调性有关。特别是,如果模型是非单调的,则可能会出现复杂的动力学,例如循环甚至是混沌行为。总体而言,我们的方法表明了定植和灭绝功能的某些特性如何影响种群动态。我们能够确定亚群的动态行为。此外,我们提供了许多用于模拟定殖和灭绝过程的功能的示例。我们的结果表明,模型的动力学与定殖和消光函数的凸性和单调性有关。特别是,如果模型是非单调的,则可能会出现复杂的动力学,例如循环甚至是混沌行为。总体而言,我们的方法表明了定植和灭绝功能的某些特性如何影响种群动态。我们能够确定亚群的动态行为。此外,我们提供了许多用于模拟定殖和灭绝过程的功能的示例。我们的结果表明,模型的动力学与定殖和消光函数的凸性和单调性有关。特别是,如果模型是非单调的,则可能会产生复杂的动力学,例如循环甚至是混沌行为。总体而言,我们的方法表明了定植和灭绝功能的某些特性如何影响种群动态。我们的结果表明,模型的动力学与定殖和消光函数的凸性和单调性有关。特别是,如果模型是非单调的,则可能会出现复杂的动力学,例如循环甚至是混沌行为。总体而言,我们的方法表明了定植和灭绝功能的某些特性如何影响种群动态。我们的结果表明,模型的动力学与定殖和消光函数的凸性和单调性有关。特别是,如果模型是非单调的,则可能会出现复杂的动力学,例如循环甚至是混沌行为。总体而言,我们的方法表明了定植和灭绝功能的某些特性如何影响种群动态。
更新日期:2021-02-02
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