Ideal Free Dispersal under General Spatial Heterogeneity and Time Periodicity
Ideal Free Dispersal under General Spatial Heterogeneity and Time Periodicity
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DOI：
10.1137/20m1332712
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发表时间：
2020-07
期刊：
影响因子：
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通讯作者：
R. S. Cantrell;C. Cosner;King-Yeung Lam
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文献类型：
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作者：
R. S. Cantrell;C. Cosner;King-Yeung Lam
如果一个种群的每个成员都以一种优化其个体适应度的方式选择了一个固定的空间位置，并考虑了拥挤的影响，那么该种群在空间异质性但在时间上恒定的环境中被称为具有理想的自由分布。在这篇文章中，我们扩展了个体适应度与空间中特定位置相关的概念，以解释个体有机体在一个周期周期内在空间和时间上所走的完整路径，并将理想自由分布的数学公式扩展到一般的时间周期环境。我们发现，就像在许多其他情况下一样，使用能够产生广义理想自由分布的扩散策略的种群相对于使用不产生理想自由分布的策略的种群具有竞争优势。一个关于环境函数的严格标准被认为是这种理想的自由分布可行的必要条件和充分条件。在满足条件的情况下，我们证明了存在可以被识别为产生理想自由分布的时间周期版本的扩散策略，并且从自适应动力学的观点来看，这些策略是进化稳定的并且是邻域入侵者。我们的结果推广了前人的工作，其中环境要么是时间不变的，要么是时间周期的，但总承载能力是时间不变的。
A population is said to have an ideal free distribution in a spatially heterogeneous but temporally constant environment if each of its members have chosen a fixed spatial location in a way that optimizes its individual fitness, allowing for the effects of crowding. In this paper, we extend the idea of individual fitness associated with a specific location in space to account for the full path that an individual organism takes in space and time over a periodic cycle, and extend the mathematical formulation of an ideal free distribution to general time periodic environments. We find that, as in many other cases, populations using dispersal strategies that can produce a generalized ideal free distribution have a competitive advantage relative to populations using strategies that do not produce an ideal free distribution. A sharp criterion on the environmental functions is found to be necessary and sufficient for such ideal free distribution to be feasible. In the case the criterion is met, we showed that there exist dispersal strategies that can be identified as producing a time-periodic version of an ideal free distribution, and such strategies are evolutionarily steady and are neighborhood invaders from the viewpoint of adaptive dynamics. Our results extend previous works in which the environments are either temporally constant, or temporally periodic but the total carrying capacity is temporally constant.