Maximizing the total population with logistic growth in a patchy environment
Maximizing the total population with logistic growth in a patchy environment
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DOI：
10.1007/s00285-021-01565-7
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发表时间：
2021-01
影响因子：
1.9
通讯作者：
Kentaro Nagahara;Y. Lou;E. Yanagida
中科院分区：
文献类型：
--
作者：
Kentaro Nagahara;Y. Lou;E. Yanagida
本文研究了种群生物学中自然出现的一个非线性优化问题。本文考虑了斑块环境中具有logistic增长的单一物种种群，研究了斑块的分散和空间异质性对种群平衡状态的影响。我们的目标是在资源总量有限的约束下，通过在斑块之间重新分配资源，使种群总数最大化。结果表明，当扩散速率足够小或足够大时，全局最大化器可以被表征为任意数量的斑块。为了证明这一点，我们计算了两个斑块情况下总种群相对于资源的第一次变化。在有三个或更多斑块的情况下，我们利用泰勒展开式计算所有斑块的渐近展开式。为了描述全局最大化器的形状，我们使用递归关系来确定所有补丁的所有系数。
This paper is concerned with a nonlinear optimization problem that naturally arises in population biology. We consider the population of a single species with logistic growth residing in a patchy environment and study the effects of dispersal and spatial heterogeneity of patches on the total population at equilibrium. Our objective is to maximize the total population by redistributing the resources among the patches under the constraint that the total amount of resources is limited. It is shown that the global maximizer can be characterized for any number of patches when the diffusion rate is either sufficiently small or large. To show this, we compute the first variation of the total population with respect to resources in the two patches case. In the case of three or more patches, we compute the asymptotic expansion of all patches by using the Taylor expansion with respect to the diffusion rate. To characterize the shape of the global maximizer, we use a recurrence relation to determine all coefficients of all patches.