In this paper, we formulate an ODE model to describe the population dynamics of one non-dispersing prey and two dispersing predators in a two-patch environment with spatial heterogeneity. The dispersals of the predators are implicitly reflected by the allocation of their presence (foraging time) in each patch. We analyze the dynamics of the model and discuss some biological implications of the theoretical results on the dynamics of the model. Particularly, we relate the results to the evolution of the allocation strategy and explore the impact of the spatial heterogeneity and the difference in fitness of the two predators on the allocation strategy. Under certain range of other parameters, we observe the existence of an evolutionarily stable strategy (ESS) while in some other ranges, the ESS disappears. We also discuss some possible extensions of the model. Particularly, when the model is modified to allow distinct preys in the two patches, we find that the heterogeneity in predation rates and biomass transfer rates in the two patches caused by such a modification may lead to otherwise impossible bi-stability for some pairs of equilibria.

中文翻译：

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关于两个补丁上的捕食工作量分配策略

在本文中，我们建立了一个ODE模型来描述在具有空间异质性的两补丁环境中一个非分散捕食者和两个分散捕食者的种群动态。捕食者的分散通过每个斑块中它们的存在（觅食时间）的分配而隐含地反映出来。我们分析了模型的动力学，并讨论了理论结果对模型动力学的一些生物学意义。特别地，我们将结果与分配策略的演变联系起来，并探讨空间异质性的影响以及两个捕食者的适应度差异对分配策略的影响。在其他参数的一定范围内，我们观察到进化稳定策略（ESS）的存在，而在其他一些范围内，ESS消失了。我们还将讨论该模型的一些可能扩展。特别是，当模型经过修改以允许两个斑块中有不同的猎物时，我们发现，由于这种修改而导致的两个斑块中捕食率和生物量转移率的异质性可能导致某些成对的平衡出现双稳态。