Abstract In nature, species typically migrate to regions of favorable habitat that provide sufficient food and conditions beneficial to survival. When resources in a certain region are insufficient, there tends to be high species motility in search of food. Starvation-driven diffusion (SDD), which is affected by the local habitat conditions in heterogeneous environments, is a dispersal strategy that increases species motility when food or another resource is limiting. In this study, to gain an understanding of how nonuniform random dispersal affects the fitness of species in a heterogeneous region, we examine a Lotka-Volterra-type predator-prey model applied to the situation where the movement of predators follows the rules of SDD. The main result of this study is that when a predator diffuses following the rules of SDD and the prey diffuses uniformly, the predator is more likely to invade a region than when it diffuses uniformly. We conclude that dispersal using an SDD strategy increases species fitness from an evolutionary perspective. The results we present are obtained based on an eigenvalue analysis of the semi-trivial solutions for a linearized operator derived from a model with nonuniform random diffusion. Furthermore, the existence and uniqueness property of coexistence state under appropriate conditions are given.

中文翻译：

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在空间异质环境中具有非均匀分散的捕食者-猎物相互作用系统

摘要 在自然界中，物种通常迁移到有利栖息地的地区，这些地区提供充足的食物和有利于生存的条件。当某个地区的资源不足时，物种寻找食物的运动性往往很高。饥饿驱动扩散 (SDD) 受异质环境中当地栖息地条件的影响，是一种在食物或其他资源有限时增加物种运动性的扩散策略。在这项研究中，为了了解非均匀随机分散如何影响异质区域中物种的适应度，我们研究了适用于捕食者运动遵循 SDD 规则的情况的 Lotka-Volterra 型捕食者-猎物模型。本研究的主要结果是，当捕食者遵循 SDD 规则扩散且猎物均匀扩散时，捕食者比均匀扩散时更有可能入侵一个区域。我们得出结论，从进化的角度来看，使用 SDD 策略的分散会增加物种的适应性。我们提出的结果是基于对从具有非均匀随机扩散的模型导出的线性化算子的半平凡解的特征值分析获得的。进一步给出了适当条件下共存态的存在性和唯一性。我们提出的结果是基于对从具有非均匀随机扩散的模型导出的线性化算子的半平凡解的特征值分析获得的。进一步给出了适当条件下共存态的存在性和唯一性。我们提出的结果是基于对从具有非均匀随机扩散的模型导出的线性化算子的半平凡解的特征值分析获得的。进一步给出了适当条件下共存态的存在性和唯一性。