Department of Mathematics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul, 02841, Republic of Korea.
Department of Mathematics, Korea University, 2511 Sejong-ro, Sejong, 30019, Republic of Korea.
Bull Math Biol. 2022 Aug 31;84(10):111. doi: 10.1007/s11538-022-01069-5.
This study considers a situation in which a predator can change its dispersal rate according to its satisfaction with foraging prey in a predator-prey interaction. However, since it is impossible to accurately determine the magnitude of the density of prey that is favorable to a predator's survival in an area, the predator determines the movement rate through inaccurate judgment. In this situation, we investigate the effect of the predator's decision about its movement on fitness. To achieve our goal, we consider a predator-prey model with nonuniform predator dispersal, called prey-induced dispersal (PYID), in which the spread of predators is small when the prey density is larger than a certain value, and when the prey density is smaller than a particular value, a large spread of predators occurs. To understand how PYID affects the dynamics and coexistence of the system in a spatially heterogeneous region, we examine a model with Holling-type II functional responses under no-flux boundary conditions wherein the predators move according to the PYID. We study the local stability of the semitrivial solution of models with PYID and linear dispersal where the predator is absent. Furthermore, we investigate the local/global bifurcation from the semitrivial solution of models with two different dispersals. We conclude that in most cases, nonuniform dispersal of predators following PYID promotes predator fitness; however, there is a case in which PYID does not increase predator fitness. If a predator's satisfaction degree regarding the prey density is higher than a certain level, there may exist a case that is not beneficial for predators in terms of their fitness. However, if the satisfaction level of predators regarding prey density is relatively low, predators following PYID will take advantage of fitness. More precisely, if predators are dissatisfied with the amount of prey in a region and move quickly, even for abundant prey density, they may not benefit from PYID. Meanwhile, if predators change their motility when they are appropriately satisfied with the amount of prey, they will obtain a survival advantage. We obtain the results by analyzing an eigenvalue problem at the semitrivial solution from the linearized operators derived from the models.
本研究考虑了一种情况，即在捕食者-猎物相互作用中，捕食者可以根据对觅食猎物的满意度改变其扩散率。然而，由于不可能准确确定有利于捕食者在一个区域中生存的猎物密度的大小，捕食者通过不准确的判断来确定移动速度。在这种情况下，我们研究了捕食者关于其运动的决策对适合度的影响。为了实现我们的目标，我们考虑了一个具有非均匀捕食者扩散的捕食者-猎物模型，称为猎物诱导扩散（PYID），其中当猎物密度大于某个值时，捕食者的扩散较小，而当猎物密度小于特定值时，捕食者的扩散较大。为了了解 PYID 如何影响空间异质区域中系统的动态和共存，我们检查了在无通量边界条件下具有 Holling 型 II 功能反应的模型，其中捕食者根据 PYID 移动。我们研究了具有 PYID 和线性扩散的模型中没有捕食者时的半平凡解的局部稳定性。此外，我们研究了两种不同扩散模型的半平凡解的局部/全局分岔。我们得出的结论是，在大多数情况下，遵循 PYID 的捕食者的非均匀扩散会促进捕食者的适合度；然而，存在一种情况不会增加捕食者的适合度。如果捕食者对猎物密度的满意度高于某个水平，可能存在一种对捕食者的适合度不利的情况。然而，如果捕食者对猎物密度的满意度相对较低，那么遵循 PYID 的捕食者将获得适合度的优势。更准确地说，如果捕食者对一个区域中的猎物数量感到不满并且快速移动，即使猎物密度丰富，它们也可能不会从 PYID 中受益。同时，如果捕食者在适当满足猎物数量时改变它们的运动能力，它们将获得生存优势。我们通过分析从模型导出的线性化算子在半平凡解处的特征值问题来获得结果。
