食饵庇护所对斑块环境下Leslie-Gower捕食系统的影响

建立了一个显式含有空间庇护所的两斑块Leslie-Gower捕食者-食饵系统。假设只有食饵种群在斑块间以常数迁移率迁移,且在每个斑块上食饵间的迁移比局部捕食者-食饵相互作用发生的时间尺度要快。利用两个时间尺度,可以构建用来描述所有斑块总的食饵和捕食者密度的综合系统。数学分析表明,在一定条件下,存在唯一的正平衡点,并且此平衡点全局稳定。进一步,捕食者的数量随着食饵庇护所数量增加而降低;在一定条件下,食饵的数量随着食饵庇护所数量增加先增加后降低,在足够强的庇护所强度下,两物种出现灭绝。对比以往研究,利用显式含有和隐含空间庇护所的数学模型所得结论不一致,这意味着在研究庇护所对捕食系统种群动态影响时,空间结构可能起着重要作用。

The effect of prey refuge in a patchy Leslie-Gower predation system

Predation is a common and important species interaction in many ecological systems. Mathematical models are important and very useful tools to understand and analyze the dynamic behavior of the predator-prey systems. Classical predator-prey models such as the Lotka-Volterra model and Leslie-Gower model can be used in a homogeneous environment. However, in general, the environment is heterogeneous and this can be represented using a set of discrete patches connected by migration. In the simplest situation, the two patches predator-prey model is used, which is composed of the local population process and the dispersal from patch to patch. Prey escaping predation in space or time is widely observed. Spatial or temporal refuges are well-known examples of this class of mechanism. Most theoretical studies have focused on how refuges add stability to the system with predator-prey interactions. The role of spatial and temporal refuges on species coexistence in communities with intraguild predation has also been investigated. These studies have two characteristics. First, most of the research is based on the Lotka-Volterra framework, only a few on the Leslie-Gower framework. Second, the traditional way to model this is to modify the functional response of predators and consider prey refuges, implicitly. The prey refuge can positively affect the growth of prey and negatively that of predators, because the decrease of predation success can lead to the reduction of prey mortality. On the other hand, the hiding behavior of prey could be either advantageous or detrimental for the involved populations. For example, the prey population in the refuges has a low or even negative growth rate because they are rarely offered feeding or mating opportunities. That is, there is a different population structure between the prey refuge and the normal habitat patch. Therefore, it is more reasonable to consider prey refuge explicitly. Based on the above consideration, this paper proposes a Leslie-Gower predator-prey model incorporating the effect of prey refuge explicitly in a two-patch environment. We assume that the prey dispersal is at a constant migration rate and is faster than the local predator-prey interaction, while the predator cannot disperse between patches. Taking advantage of the two different time scales, we use aggregation methods to obtain a reduced (aggregated) model governing the total prey and predator densities. The mathematical analysis of the aggregated model shows that there exists a unique and globally stable positive equilibrium under a certain condition. Simple mathematical analysis shows that increasing the amount of refuge can increase predator densities. As far as the prey species is concerned, under a certain condition, there exists a threshold, such that, for the prey refuge smaller than this threshold, increasing the amount of prey refuge can increase the prey densities, and if the prey refuge is larger than this threshold, increasing the amount of prey refuge can decrease the prey densities. Furthermore, prey and predator will become extinct when the effect of prey refuge is strong enough. In contrast to previous research, the effects of refuges used by the prey are different in spatially implicit and spatially explicit models. The discrepancy suggests that the spatial structure is important when refuges are included.