Berezovskaya Faina, Wirkus S, Song B, Castillo-Chavez C
Department of Mathematics, Howard University, Washington, DC 20059, USA.
Math Med Biol. 2011 Jun;28(2):129-52. doi: 10.1093/imammb/dqq022. Epub 2010 Dec 24.
The population dynamics of predator-prey systems in the presence of patch-specific predators are explored in a setting where the prey population has access to both habitats. The emphasis is in situations where patch-prey abundance drives prey dispersal between patches, with the fragile prey populations, i.e. populations subject to the Allee effect. The resulting 3D and 4D non-linear systems depending on some parameters, which reflect 'measures' of factors under consideration, support rich dynamics and in particular a diverse number of predator-prey life history outcomes. The model's mathematical analysis is carried out via submodels that focus in lower-dimensional settings. The outcomes depend on and, in fact, are quite sensitive to the structure of the system, the range of parameter values and initial conditions. We show that the system can support multistability and a diverse set of predator-prey life-history dynamics that include rather complex dynamical system outcomes. It is argued that, in general, evolution should favour heterogeneous settings including Allee effects, prey refuges and patch-specific predators.
在猎物种群可以进入两个栖息地的环境中，研究了存在斑块特异性捕食者时捕食者 - 猎物系统的种群动态。重点在于斑块猎物丰度驱动猎物在斑块间扩散的情况，以及脆弱的猎物种群，即受阿利效应影响的种群。由此产生的依赖于某些参数的三维和四维非线性系统，这些参数反映了所考虑因素的“度量”，支持丰富的动态，特别是多种捕食者 - 猎物生活史结果。该模型的数学分析通过专注于低维环境的子模型进行。结果取决于系统结构、参数值范围和初始条件，实际上对这些因素非常敏感。我们表明，该系统可以支持多稳定性以及一系列多样的捕食者 - 猎物生活史动态，包括相当复杂的动态系统结果。一般认为，进化通常应有利于包括阿利效应、猎物避难所和斑块特异性捕食者在内的异质环境。
