Mathematical Sciences: Modelling Territorial Patterns and Stability of Wolf-Deer Interactions

研究者们研究了 狼（Canis lupus）的领地形成， 对白尾鹿（Odocoileus）分布的影响 弗吉尼亚人）。 他们的模型是基于实地研究， 明尼苏达州西北部的证据表明 形成由“缓冲区”分隔的不同领土 共生体很少侵入的地方 这些缓冲区可以提供 主要猎物的空间避难所：白尾鹿。 野外调查表明，鹿群密度较高的地区是： 领土区域（避难所）并且中心附近地势较低 已建立的领土（鹿种群可能会受到 强烈的捕食）。 缓冲区也可以稳定狼- 鹿的互动，提供了一个水库的鹿， 将狼领地中遭受严重破坏的地区 捕食损失 研究人员开发的数学模型描述了 狼和鹿之间的行为互动， 非线性偏微分方程组的耦合， 并描述了长期的生态环境中的鹿鹿相互作用 使用耦合的非线性差分方程系统。的 模型方程的分析将采用数学和 数值技术领域，如微扰理论和 有限差分数值方法 这应该会导致 对狼领地模式的详细定量了解 形成，并说明领土如何影响 鹿的分布和数量 该研究将有一个 更广泛地适用于领土模式的一般领域 形成;这种模式提供了社会基础 在许多哺乳动物和鸟类中。

The investigators study the spatial and temporal dynamics of territory formation for wolves (Canis lupus) and the resulting impact on the distribution of white-tailed deer(Odocoileus virginians). Their model is based on field studies from northwestern Minnesota that indicate that adjacent wolf packs form distinct territories that are separated by "buffer zones" where packs rarely trespass. These buffer zones can provide a spatial refuge for the primary prey species: white-tailored deer. The field studies show that deer density is higher in the inter- territorial areas (refuges) and is lower near the center of established territories (where deer populations may be subject to intense predation). The buffer zones may also stabilize wolf- deer interactions by providing a reservoir of deer that can recolonize areas of wolf territory that have suffered heavy predation losses. The mathematical model the investigators develop describes the behavioral wolf-wolf and wolf-deer interactions using a system of coupled of nonlinear partial differential equations, and describes the long-term ecological wolf-deer interactions using a system of coupled nonlinear difference equations. The analysis of the model equations will employ mathematical and numerical techniques from areas such as perturbation theory and finite difference numerical methods. This should lead to a detailed quantitative understanding of wolf territorial pattern formation, and an illustration of how territoriality influences the distribution and abundance of deer. The research will have a wider application to the general area of territorial pattern formation; such patterns provide the basis for social organization in many mammals and birds.