Mathematical Sciences: Modelling Territoriality 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 virginianus）。 他们的模型是基于实地研究， 明尼苏达州东北部的研究表明，邻近的狼群 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 主要猎物白尾鹿的空间避难所 野外调查表明， 区域间地区（避难所），中心附近较低， 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 通过提供一个鹿的水库， 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， 耦合非线性偏微分方程组，以及 描述了长期的生态鹿的相互作用，使用 耦合非线性差分方程组 分析 的模型方程将采用数学和数值 技术领域，如微扰理论和有限 差分数值方法 这将导致详细的 对狼领地模式形成的定量理解， 以及领土如何影响 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 virginianus). Their model is based on field studies from northeastern 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-tailed 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 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.