Metacommunity Dynamics: Integrating Local Dynamics, Stochasticity, and Connectivity

该项目将开发一种新的数学方法，用于描述大空间尺度上生态群落的动态，这种动态描述称为亚稳态。 从数学的角度来看，该项目将从相对简单的描述物种之间的相互作用开始，例如在小空间尺度上的竞争和捕食，再加上对连通性的描述，即物种在不同地点之间移动的方式。 然后，数学描述将扩展到包括物种之间的相互作用和潜在的环境变化的更详细和现实的描述。 将对模型进行分析，以确定长期行为和动态。 然后，数学模型将被用来回答重要的生态问题，重点是如何改变栖息地的质量和可用性和不同的栖息地之间的连接将影响这些metacompatibility的组成和动态。 反过来，这将提供有关影响生境和连通性的人类活动如何影响物种组成和动态的信息，并可为保护和恢复工作提供指导。 所使用的多密度数学模型将主要以一年为一个时间步长的离散时间来表述，以反映季节性环境中的动态以及数据的收集方式。最简单的模型将只关注物种的存在或不存在，并且将是差分方程，因此相对完整的分析处理将是可能的。可以计算平衡及其稳定性。更复杂的描述都将被表述为积分差分方程，其中时间是离散的，但状态空间是连续的。 潜在的因变量将是所考虑的物种丰度的密度函数，积分差分方程中的内核将描述潜在的生态动态。 最初的分析将是数值的期望，分析处理的条件，持久性和共存将是可能的，建立在最近的数学工作的积分差分方程。 为了处理随时间变化的条件，内核将被修改为包括显式的时间依赖性。 该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project will develop a novel mathematical approach for describing the dynamics of ecological communities at large spatial scales, a description of dynamics called metacommunities. From a mathematical standpoint, the project will start with relatively simple descriptions of interactions among species, such as competition and predation, at small spatial scales, coupled with descriptions of connectivity, the way species move between locations. The mathematical descriptions will then be expanded to include more detailed and realistic descriptions of interactions among species and underlying environmental changes. The models will be analyzed to determine both long-term behavior and dynamics. The mathematical models will then be used to answer important ecological questions focused on how changes in habitat quality and availability and connectivity between different habitats will affect the composition and dynamics of these metacommunities. This, in turn, will provide information about how human activities that affect habitats and connectivity will affect species composition and dynamics and can provide guidance for both conservation and restoration efforts. The mathematical models of metacommunities used will be primarily phrased in discrete time with a time step of one year, both to reflect dynamics in seasonal environments and how data is gathered. The simplest models will focus only on species presence or absence and will be difference equations, so a relatively complete analytical treatment will be possible. Equilibria and their stability can be calculated. The more complex descriptions will all be phrased as integro-difference equations where time is discrete, but the state space is continuous. The underlying dependent variables will be density functions for the abundance of the species under consideration, and the kernels in the integro-difference equations will describe the underlying ecological dynamics. Initial analyses will be numerical with the expectation that analytic treatment of conditions for persistence and coexistence will be possible, building on recent mathematical work on integro-difference equations. To treat changing conditions through time, the kernels will be modified to include explicit time dependence. The mathematical analyses will then be used to answer the underlying ecological questions.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.