Mathematical Sciences: Interacting Particle System Models ofEcosystem Dynamics

两位首席研究员Richard Durrett和Simon Levin为这个探索性研究项目提供了随机过程（数学）和生态学（生物学）方面的专业知识。他们将运用相互作用粒子系统理论的思想来研究入侵物种的传播和持久性，以及种群和群落动态中扩散的作用。具体问题包括：(i)环境不均匀性对浣熊狂犬病传播的影响；（ii）流行病在空间分布的种群中传播；（iii）梅纳德·史密斯进化博弈的空间版本。这些应用将需要发展一些新的理论，例如估计临界值的方法，因为相互作用的粒子系统尚未应用于实际数据。

The two principal investigators, Richard Durrett and Simon Levin, bring to this Small Grants for Exploratory Research project expertise in stochastic processes (mathematics) and ecology (biology). They will apply ideas from the theory of interacting particle systems to study the spread and persistence of invading species and the role of dispersal in the dynamics of populations and communities. Concrete problems include (i) the effect of environmental inhomogeneity on the spread of raccoon rabies (ii) epidemics in spatially distributed populations, and (iii) a spatial version of Maynard Smith's evolutionary game. These applications will require the development of some new theory, e.g. methods for estimating critical values, since interacting particle systems have not yet been applied to real data.