Mathematical Sciences: Interacting Particle System Models ofEcosystem Dynamics

两位首席研究员Richard Durrett和Simon Levin为这个小型探索性研究项目带来了随机过程(数学)和生态学(生物学)方面的专业知识。他们将应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，以及扩散在种群和群落动态中的作用。具体问题包括(I)环境不均质性对浣熊狂犬病传播的影响(Ii)在空间分布的人群中的流行病，以及(Iii)Maynard Smith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还没有应用于实际数据。

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.