Resubmission (due to requested amendments): New models for spatially structured populations

由于对种群结构的内在兴趣和对人类序列变异的现实统计模型的需要，人们对空间扩展的种群中的遗传多样性非常感兴趣。目前的分析主要假设种群被限制为以恒定密度生活在格点上。然而，真实的人口并不是以这种方式细分的，他们也不是长期稳定的。事实上，遗传多样性主要是由大规模的种群运动形成的。这个项目的主要目的是调查短期和长期波动对进化种群的相对影响。这将在一个新的数学模型框架内完成，该模型用于空间扩展的种群的进化，该模型明确包含了大规模波动。它包括经典的岛模型和垫脚石模型作为特例，但也可以用公式来描述种群在一个连续统中的演化。利用分析和模拟相结合的方法，我们的目标是识别长期波动的特征，这些特征可以通过从空间分布的种群收集的遗传数据来测量。

There is great interest in understanding genetic diversity in spatially extended populations, both because of the intrinsic interest in population structure and because of the need for realistic statistical models of human sequence variation. Current analyses mainly assume that populations are restricted to live at points of a lattice at constant density. Yet real populations are not subdivided in this way and nor are they stable over long times. Indeed genetic diversity is shaped primarily by large-scale population movements.The principal aim of this project is to investigate the relative effects of short and long range fluctuations on evolving populations. This will be done in the framework of a new mathematical model for evolution in spatially extended populations which explicitly incorporates large scale fluctuations. It includes the classical island and stepping stone models as special cases, but can also be formulated to describe populations evolving in a continuum. Using a combination of analysis and simulation we aim to identify signatures of long-range fluctuations which could be measured in genetic data collected from spatially distributed populations.