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

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There is great interest in understanding genetic diversity in spatially extended populations, bothbecause 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 populationsare 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 bylarge-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.