title: Neutral evolution in spatially continuous populations.
abstract: We introduce a general recursion for the probability of identity in state of two individuals sampled from a population subject to mutation, migration, and random drift in a two-dimensional continuum. The recursion allows for the interactions induced by density-dependent regulation of the population, which are inevitable in a continuous population. We give explicit series expansions for large neighbourhood size and for low mutation rates respectively and investigate the accuracy of the classical Malécot formula for these general models. When neighbourhood size is small, this formula does not give the identity even over large scales. However, for large neighbourhood size, it is an accurate approximation which summarises the local population structure in terms of three quantities: the effective dispersal rate, sigma(e); the effective population density, rho(e); and a local scale, kappa, at which local interactions become significant. The results are illustrated by simulations.
authors.affiliation: Institute of Cell, Animal and Population Biology, University of Edinburgh, King's Building, West Mains Road, Edinburgh, EH9 3JT, United Kingdom.
authors.forename: Nick H
authors.initials: NH
authors.lastname: Barton
authors.forename: Frantz
authors.initials: F
authors.lastname: Depaulis
authors.forename: Alison M
authors.initials: AM
authors.lastname: Etheridge
mesh_terms: D000483:Alleles; D025041:Animal Migration; D000818:Animals; D005075:Biological Evolution; D003627:Data Interpretation, Statistical; D008954:Models, Biological; D009154:Mutation; D011156:Population Density; D011157:Population Dynamics