Isolation by distance in a continuous population under stochastic demographic fluctuations


François Rousset, Institut des Sciences de l'Evolution, Université de Montpellier II, Place E. Bataillon Bât. 22/1er étage/CC 065, 34095 Montpellier Cedex 05, France.
Tel.: +33 467 144 630; fax: +33 467 143 622;


The local density of individuals is seldom uniform in space and time within natural populations. Yet, formal approaches to the process of isolation by distance in continuous populations have encountered analytical difficulties in describing genetic structuring with demographic heterogeneities, usually disregarding local correlations in the movement and reproduction of genes. We formulate exact recursions for probabilities of identity in continuous populations, from which we deduce definitions of effective dispersal (inline image) and effective density (De) that generalize results relating spatial genetic structure, dispersal and density in lattice models. The latter claim is checked in simulations where estimates of effective parameters obtained from demographic information are compared with estimates derived from spatial genetic patterns in a plant population evolving in a heterogeneous and dynamic habitat. The simulations further suggest that increasing spatio-temporal correlations in local density reduce inline image and generally decrease the product inline image, with dispersal kurtosis influencing their sensitivity to density fluctuations. As in the lattice model, the expected relationship between the product inline image and the genetic structure statistic ar holds under fluctuating density, irrespective of dispersal kurtosis. The product D σ2 between observed census density and the observed dispersal rate over one generation will generally be an upwardly biased (up to 400% in simulations) estimator of inline image in populations distributed in spatially aggregated habitats.