Isolation by distance in a continuous population under stochastic demographic fluctuations.

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 () and effective density (D(e)) 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 and generally decrease the product , with dispersal kurtosis influencing their sensitivity to density fluctuations. As in the lattice model, the expected relationship between the product and the genetic structure statistic a(r) holds under fluctuating density, irrespective of dispersal kurtosis. The product D sigma(2) 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 in populations distributed in spatially aggregated habitats.