Isolation by distance in a continuous population: reconciliation between spatial autocorrelation analysis and population genetics models

Analysis of the spatial genetic structure within continuous populations in their natural habitat can reveal acting evolutionary processes. Spatial aut ocorrelation statistics are often used for this purpose, but their relation ships with population genetics models have not been thoroughly established. Moreover, it has been argued that the dependency of these statistics on va riation in mutation rates among loci strongly limits their interest for inf erential purposes. In the context of an isolation by distance process, we d escribe relationships between a descriptor of the spatial genetic structure used in empirical studies, Moran's I statistic and population genetics par ameters. In particular, we point out that, when Moran's I statistic is used to describe correlation in allele frequencies at the individual level, it provides an estimator of Wright's coefficient of relationship. We also show that the latter parameter, as a descriptor of genetic structure, is not in fluenced by selfing rate or ploidy level. Under specific finite population models, numerical simulations show that values of Moran's I statistic can b e predicted from analytical theory. These simulations are also used to esti mate the time taken to approach a structure at equilibrium. Finally, we dis cuss the conditions under which spatial autocorrelation statistics are litt le influenced by variation in mutation rates, so that they could be used to estimate gene dispersal parameters.