Non-parametric smoothing of multivariate genetic distances in the analysis of spatial population structure at fine scale.

Species dispersal studies provide valuable information in biological research. Restricted dispersal may give rise to a non-random distribution of genotypes in space. Detection of spatial genetic structure may therefore provide valuable insight into dispersal. Spatial structure has been treated via autocorrelation analysis with several univariate statistics for which results could dependent on sampling designs. New geostatistical approaches (variogram-based analysis) have been proposed to overcome this problem. However, modelling parametric variograms could be difficult in practice. We introduce a non-parametric variogram-based method for autocorrelation analysis between DNA samples that have been genotyped by means of multilocus-multiallele molecular markers. The method addresses two important aspects of fine-scale spatial genetic analyses: the identification of a non-random distribution of genotypes in space, and the estimation of the magnitude of any non-random structure. The method uses a plot of the squared Euclidean genetic distances vs. spatial distances between pairs of DNA-samples as empirical variogram. The underlying spatial trend in the plot is fitted by a non-parametric smoothing (LOESS, Local Regression). Finally, the predicted LOESS values are explained by segmented regressions (SR) to obtain classical spatial values such as the extent of autocorrelation. For illustration we use multivariate and single-locus genetic distances calculated from a microsatellite data set for which autocorrelation was previously reported. The LOESS/SR method produced a good fit providing similar value of published autocorrelation for this data. The fit by LOESS/SR was simpler to obtain than the parametric analysis since initial parameter values are not required during the trend estimation process. The LOESS/SR method offers a new alternative for spatial analysis.