Measures of spatial structure in samples of genotypes for multiallelic loci

Various spatial autocorrelation statistics have been widely used both in theoretical population genetics and to study the spatial distribution of diploid genotypes in many plant and animal populations. However, previous simulation studies have considered only diallelic loci. In this paper, we use a large number of space-time simulations to characterize for the first time the parametric and statistical values of Moran's I-statistics for converted individual genotypes as well as for join-count statistics. A wide range of levels of dispersal and numbers of alleles and allele frequencies are modelled and the results reveal the different general effects of each of these factors on these statistics. We also examine the range of appropriate sampling designs and sizes for which predicted values can be interpolated for specific sampling schemes for any given population genetic field survey. Numbers of alleles and allele frequencies each affect some statistics but not others. The results indicate generally low standard deviations. The results also develop precise and efficient methods of estimating gene dispersal, based on the various autocorrelation measures of standing spatial patterns of genetic variation within populations. The results also extend these methods to loci with multiple alleles, typical of those studied through modern molecular methods.