Abstract
Spatial structure of genetic variation within populations is well measured by statistics based on the distribution of pairs of
individual genotypes, and various such statistics have been widely used in experimental studies. However, the problem of
uncharacterized correlations among statistics for different alleles has limited the applications of multiallelic, multilocus summary
measures, since these had unknown sampling distributions. Usually multiple alleles and/or multiple loci are required in order to
precisely measure spatial structures, and to provide precise indirect estimates of the amount of dispersal in samples of reasonable
size. This article examines the correlations among pair-wise statistics, including Moran I-statistics and various measures of
conditional kinship, for different alleles of a locus. First the correlations are mathematically derived for random spatial
distributions, which allow averages over alleles and loci to be used as more powerful yet exact test statistics for the null hypothesis.
Then extensive computer simulations are conducted to examine the correlations among values for different alleles under isolation by
distance processes. For loci with more than three alleles, the results show that the correlations are remarkably and perhaps
surprisingly small, establishing the principle that then alleles behave as nearly independent realizations of spacetime stochastic
processes. The results also show that the correlations are largely robust with respect to the degree of spatial structure, and they can
be used in a straightforward manner to form confidence intervals for averages. The results allow a precise connection between
observations in experimental studies and levels of dispersal in theoretical models.
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