Spatial autocorrelation statistics have been studied in theoretical po
pulation genetic models and widely used in experimental studies of spa
tial structure in many plant and animal populations. However, the stat
istical properties of spatial autocorrelation statistics have remained
uncharacterized. Little is known about how values of spatial autocorr
elation statistics in population samples depend on the level of disper
sal and scheme of sampling. In this paper, we characterize the statist
ical properties of join-count spatial autocorrelation statistics for p
opulation genetic surveys under various conditions of dispersal and sa
mpling. The results indicate generally high statistical power. These r
esults can provide a method to estimate gene dispersal based on standi
ng spatial patterns of genetic variation observed within populations.