Abstract
Rare variants are important for drawing inference about past demographic events ina species history. A singleton is a rare variant for which genetic variation is carried bya unique chromosome in a sample. How singletons are distributed across geographicspace provides a local measure of genetic diversity that can be measured at the individuallevel. Here, we define the empirical distribution of singletons in a sample of chromosomesas the proportion of the total number of singletons that each chromosome carries, andwe present a theoretical background for studying this distribution. Next, we use computersimulations to evaluate the potential for the empirical distribution of singletons to providea description of genetic diversity across geographic space. In a Bayesian framework,we show that the empirical distribution of singletons leads to accurate estimates of thegeographic origin of range expansions. We apply the Bayesian approach to estimatingthe origin of the cultivated plant species Pennisetum glaucum [L.] R. Br. (pearl millet) inAfrica, and find support for range expansion having started from Northern Mali. Overall,we report that the empirical distribution of singletons is a useful measure to analyze resultsof sequencing projects based on large scale sampling of individuals across geographicspace.