Statistical properties of two tests that use multilocus data sets to detect population expansions

We describe two methods for detecting population expansions based on variation at unlinked microsatellite loci. The tests were first used in a study of human demographic history that showed evidence for a Paleolithic human population expansion in Africa. Here, we provide a simple recipe for applying the tests to other data sets and describe the power of the tests as a function of the sample size, number of loci, mutation rate, diploid population size N-0, and time since expansion. An important property of the tests is that as long as the population doubles at least once every 0.1N(0) generations, where N-0 now represents the pre-expansion population size, and the overall factor of expansion is sufficiently large, the signal of growth will be nearly identical to one generated by a sudden and massive expansion. This greatly simplifies the mathematical modeling necessary to evaluate the test results but also means that many patterns of growth will be indistinguishable using the tests. A second conclusion from our analysis is that the tests show different sensitivities to specific deviations from the biological and demographic models. Hence, more information can be garnered from the two tests taken together than from either alone.