Statistical tests for detecting positive selection by utilizing high-frequency variants

By comparing the low-, intermediate-, and high-frequency parts of the frequency spectrum, we gain information on the evolutionary forces that influence the pattern of polymorphism in population samples. We emphasize the high-frequency variants on which positive selection and negative (background) selection exhibit different effects. We propose a new estimator of 0 (the product of effective population size and neutral mutation rate), theta(L), which is sensitive to the changes in high-frequency variants. The new theta(L) allows us to revise Fay and Wu's H-test by normalization. To complement the existing statistics (the H-test and Tajima's D-test), we propose a new test, E, which relies on the difference between theta(L) and Watterson's theta(w). We show that this test is most powerful in detecting the recovery phase after the loss of genetic diversity, which includes the postselective sweep phase. The sensitivities of these tests to (or robustness against) background selection and demographic changes are also considered. Overall, D and H in combination can be most effective in detecting positive selection while being insensitive to other perturbations. We thus propose a joint test, referred to as the DH test. Simulations indicate that DH is indeed sensitive primarily to directional selection and no other driving forces.