Optimal neutrality tests based on the frequency spectrum.

The ascertainment of the demographic and selective history of populations has been a major research goal in genetics for decades. To that end, numerous statistical tests have been developed to detect deviations between expected and observed frequency spectra, e.g., Tajima's D, Fu and Li's F and D tests, and Fay and Wu's H. Recently, Achaz developed a general framework to generate tests that detect deviations in the frequency spectrum. In a further development, we argue that the results of these tests should be as independent on the sample size as possible and propose a scale-free form for them. Furthermore, using the same framework as that of Achaz, we develop a new family of neutrality tests based on the frequency spectrum that are optimal against a chosen alternative evolutionary scenario. These tests maximize the power to reject the standard neutral model and are scalable with the sample size. Optimal tests are derived for several alternative evolutionary scenarios, including demographic processes (population bottleneck, expansion, contraction) and selective sweeps. Within the same framework, we also derive an optimal general test given a generic evolutionary scenario as a null model. All formulas are relatively simple and can be computed very fast, making it feasible to apply them to genome-wide sequence data. A simulation study showed that, generally, the tests proposed are more consistently powerful than standard tests like Tajima's D. We further illustrate the method with real data from a QTL candidate region in pigs.