An asymptotically normal test for the selective neutrality hypothesis

Abstract

An important parameter in the study of population evolution is θ=4Nν, where N is the effective population size and ν is the rate of mutation per locus per generation. Therefore, θ represents the mean number of mutations per site per generation. There are many estimators of θ, one of them being the mean number of pairwise nucleotide differences, which we call T₂. Other estimators are T₁, based on the number of segregating sites and T₃, based on the number of singletons. The concept of selective neutrality can be interpreted as a differentiated nucleotide distribution for mutant sites when compared to the overall nucleotide distribution. Tajima (1989) has proposed the so-called Tajima’s test of selective neutrality based on T₂−T₁. Its complex empirical behavior (Kiihl, 2005) motivates us to propose a test statistic solely based on T₂. We are thus able to prove asymptotic normality under different assumptions on the number of sequences and number of sites via U-statistics theory.