An asymptotically normal test for the selective neutrality hypothesis

TL;DR

This paper introduces a new asymptotically normal statistical test for detecting selective neutrality in population genetics, based solely on the mean number of pairwise nucleotide differences, with proven theoretical properties.

Contribution

It proposes a novel neutrality test statistic based on $ ext{T}_2$ and proves its asymptotic normality under various conditions, simplifying previous complex methods.

Findings

The test statistic is asymptotically normal.

The method simplifies neutrality testing.

Theoretical proof under different assumptions.

Abstract

An important parameter in the study of population evolution is $\theta=4N\nu$, where $N$ is the effective population size and $\nu$ is the rate of mutation per locus per generation. Therefore, $\theta$ represents the mean number of mutations per site per generation. There are many estimators of $\theta$, one of them being the mean number of pairwise nucleotide differences, which we call $\mathcal{T}_2$. Other estimators are $\mathcal{T}_1$, based on the number of segregating sites and $\mathcal{T}_3$, 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 $\mathcal{T}_2-\mathcal{T}_1$. Its complex empirical behavior (Kiihl, 2005) motivates us to propose a test statistic solely based on $\mathcal{T}_2$. We are thus able to prove asymptotic normality under different assumptions on the number of sequences and number of sites via $U$-statistics theory.