Estimation of the covariance structure from SNP allele frequencies

TL;DR

This paper introduces two new statistics, V and S, for analyzing SNP frequency data to accurately infer population tree roots, outperforming standard methods like F2-statistics.

Contribution

The paper presents novel statistics V and S that improve the accuracy of population tree root identification from SNP data, supported by theoretical and simulation results.

Findings

V statistic estimates true covariance matrix of SNP frequencies

S statistic uses joint distribution of SNP pairs for better inference

New mathematical results relate old and new statistics

Abstract

We propose two new statistics, V and S, to disentangle the population history of related populations from SNP frequency data. If the populations are related by a tree, we show by theoretical means as well as by simulation that the new statistics are able to identify the root of a tree correctly, in contrast to standard statistics, such as the observed matrix of F2-statistics (distances between pairs of populations). The statistic V is obtained by averaging over all SNPs (similar to standard statistics). Its expectation is the true covariance matrix of the observed population SNP frequencies, offset by a matrix with identical entries. In contrast, the statistic S is put in a Bayesian context and is obtained by averaging over pairs of SNPs, such that each SNP is only used once. It thus makes use of the joint distribution of pairs of SNPs. In addition, we provide a number of novel mathematical results about old and new statistics, and their mutual relationship.