Enhancing the mathematical properties of new haplotype homozygosity statistics for the detection of selective sweeps.

Soft selective sweeps represent an important form of adaptation in which multiple haplotypes bearing adaptive alleles rise to high frequency. Most statistical methods for detecting selective sweeps from genetic polymorphism data, however, have focused on identifying hard selective sweeps in which a favored allele appears on a single haplotypic background; these methods might be underpowered to detect soft sweeps. Among exceptions is the set of haplotype homozygosity statistics introduced for the detection of soft sweeps by Garud et al. (2015). These statistics, examining frequencies of multiple haplotypes in relation to each other, include H12, a statistic designed to identify both hard and soft selective sweeps, and H2/H1, a statistic that conditional on high H12 values seeks to distinguish between hard and soft sweeps. A challenge in the use of H2/H1 is that its range depends on the associated value of H12, so that equal H2/H1 values might provide different levels of support for a soft sweep model at different values of H12. Here, we enhance the H12 and H2/H1 haplotype homozygosity statistics for selective sweep detection by deriving the upper bound on H2/H1 as a function of H12, thereby generating a statistic that normalizes H2/H1 to lie between 0 and 1. Through a reanalysis of resequencing data from inbred lines of Drosophila, we show that the enhanced statistic both strengthens interpretations obtained with the unnormalized statistic and leads to empirical insights that are less readily apparent without the normalization.