Long-term balancing selection results in a build-up of alleles at similar frequencies and a deficit of substitutions when compared with an outgroup at a locus. The previously published β(1) statistics detect balancing selection using only polymorphism data. We now propose the β(2) statistic which detects balancing selection using both polymorphism and substitution data. In addition, we derive the variance of all β statistics, allowing for their standardization and thereby reducing the influence of parameters which can confound other selection tests. The standardized β statistics outperform existing summary statistics in simulations, indicating β is a well-powered and widely applicable approach for detecting balancing selection. We apply the β(2) statistic to 1000 Genomes data and report two missense mutations with high β scores in the ACSBG2 gene. An implementation of all β statistics and their standardization are available in the BetaScan2 software package at https://github.com/ksiewert/BetaScan.
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