Modified HKA Test and Two-Dimensional Evaluation of Neutrality Tests

There are a number of polymorphism-based statistical tests of neutrality, but most of them focus on either the amount or pattern of polymorphism. In this article, a new test called the two-dimensional (2D) test is developed. This test evaluates a pair of summary statistics in a two-dimentional field. One statistic should summarize the pattern of polymorphism, while the other could be a measure of the level of polymorphism. For the latter summary statistic, the polymorphism-divergence ratio is used following the idea of the Hudson-Kreitman-Aguadé (HKA) test. To incorporate the HKA test in the 2D test, a summary statistic-based version of the HKA test is developed such that the polymorphism-divergence ratio at a particular region of interest is examined if it is consistent with the average of those in other independent regions. Since the development of the coalescent theory (Kingman 1982; Hudson 1983; Tajima 1983), a number of polymoprhism-based statistical tests have been developed to examine a neutral null model (i.e., neutrality tests). With increasing intra-specific variation data in various species, these tests have been ubiquitous tools in molecular population genetic analysis (Kreitman 2000). Neutrality tests include the following two major categories, although there are other types of tests available such as haplotype tests (Hudson et al. 1994; Fu 1996; Sabeti et al. 2002) (see Innan et al. 2005, for a recent review of haplotype tests). The first category focuses on the amount of polymorphism. Balancing selection increases the level of polymorphism because multiple alleles are likely maintained for a long time (Hudson and Kaplan 1988), while the level of polymorphism is reduced shortly after a fixation of adaptive mutation. This event is called a selective sweep because the fixation of a beneficial allele could sweep out the variation in the surrounding region of the selection target site by the hitchhiking effect (Kaplan et al. 1989). The Hudson-Kreitman-Aguadé (HKA) test (Hudson et al. 1987) focuses on this effect of selection by comparing the levels of polymorphism and divergence from an outgroup (see also Wright and Charlesworth 2004) The second major category of neutrality tests examines whether the observed frequency spectrum of nucleotide 1Corresponding author: Human Genetics Center, School of Public Health, University of Texas Health Science Center, 1200 Hermann Pressler, Houston, TX 77030. E-mail: hideki.innan@uth.tmc. edu polymorphism is consistent with the neutral expectation. Tajima (1989) has devised a simple method that compares θ̂π and θ̂S , two unbiased estimators of θ, the population mutation rate. θ̂π is identical to the average number of pairwise nucleotide differences, which can be a direct estimator of θ (Tajima 1983). θ̂S is an estimator based on the number of segregating site, S (Watterson 1975). Tajima’s D is defined as (θ̂π−θ̂S)/ √ V ar(θ̂π − θ̂S), and its expectation under the standard neutral model of a constant-size population is approximately 0. Balancing selection creates an excess of alleles in intermediate frequencies so that Tajima’s D is likely positive, while Tajima’s D tends to be negative in a region shortly after a selective sweep or under the pressure of purifying selection due to an excess of variation in low frequencies. A number of tests similar to Tajima’s D have been developed (Fu and Li 1993; Simonsen et al. 1995; Fay and Wu 2000). Thus, most neutrality tests use either the amount or allele frequency spectrum of polymorphism. That is, those tests do not use part of the important information, which could result in a loss of power to detect selection. For example, consider a gene that experienced a recent selective sweep so that no polymorphism is observed. The HKA test could work, but the second category of tests can not be performed when the number of segregating sites is zero. This article introduces a simple algorithm to examine both the amount and freqeuncy spectrum of polymorphism simultaneously, which is referred to as the two-dimensional (2D) test because it examines a pair of test statistics in a two-dimensional field. Genetics: Published Articles Ahead of Print, published on April 19, 2006 as 10.1534/genetics.106. 056242