Accuracy and power of the likelihood ratio test in detecting adaptive molecular evolution

The selective pressure at the protein level is usually measured by the nonsynonymous/synonymous rate ratio (omega = dN/dS), with omega < 1, omega = 1, and omega > 1 indicating purifying (or negative) selection, neutral evolution, and diversifying (or positive) selection, respectively. The omega ratio is commonly calculated as an average over sites. As every functional protein has some amino acid sites under selective constraints, averaging rates across sites leads to low power to detect positive selection. Recently developed models of codon substitution allow the omega ratio to vary among sites and appear to be powerful in detecting positive selection in empirical data analysis. In this study, we used computer simulation to investigate the accuracy and power of the likelihood ratio test (LRT) in detecting positive selection at amino acid sites. The test compares two nested models: one that allows for sites under positive selection (with omega > 1), and another that does not, with the chi2 distribution used for significance testing. We found that use of the chi(2) distribution makes the test conservative, especially when the data contain very short and highly similar sequences. Nevertheless, the LRT is powerful. Although the power can be low with only 5 or 6 sequences in the data, it was nearly 100% in data sets of 17 sequences. Sequence length, sequence divergence, and the strength of positive selection also were found to affect the power of the LRT. The exact distribution assumed for the omega ratio over sites was found not to affect the effectiveness of the LRT.