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 nons ynonymous/synonymous rate ratio (omega = d(N)/d(s)), with omega < 1, <omega > = 1, and omega > 1 indicating purifying (or negative) selection, neutral evolution, and diversifying (or positive) selection, respectively. The w ra tio is commonly calculated as an average over sites. As every functional pr otein has some amino acid sites under selective constraints, averaging rate s across sites leads to low power to detect positive selection. Recently de veloped models of codon substitution allow the co ratio to vary among sites and appear to be powerful in detecting positive selection in empirical dat a analysis. In this study, we used computer simulation to investigate the a ccuracy and power of the likelihood ratio test (LRT) in detecting positive selection at amino acid sites. The test compares two nested models: one tha t allows for sites under positive selection (with omega > 1), and another t hat does not, with the chi (2) 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. N evertheless, 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 sequence s. Sequence length, sequence divergence, and the strength of positive selec tion 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 effecti veness of the LRT.