d/d-H, a New Test to Distinguish Different Selection Modes in Protein Evolution and Cancer Evolution.

One of the most popular measures in the analysis of protein sequence evolution is the ratio of nonsynonymous distance (d) to synonymous distance (d). Under the assumption that synonymous substitutions in the coding region are selectively neutral, the d/d ratio can be used to statistically detect the adaptive evolution (or purifying selection) if d/d > 1 (or d/d < 1) significantly. However, due to strong structural constraints and/or variable functional constraints imposed on amino acid sites, most encoding genes in most species have demonstrated d/d < 1. Consequently, the statistical power for testing d/d = 1 may be insufficient to distinguish between different selection modes. In this paper, we propose a more powerful test, called d/d-H, in which a new parameter H, a relative measure of rate variation among sites, was introduced. Given the condition of strong purifying selections at some sites, the d/d-H model predicts d/d = 1-H for neutral evolution, d/d < 1-H for nearly neutral selection, and d/d > 1-H for adaptive evolution. The potential of this new method for resolving the neutral-adaptive debates is illustrated by the protein sequence evolution in vertebrates, Drosophila and yeasts, as well as somatic cancer evolution (specialized as the C/C-H test).