Strong evolutionary convergence of receptor-binding protein spike between COVID-19 and SARS-related coronaviruses

Yonghua Wu

We employed the branch and branch-site models implemented in the codeml program of PAML 17 to examine the adaptive evolution of our focal genes. For this, a codon-based maximum-likelihood method was used to estimate the ratio of non-synonymous to synonymous substitutions per site (dN/dS or ω), and likelihood ratio tests (LRTs) were used to calculate statistical significance. A statistically significant value of ω > 1 suggests positive selection. Upon analysis, an unrooted taxon tree (Fig. 1) was constructed based on two published studies 5,6 . For branch model analysis, we used a two-rate branch model, and our focal branches were labelled as foreground branches, while others were treated as background branches. The two-rate branch model was compared with the one-rate branch model, which assumes a single ω value across the tree, to determine statistical significance. If a statistically significant value of ω > 1 in a foreground branch was detected, the two-ratio branch model was then compared with the two-ratio branch model with a constraint of ω = 1 to further determine whether the ω > 1 of the foreground branch was statistically significant. In addition to the branch model, we also used a branchsite model (Test 2) to detect positively selected sites for a particular branch. Test 2 compares a modified model A with its corresponding null model with a constraint of ω = 1 to determine the statistical significance. Positively selected sites were found using an empirical Bayes method. For result robustness, we evaluated the dependence of the signal of positive selection on parameter variation. For this, we used two different initial values of kappa (kappa = 0.5, 3.0) and of omega (ω = 0.5, 2.0), and eventually, several independent runs were conducted for each of the positively selected genes found.