This approach was incorporated in PAML software, which included branch model, site model, and branch-site model, allowing ω varying across branches, or sites among proteins, and both across branch and among proteins, respectively (Yang, 1997, 1998; Yang and Nielsen, 2002; Zhang et al., 2005; Yang, 2007; Yang and Nielsen, 2008; Yang and dos Reis, 2011).
These models allow ω values to vary among different codons.
Branch models allow ω to vary across branches in the phylogeny but not across sites.
The site models allow ω to vary across sites and presence of sites with ω is tested with a LRT (Yang et al. 2000).
These models allow ω to vary among codon sites; model M8 assumes that positive selection might occur and ω values can exceed 1 while the null model, M8a, fixes ω at 1.
Unlike branch-site model, site-specific models allowing ω to vary among sites [ 55, 88, 89] were used to determine whether particular amino-acid residues within GAox families have been subject to positive selection.
Hierarchical likelihood ratio tests performed between different branch models allowing ω to vary among branches of the phylogeny revealed that strong positive selection has occurred in Catarrhini (Table 1).
Branch-site models allow ω to vary both among sites in the protein and across branches on the tree, and aim to detect positive selection affecting a few sites along particular lineages [ 64].
Because the branch models average the ω ratio over all sites and were unable to detect a positive signal in many cases, site-specific models allowing ω to vary among sites [ 50, 51] were subsequently used to determine whether particular amino-acid residues within FDS gene families have been subject to positive selection.
