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The most general model – 'free-ratio' model – assumes an independent dN/dS ratio for each branch in the phylogeny.
We tested variable dN/dS ratios for PCSK9 among lineages, using the free-ratio model, which assumes a different dN/dS ratio for each branch in the phylogeny (Figure S1).
The free-ratio (FR) model assumes an independent ω ratio for each branch in the phylogeny.
To investigate lineage-specific patterns of brain reorganization, 41 we quantified rates of evolution for each branch in the phylogeny.
Estimates of ω for each branch in the phylogeny were used for testing the possibility of purifying selection [ 29, 30].
Brownian motion was generated by adding a random number, from a normal distribution with average zero and standard deviation one, stepwise for each branch in the phylogeny from root to tips (Table 1, step 1; e.g., refs. [ 32, 33]).
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To estimate dn/ds ratio for each avian branch in the phylogeny, we ran the "free-ratio" model for a concatenate alignment of the retained genes.
This ratio was calculated using a maximum likelihood model that individually estimates d N/d S for each branch in a phylogeny, following Chain et al. (2011).
We then calculated the evolutionary rates for each branch of the phylogeny using the Codeml free branch model [ 41].
Other models, referred to as alternatives, specify independent ω ratio for the corresponding branch in the phylogeny (see Table 2).
The ω values for branches in the phylogeny for each gene are available at additional file 5.
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