Given an observed parallel substitution between a pair of branches, we classified it as a radical amino acid substitution if the ancestral and the derived amino acid belong to a different physicochemical group, using an amino acid classification that is based on charge, polarity, and aromaticity: aliphatic and nonpolar (A,I,L,M,V,G), polar and uncharged (S,T,C,P,N,Q), positive charge (R,K,H), negative charge (E,D), and nonpolar and aromatic (F,W,Y). A parallel substitution in a conserved position satisfies the following two criteria. First, all species that descend from both branches share the derived amino acid. Second, at least 90% of the species outside of the two convergent lineages share the ancestral amino acid (fig. S1, B to E). By filtering for radical substitutions in conserved positions, we enrich for parallel substitutions that are more likely to affect protein function, regardless of whether these amino acid substitutions involve a single or more than one nucleotide mutation.

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