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A general model for estimating the number of amino acid substitutions per site (d) from the fraction of identical residues between two sequences (q) is proposed. The well-known Poisson-correction formula q = e (-d) corresponds to a site-independent and amino-acid-independent substitution rate. Equation q = (1 - e(-2d)/2d, derived for the case of substitution rates that are site-independent, but vary among amino acids, approximates closely the empirical method, suggested by Dayhoff et al. (1978). Equation q = 1/(1 + d) describes the case of substitution rates that are amino acid-independent but vary among sites. Lastly, equation q = [ln(1 + 2d)]/2d accounts for the general case where substitution rates can differ for both amino acids and sites.

Estimation of the number of amino acid substitutions per site when the substitution rate varies among sites