UNBIASED ESTIMATES OF THE NUMBER OF NUCLEOTIDE SUBSTITUTIONS WHEN SUBSTITUTION RATE VARIES AMONG DIFFERENT SITES

When the number of nucleotides examined is relatively small, the estim ators of nucleotide substitutions between DNA sequences often introduc e systematic error even if the data used fit the mathematical model un derlying the estimation formula. The systematic error of this kind is especially large for models that allow variation in substitution rate among different sites. In the present paper we present a number of for mulas that produce virtually bias-free estimates of evolutionary dista nces for these models.