two sequences, or estimating this number by multiplying the sequence length by the proportion of each class of substitution; (2) counting the number of synonymous and nonsynonymous substitutions; and (3) correcting for multiple substitutions. These steps, particularly the latter, require simplistic assumptions to be made if they are to be achieved computationally; for reasons discussed later, it is impossible to exactly determine the number of multiple substitutions. Maximum-likelihood methods The maximum-likelihood approach uses probability theory to complete all three steps simultaneously. It estimates critical parameters, including the divergence between sequences and the transition/transversion ratio, by deducing the most likely values to produce the input data. Counting methods In order to quantify the number of substitutions, one may reconstruct the ancestral sequence and record the inferred changes at sites (straight counting – likely to provide an underestimate); fitting the substitution rates at sites into predetermined categories (Bayesian approach; poor for small data sets); and generating an individual substitution rate for each codon (computationally expensive). Given enough data, all three of these approaches will tend to the same result. Interpreting results The Ka/Ks ratio is used to infer the direction and magnitude of natural selection acting on protein coding genes. A ratio greater than 1 implies positive or Darwinian selection (driving change); less than 1 implies purifying or stabilizing selection (acting against change); and a ratio of exactly 1 indicates neutral (i.e. no) selection. However, a combination of positive and purifying selection at different points within the gene or at different times along its evolution may cancel each other out. The resulting averaged value can mask the presence of one of the selections and lower the seeming magnitude of another selection. Of course, it is necessary to perform a statistical analysis to determine whether a result is significantly different from 1, or whether any apparent difference may occur as a result of a limited data set. The appropriate statistical test for an approximate method involves approximating dN − dS with a normal approximation, and determining whether 0 falls within the central region of the approximation. More sophisticated likelihood techniques can be used to analyse the results of a Maximum Likelihood analysis, by performing a chi-squared test to distinguish between a null model (Ka/Ks = 1) and the observed results. Utility The Ka/Ks ratio is a more powerful test of the neutral model of evolution than many others available in population genetics as