Estimation of the neutrality index

The McDonald-Kreitman (MK) test is a simple and widely used test of selection in which the numbers of nonsilent and silent substitutions (D(n) and D(s)) are compared with the numbers of nonsilent and silent polymorphisms (P(n) and P(s)). The neutrality index (NI = D(s)P(n)/D(n)P(s)), the odds ratio (OR) of the MK table, measures the direction and degree of departure from neutral evolution. The mean of NI values across genes is often taken to summarize patterns of selection in a species. Here, we show that this leads to statistical bias in both simulated and real data to the extent that species, which show a pattern of adaptive evolution, can apparently be subject to weak purifying selection and vice versa. We show that this bias can be removed by using a variant of the Cochran-Mantel-Haenszel procedure for estimating a weighted average OR. We also show that several point estimators of NI are statistically biased even when cutoff values are employed. We therefore suggest that a new statistic be used to study patterns of selection when data are sparse, the direction of selection: DoS = D(n)/(D(n) + D(s)) - P(n)/(P(n) + P(s)).