Small-sample tests of episodic adaptive evolution: a case study of primate lysozymes.

Positive Darwinian selection at the molecular level is often studied by comparing the number of synonymous nucleotide substitutions per synonymous site (d,) and the number of nonsynonymous substitutions per nonsynonymous site (dN) between homologous gene sequences, and a t-test with an infinite number of degrees of freedom is usually used for determining the statistical significance of the difference between ds and dN (Hughes and Nei 1988; Kumar, Tamura, and Nei 1993). An assumption required for this test is that the sample size (number of substitutions between the sequences) is so large that ds and dN are approximately normally distributed. However, it is unclear how well the t-test performs when the sample size is small and whether there is a better way of testing positive selection. In this letter, we address these issues by using a recently published data set of primate lysozyme sequences (Messier and Stewart 1997) as an example. where SE(ds) and SE(d,) are the standard errors of ds and dN, respectively. In this case, the test statistic (t,) becomes