Detecting heterogeneity of substitution along DNA and protein sequences.

Regions of differing constraint, mutation rate or combination along a sequence of DNA or amino acids lead to a nonuniform distribution of polymorphism within species or fixed differences between species. The power of five tests to reject the null hypothesis of a uniform distribution is studied for four classes of alternate hypothesis. The tests explored are the variance of interval lengths; a modified variance test, which includes covariance between neighboring intervals; the length of the longest interval; the length of the shortest third-order interval; and a composite test. Although there is no uniformly most powerful test over the range of alternate hypotheses tested, the variance and modified variance tests usually have the highest power. Therefore, we recommend that one of these two tests be used to test departure from uniformity in all circumstances. Tables of critical values for the variance and modified variance tests are given. The critical values depend both on the number of events and the number of positions in the sequence. A computer program is available on request that calculates both the critical values for a specified number of events and number of positions as well as the significance level of a given data set.