Predictive tests for linked changes

Mutations may confer a survival advantage to an organism and they can also reduce their fitness. In particular, we are interested in identifying correlated changes in genomic sequences. We consider the general situation where the observed characters at two genomic positions are summarized by an r x c contingency table. The test statistic focusses on double departures from the consensus configuration. When the original data are aggregated into two possible categories at each position (consensus vs non-consensus character), we obtain a 2 x 2 table to derive a test statistic that deals with the total number of double changes. Expected values and variances are predicted, under the assumption of independence, from table entries corresponding to single-mutation events. In some situations, the resulting tests are more powerful than those previously proposed.