A test for heterotachy using multiple pairs of sequences

Heterotachy is a general term to describe positions that evolve at different rates in different lineages. Heterotachy also can generally be viewed as multivariate rates-across-sites variation, which can be described as randomly drawing rates (or branch lengths) from a multivariate distribution for each branch at each site (Wu J, Susko E. 2009. General heterotachy and distance method adjustments. Mol Biol Evol. 26:2689-2697). Motivated by this result, we propose three new distance-based tests: a heterogeneity test, a heterotachy test, and a within-gene heterotachy test and demonstrate with simulations that they perform well under a wide range of conditions. We also applied the first two tests to two real data sets and found that although all these data sets showed significant evidence of heterotachy, there were subtrees for which the data were consistent with an equal rates or rates-across-sites model.heterogeneity, heterotachy, within-gene heterotachy, covarion model, distance method, hypothesis test.