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.