BACKGROUND: The evolutionary rate at a given homologous position varies across 
time. When sufficiently pronounced, this phenomenon - called heterotachy - may 
produce artefactual phylogenetic reconstructions under the commonly used models 
of sequence evolution. These observations have motivated the development of 
models that explicitly recognize heterotachy, with research directions proposed 
along two main axes: 1) the covarion approach, where sites switch from variable 
to invariable states; and 2) the mixture of branch lengths (MBL) approach, where 
alignment patterns are assumed to arise from one of several sets of branch 
lengths, under a given phylogeny.
RESULTS: Here, we report the first statistical comparisons contrasting the 
performance of covarion and MBL modeling strategies. Using simulations under 
heterotachous conditions, we explore the properties of three model comparison 
methods: the Akaike information criterion, the Bayesian information criterion, 
and cross validation. Although more time consuming, cross validation appears 
more reliable than AIC and BIC as it directly measures the predictive power of a 
model on 'future' data. We also analyze three large datasets (nuclear proteins 
of animals, mitochondrial proteins of mammals, and plastid proteins of plants), 
and find the optimal number of components of the MBL model to be two for all 
datasets, indicating that this model is preferred over the standard homogeneous 
model. However, the covarion model is always favored over the optimal MBL model.
CONCLUSION: We demonstrated, using three large datasets, that the covarion model 
is more efficient at handling heterotachy than the MBL model. This is probably 
due to the fact that the MBL model requires a serious increase in the number of 
parameters, as compared to two supplementary parameters of the covarion 
approach. Further improvements of the both the mixture and the covarion 
approaches might be obtained by modeling heterogeneous behavior both along time 
and across sites.