Capturing heterotachy through multi-gamma site models

Most methods for performing a phylogenetic analysis based on sequence alignments of gene data assume that the mechanism of evolution is constant through time. It is recognised that some sites do evolve somewhat faster than others, and this can be captured using a (gamma) rate heterogeneity model. Further, some species have shorter replication times than others, and this results in faster rates of substitution in some lineages. This feature of lineage specific rate variation can be captured to some extent, by using relaxed clock models. However, it is also clear that there are additional poorly characterised features of sequence data that can sometimes lead to extreme differences in lineage specific rates. This variation is poorly captured by constant time reversible substitution models. The significance of extreme lineage specific rate differences is that they lead both to errors in reconstructing evolutionary relationships as well as biased estimates for the age of ancestral nodes. We propose a new model that allows gamma rate heterogeneity to change on branches, thus offering a more realistic model of sequence evolution. It adds negligible computational cost to likelihood calculations. We illustrate its effectiveness with an example of green algae and land-plants. For many real world data sets, we find a much better fit with multi-gamma sites models as well as substantial differences in ancestral node date estimates.