Itay Mayrose & Sally Otto have just published (Molecular Biology and Evolution Advance Access) a neat new method to test the hypothesis of a discrete extrinsic cause for shifts in the rate of molecular evolution on a phylogeny.
According to this method, the authors first obtain an ultrametric phylogenetic tree for the species in their study. They then generate a set of stochastic character histories (Nielsen, 2002; Huelsenbeck et al., 2003) for the discrete character of interest. Example discrete characters might be a "life history trait, morphological feature, or habitat association" - in their empirical test they examine halophilic and freshwater Daphnia species.
Now armed with a distribution of possible character histories on their estimated phylogeny, the authors simultaneously maximize the likelihood of their sequence evolution model and a scaling factor r, a parameter that increases or suppresses the rate of molecular evolution along stochastically mapped branches in the tree. Then they average across character maps.
In an extremely clear analysis of their method, the authors show it capable of producing remarkably good estimates of r for trees with even a modest number of tips (e.g., 20-60) when the true underlying phylogeny is known without error (Figure panel A). Under these idealized circumstances, estimation of r is only slightly biased for small numbers of species - as is common for maximum likelihood methods.
The situation is slightly more complicated when an estimated phylogeny (rather than the true underlying tree and branch lengths) is used. Here, they show that estimation of r can be quite severely downwardly biased, particularly for large values of r (Figure panel B). They think that this is actually due to error in the ultrametricization of their phylogenies - since in their study they used the same data for phylogenetic inference as they do for the estimation of r. This problem is not at all ameliorated for ultrametric phylogenies obtained by Bayesian relaxed clock methods. In the end, this issue argues strongly for the simultaneous estimation of the phylogeny, the character history, and the concomitant variation in nucleotide substitution rates - something that the authors also recommend.
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