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In recent years there has been a trend of leaving the strict molecular clock in order to infer dating of speciations and other evolutionary events.

Explicit modeling of substitution rates and divergence times makes formulation of informative prior distributions for branch lengths possible.

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Recently, however, the field has seen considerable advances in speed of the best methods, among which PHYML [], the use of Bayesian methods in phylogenetic inference has been a field of active research in which not only the phylogeny itself has been sought, but also additional issues have been addressed, such as substitution rate hypotheses, accuracy of ancestral state inference, and the rooting problem, see [] and also a range of models with rate variation over lineages; these include auto-correlated models, i.e., the rate distribution for a particular branch depends on the rate value of the parent branch [] (Sennblad et al.: Parental guidance vs.

One might think that a model containing a birth-death prior on the tree branching would necessarily be consistent with a molecular clock, since the birth-death process generates ultrametric trees.

The molecular clock can be avoided, however, by modeling the substitution rates and branching times separately.

Models with birth-death priors on tree branching and auto-correlated or substitution rates among lineages have been proposed, enabling simultaneous inference of substitution rates and divergence times.

This problem has, however, mainly been analysed in the Markov chain Monte Carlo (MCMC) framework, an approach requiring computation times of hours or days when applied to large phylogenies.


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