Partition number, rate priors and unreliable divergence times in Bayesian phylogenetic dating.

More loci/partitions should improve Bayesian estimation of divergence times on phylogenies but it has recently been shown that this can lead to surprisingly poor estimation due to the way it affects the prior on mean substitution rate. Here we consider the likely impact of partition number on divergence time analyses carried out using the program BEAST. Mitochondrial genome data from toad-headed lizards (genus Phrynocephalus) from the Qinghai-Tibetan Plateau were used to examine this effect. Under increased partitioning of the sequences, BEAST posterior divergence times became unreasonably narrow and downwardly biased due to misspecification of the mean substitution rate prior. This effect was detectable when relatively few partitions were used (i.e. between four and eight), but became very acute for 27-86 partitions. Fortunately, a correction that adjusts the standard deviation of the mean of locus rates led to results that were equivalent to those obtained using the latest version of the program MCMCtree, which implements a new gamma-Dirichlet prior to overcome this problem. A review of the literature shows that a substantial number of BEAST dating studies are likely to have been affected by this misspecification of the rate prior.