A General Comparison of Relaxed Molecular Clock Models

Abstract

Several models have been proposed to relax the molecular clock in order to estimate divergence times. However, it is unclear which model has the best fit to real data and should therefore be used to perform molecular dating. In particular, we do not know whether rate autocorrelation should be considered or which prior on divergence times should be used. In this work, we propose a general bench mark of alternative relaxed clock models. We have reimplemented most of the already existing models, including the popular lognormal model, as well as various prior choices for divergence times (birth-death, Dirichlet, uniform), in a common Bayesian statistical framework. We also propose a new autocorrelated model, called the "CIR" process, with well-defined stationary properties. We assess the relative fitness of these models and priors, when applied to 3 different protein data sets from eukaryotes, vertebrates, and mammals, by computing Bayes factors using a numerical method called thermodynamic integration. We find that the 2 autocorrelated models, CIR and lognormal, have a similar fit and clearly outperform uncorrelated models on all 3 data sets. In contrast, the optimal choice for the divergence time prior is more dependent on the data investigated. Altogether, our results provide useful guidelines for model choice in the field of molecular dating while opening the way to more extensive model comparisons.

A molecular palaeobiological hypothesis for the origin of aplacophoran molluscs and their derivation from chiton-like ancestors

“…These estimates varied only moderately, regardless of the model used to estimate branch lengths (CAT þ GTR þ G 4 versus WAG þ G 4 ), the relaxed molecular clock model applied (autocorrelated CIR versus uncorrelated white noise) or whether cephalopods were included (tables S2 and S3 in the electronic supplementary material). The most likely age for crown Aculiferans is 488 Ma (credibility interval: 517 -453 Ma); this is the estimate derived from the autocorrelated CIR model (figure 4), which has been shown to be the best-fitting model for amino acid datasets [41,51].…”

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“…hordei and B.g. tritici was used as the calibration point (5.2-7.4 million years ago 4 or 10,000-14,000 years ago 45 ) (Supplementary Note) under the independent gamma rate relaxed-clock model (white noise model) 46 .…”

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“…Consequently, RMC methods were developed that allow the rate of sequence evolution to vary across different branches (for reviews, see Welch and Bromham 2005;Lepage et al 2007;Ho and Phillips 2009). A number of different methods have been developed and debate continues as to which best captures biological reality (Drummond et al 2006;Lepage et al 2007;Ho and Phillips 2009;Linder et al 2011).…”

“…When rates are not autocorrelated, each rate is independent from the neighboring ones and randomly sampled from a probability distribution (e.g., the uncorrelated models introduced by Drummond et al 2006). In autocorrelated models, rates follow a diffusion process along lineages, with the rate in each branch being drawn a priori from a parametric distribution whose mean is a function of the rate on the parent branch (e.g., the log-normal [LogN] distribution) (Thorne et al 1998;Kishino et al 2001), in which the evolutionary rate varies according to a lognormal distribution; or the Cox -Ingersoll -Rand distribution (CIR) (Lepage et al 2007), which possesses a stationary distribution, contrasting with the linearly increasing variance of the LogN model.…”