A mixed relaxed clock model

Abstract

Over recent years, several alternative relaxed clock models have been proposed in the context of Bayesian dating. These models fall in two distinct categories: uncorrelated and autocorrelated across branches. The choice between these two classes of relaxed clocks is still an open question. More fundamentally, the true process of rate variation may have both long-term trends and short-term fluctuations, suggesting that more sophisticated clock models unfolding over multiple time scales should ultimately be developed. Here, a mixed relaxed clock model is introduced, which can be mechanistically interpreted as a rate variation process undergoing short-term fluctuations on the top of Brownian long-term trends. Statistically, this mixed clock represents an alternative solution to the problem of choosing between autocorrelated and uncorrelated relaxed clocks, by proposing instead to combine their respective merits. Fitting this model on a dataset of 105 placental mammals, using both node-dating and tip-dating approaches, suggests that the two pure clocks, Brownian and white noise, are rejected in favour of a mixed model with approximately equal contributions for its uncorrelated and autocorrelated components. The tip-dating analysis is particularly sensitive to the choice of the relaxed clock model. In this context, the classical pure Brownian relaxed clock appears to be overly rigid, leading to biases in divergence time estimation. By contrast, the use of a mixed clock leads to more recent and more reasonable estimates for the crown ages of placental orders and superorders. Altogether, the mixed clock introduced here represents a first step towards empirically more adequate models of the patterns of rate variation across phylogenetic trees.This article is part of the themed issue ‘Dating species divergences using rocks and clocks’.

Synonymous mutations and the molecular evolution of SARS-Cov-2 origins

“…However, we warn that a residual cause of unmodeled statistical uncertainty is deviations from the molecular clock. Variation in the molecular clock could be modeled statistically (see e.g., Drummond, et al 2006 and Lartillot, et al 2016), but the fact that synonymous mutations are mostly saturated for more divergent viruses that would be needed to train such models, is a challenge to such efforts. On the positive side, we note that the estimates of d S given in Table 3 in general are highly compatible with a constant molecular clock.…”

A new method for detecting autocorrelation of evolutionary rates in large phylogenies

“…Knowledge that evolutionary rates are generally autocorrelated within lineages will foster unbiased and precise dating of the tree of life, whenever one needs to choose a rate model to generate accurate Bayesian time estimates for use in studies of biodiversity, phylogeography, development, and genome evolution. However, it is important to appreciate that no single rate model may be adequate for Bayesian dating analyses, and one may need to use a mixture of models because different groups of species and genes in a large phylogeny may have evolved with different levels of autocorrelation (e.g., Lartillot et al (2016)). In this sense, the results produced by CorrTest (and by Bayes Factor) analyses primarily detect the presence of rate autocorrelation, but they do not tell us if the rate autocorrelation exists in every clade of a phylogeny or if the degree of autocorrelation is the same in all the clades.…”

Timing the extant avian radiation: The rise of modern birds, and the importance of modeling molecular rate variation

“…However, further development of these models is made more challenging by the enormous number of factors that can influence substitution rates, including but not limited to aspects of molecular biology, physiology, life history, and demography (Mooers and Harvey 1994;Welch et al 2008;Bromham 2009;Lanfear et al 2010aLanfear et al , 2014Hodgkinson and Eyre-Walker 2011). Perhaps because of this complexity, most approaches to modelling substitution rate variation among lineages use sophisticated statistical models that largely ignore the biological causes and correlates of substitution rate variation, although there are notable exceptions (Lartillot and Poujol 2010;Lartillot et al 2016). If we are to time-calibrate the evolutionary history of birds, let alone all life, it will be important to consider instances where the most widely-used models of substitution rate variation may be misleading.…”

“…Encouragingly, such models are already being developed (Lartillot and Poujol 2010), providing a more sophisticated framework from which to account for the issues outlined above. This class of models could be further expanded to guide expectations of rate changes along specific branches of a given tree using advances in divergence dating that incorporate fossils as terminal taxa (Ronquist et al 2012;Zhang et al 2015) and mixed clock models that allow the degree of rate-autocorrelation to fluctuate (Lartillot et al 2016). By reconstructing ancestral states using fossil data (potentially incorporating expectations of preservation bias or temporal gaps), this would highlight where on a tree to expect changes in traits that might otherwise be masked by the absence of fossil taxa.…”