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’.
Highlights
It is universally recognized that the substitution rate undergoes substantial variation through time
By tuning the relative variance of its two components, the mixed clock interpolates between the uncorrelated and correlated relaxed clocks, containing them as particular cases. Applying this mixed clock model to an empirical dataset leads to a simple measure of how the total variation in substitution rate across the tree is partitioned into the Brownian and the white noise components, which yields potentially useful insight about how rate variation unfolds over different time scales
Isolated spikes of high rates of substitution can be observed at specific locations, in particular, at the base of Strepsirhini (Primates), Hystricomorpha (Rodentia), Yangochiroptera (Chiroptera) and Cetartiodactyla. In contrast to this complex history of rate variation inferred under the pure Brownian clock, the Brownian component of the mixed clock shows much simpler broad-scale patterns, essentially attributing high, medium or low rates across entire mammalian orders, in a way that seems to correlate with the typical body mass characterizing the members of these clades
Summary
It is universally recognized that the substitution rate undergoes substantial variation through time. By tuning the relative variance of its two components, the mixed clock interpolates between the uncorrelated and correlated relaxed clocks, containing them as particular cases Applying this mixed clock model to an empirical dataset leads to a simple measure of how the total variation in substitution rate across the tree is partitioned into the Brownian and the white noise components, which yields potentially useful insight about how rate variation unfolds over different time scales. In part because it offers less opportunity for locally controlling the impact of specific fossil calibrations, tip-dating may show—or perhaps more fundamentally reveal—a strong sensitivity of the dating analysis to the choice of the relaxed clock model and of the prior on divergence times In this context, complex interactions between the priors on times and on rates could make the interpretation of formal model comparison or selection less straightforward. The two methods are not provided with comparable fossil information, and no meaningful conclusion can be drawn, as to their relative merits, from the results presented
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