Rate variation and estimation of divergence times using strict and relaxed clocks

Abstract

Background: Understanding causes of biological diversity may be greatly enhanced by knowledge of divergence times. Strict and relaxed clock models are used in Bayesian estimation of divergence times. We examined whether: i) strict clock models are generally more appropriate in shallow phylogenies where rate variation is expected to be low, ii) the likelihood ratio test of the clock (LRT) reliably informs which model is appropriate for dating divergence times. Strict and relaxed models were used to analyse sequences simulated under different levels of rate variation. Published shallow phylogenies (Black bass, Primate-sucking lice, Podarcis lizards, Gallotiinae lizards, and Caprinae mammals) were also analysed to determine natural levels of rate variation relative to the performance of the different models.

Results: Strict clock analyses performed well on data simulated under the independent rates model when the standard deviation of log rate on branches, σ, was low (≤ 0.1), but were inappropriate when σ>0.1 (95% of rates fall within 0.0082-0.0121 subs/site/Ma when σ = 0.1, for a mean rate of 0.01). The independent rates relaxed clock model performed well at all levels of rate variation, although posterior intervals on times were significantly wider than for the strict clock. The strict clock is therefore superior when rate variation is low. The performance of a correlated rates relaxed clock model was similar to the strict clock. Increased numbers of independent loci led to slightly narrower posteriors under the relaxed clock while older root ages provided proportionately narrower posteriors. The LRT had low power for σ = 0.01-0.1, but high power for σ = 0.5-2.0. Posterior means of σ2 were useful for assessing rate variation in published datasets. Estimates of natural levels of rate variation ranged from 0.05-3.38 for different partitions. Differences in divergence times between relaxed and strict clock analyses were greater in two datasets with higher σ2 for one or more partitions, supporting the simulation results.

Conclusions: The strict clock can be superior for trees with shallow roots because of low levels of rate variation between branches. The LRT allows robust assessment of suitability of the clock model as does examination of posteriors on σ2.

Figure 1

Summaries of dating analyses on simulated data (frequencies). Frequencies of recovery of all node ages by strict and relaxed clock analyses in MCMCTREE and MULTIDIVTIME, for different standard deviations of the log rate (σ).

Figure 2

Summaries of dating analyses on simulated data (posterior means). A. Posterior means and 95% interval widths (means from 100 simulations) for MCMCTREE strict clock (circles) and independent rates (squares) analyses for nodes with true ages of 0.6 and 0.2 (shown in Figure 4A). B. Posterior means and 95% interval widths (means from 100 simulations) for MULTIDIVTIME strict clock (circles) and correlated rates (squares) analyses.

Figure 3

Summary of likelihood ratio tests on simulated data. Frequency of rejection of the clock for replicates generated under different σ.

Figure 4

Trees used in simulations. The 10 species (A), 5 species (B), and 20 species (C) trees used in the simulations. Posteriors on nodes marked with filled circles are summarized in Figire 2.

Figure 5

Trees used for dating the five real datasets. A. Black bass, B. Primate-sucking lice, C. Podarcis lizards, D. Gallotiinae, E. Caprinae. Trees are shown as chronograms which use the posterior mean node ages from the MCMCTREE relaxed clock analyses.