Comparison of different strategies for using fossil calibrations to generate the time prior in Bayesian molecular clock dating

Abstract

Fossil calibrations are the utmost source of information for resolving the distances between molecular sequences into estimates of absolute times and absolute rates in molecular clock dating analysis. The quality of calibrations is thus expected to have a major impact on divergence time estimates even if a huge amount of molecular data is available. In Bayesian molecular clock dating, fossil calibration information is incorporated in the analysis through the prior on divergence times (the time prior). Here, we evaluate three strategies for converting fossil calibrations (in the form of minimum- and maximum-age bounds) into the prior on times, which differ according to whether they borrow information from the maximum age of ancestral nodes and minimum age of descendent nodes to form constraints for any given node on the phylogeny. We study a simple example that is analytically tractable, and analyze two real datasets (one of 10 primate species and another of 48 seed plant species) using three Bayesian dating programs: MCMCTree, MrBayes and BEAST2. We examine how different calibration strategies, the birth-death process, and automatic truncation (to enforce the constraint that ancestral nodes are older than descendent nodes) interact to determine the time prior. In general, truncation has a great impact on calibrations so that the effective priors on the calibration node ages after the truncation can be very different from the user-specified calibration densities. The different strategies for generating the effective prior also had considerable impact, leading to very different marginal effective priors. Arbitrary parameters used to implement minimum-bound calibrations were found to have a strong impact upon the prior and posterior of the divergence times. Our results highlight the importance of inspecting the joint time prior used by the dating program before any Bayesian dating analysis.

Keywords: Bayesian inference; Divergence times; Fossil calibration; Molecular clock dating; Time prior.

Graphical abstract

Fig. 1

A five-species phylogeny used in the analytical example of fossil calibration strategies.

Fig. 2

Probability densities for describing uncertainties in fossil calibrations: (a) soft minimum bound represented by a shifted-exponential distribution specified as t_L = 20, p = 0.1, c = 0.1, p_L = 0.01; (b) soft maximum bound specified as “t_U = 80, p_R = 0.05”; and (c) soft lower and upper bound, specified as “t_L = 20, t_U = 80, p_L = 0.01, p_U = 0.05”. Black solid lines represent calibration densities. Red dashed lines represent (a) minimum age (t_L,), (b) maximum age (t_U) and (c) both (t_L, t_U). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 3

User-specified calibrations and effective priors for node ages t₁ and t₄ under three calibration strategies (st1, st2, st3) in a simple example of five species (Fig. 1), generated using the (a) conditional and (b) the multiplicative construction. Dashed lines represent the user-specified calibration densities, while dotted lines represent the effective prior densities.

Fig. 4

Phylogenies for (a) 10 primate species, and (b) 48 seed plant species. Calibration nodes are indicated by black solid circles.

Fig. 5

User-specified calibrations and effective priors for node ages t₁ and t₄ under three calibration strategies (st1, st2, st3) in a simple example of five species (Fig. . 1), generated using (a) MCMCTree; (b) MrBayes; (c) BEAST1 and (d) BEAST2. Dashed lines represent the user-specified calibration densities, while dotted lines represent the effective prior densities.

Fig. 6

Means and 95% CIs in the time prior (the prior for node ages) on the primate phylogeny (Fig. 5a) generated using calibration strategies st1 and st2 and three dating programs: MCMCTree, BEAST2 and MrBayes.

Fig. 7

User-specified calibration densities (dashed lines), effective time priors (dotted lines), and the posterior (solid lines) for the primate dataset, under calibration strategies st1 (red) and st2 (black), implemented in MCMCTree, BEAST2 and MrBayes.

Fig. 8

Timetrees showing posterior divergence time estimates for the primates. The branches are drawn to reflect the posterior means of node ages and the bars represent 95% HPD intervals. The dataset was analysed using MCMCTree, MrBayes amd BEAST2 under the independent-rates model, using calibration strategies st1 and st2.

Fig. 9

Means and 95% CIs in the time prior for node ages on the seed plant phylogeny (Fig. 5b) generated using three calibration strategies (st1-3) and three dating programs: MCMCTree, BEAST2 and MrBayes. Calibration nodes are highlighted in red.

Fig. 10

User-specified calibration densities (dashed lines), effective time priors (dotted lines), and the posterior (solid lines) for the seed plant dataset, under calibration strategies st1 (red), st2 (black), and st3 (blue), implemented in MCMCTree, BEAST2 and MrBayes. Only the 15 calibration nodes are used in the plots.

Fig. 11

Timetrees showing posterior divergence time estimates for major seed plant groups. The branches are drawn to reflect the posterior means of node ages and the bars represent 95% HPD intervals. The dataset was analysed using MCMCTree, MrBayes amd BEAST2 under the independent-rates model, using three calibration strategies: st1, st2, and st3.