The Implications of Lineage-Specific Rates for Divergence Time Estimation

Abstract

Rate variation adds considerable complexity to divergence time estimation in molecular phylogenies. Here, we evaluate the impact of lineage-specific rates-which we define as among-branch-rate-variation that acts consistently across the entire genome. We compare its impact to residual rates-defined as among-branch-rate-variation that shows a different pattern of rate variation at each sampled locus, and gene-specific rates-defined as variation in the average rate across all branches at each sampled locus. We show that lineage-specific rates lead to erroneous divergence time estimates, regardless of how many loci are sampled. Further, we show that stronger lineage-specific rates lead to increasing error. This contrasts to residual rates and gene-specific rates, where sampling more loci significantly reduces error. If divergence times are inferred in a Bayesian framework, we highlight that error caused by lineage-specific rates significantly reduces the probability that the 95% highest posterior density includes the correct value, and leads to sensitivity to the prior. Use of a more complex rate prior-which has recently been proposed to model rate variation more accurately-does not affect these conclusions. Finally, we show that the scale of lineage-specific rates used in our simulation experiments is comparable to that of an empirical data set for the angiosperm genus Ipomoea. Taken together, our findings demonstrate that lineage-specific rates cause error in divergence time estimates, and that this error is not overcome by analyzing genomic scale multilocus data sets. [Divergence time estimation; error; rate variation.].

Figure 1.

A summary of different classes of molecular evolutionary rate variation. The trees shown are phylograms, and in all cases taxa are sampled at the present. In all trees, the two divergence events occurred at time in the past, and time in the past. Therefore, branch length variation reflects molecular evolutionary rate variation. a) Lineage-specific rates. Among-branch-rate-variation is observed in each gene tree, but the pattern of among-branch-rate-variation is the same for each gene tree. The average rate for each branch therefore differs in the species tree. b) Gene-specific rates. The average rate across all branches differs for each gene tree but does so consistently for all branches. The average rate for each branch is therefore the same in the species tree. c) Residual rates. Among-branch-rate-variation is observed in all gene trees, but the pattern of among-branch-rate-variation is different for each gene tree. If a large number of loci are sampled, the average rate for each branch is the same in the species tree. d) Residual rates and lineage-specific rates. Because of the underlying lineage-specific rate, the average rate for each branch differs in the species tree.

Figure 2.

Summary of results from simulation experiments with different classes of rate variation and different numbers of sampled loci (each locus has a length of 800 bp). The unknown divergence time is inferred with a UCLN relaxed clock. Mean posterior age estimates from each experiment are plotted within bins of 0.2. The length of each plotted line corresponds to the number of estimates within each bin (see key). The line is plotted in gray if for more than 50% of replicate experiments plotted within a bin, the 95% HPD did not include the correct value. Otherwise the line is plotted in black. a) No rate variation, b) gene-specific rates, c) residual rates, d) lineage-specific rates, and d) lineage-specific rates and residual rates.

Figure 3.

The impact of increasingly strong lineage-specific rates on divergence time estimates. Points are plotted according to the same bins, sizes, and colors as Figure 2. In all cases, the unknown divergence time is inferred from 400 loci. a) of the UCLN relaxed clock is corrected such that it exactly matches of the distribution from which lineage-specific rates are simulated. b) of the UCLN relaxed clock is fixed at 0.15.