We provided the first comprehensive analysis of two of the most frequently used fast dating methodologies against Bayesian molecular dating employing several empirical phylogenomic datasets from distinct biological groups, including up to hundreds of taxa. We measured differences in node age estimates, coverage of the Bayesian credibility intervals and computational time efficiency. Our findings indicate that RFF, as implemented in RelTime, is a fast alternative to time-consuming molecular dating softwares. RelTime was much faster and generally provided time estimates closer to the Bayesian node ages than treePL. TreePL, which is considered a fast algorithm to perform molecular dating, required a significant computational time. This was due to the bootstrapping strategy used to compute confidence intervals of time estimates. As CIs are necessary to interpret biological scenarios derived from timetrees, their calculation entailed a running time that were comparable to Bayesian approaches, with some running times of more than one month.
Studies that have evaluated treePL performance against other approaches are scarce. The original work describing its implementation performed an evaluation using simulated and empirical data [40]. However, simulations did not include alignments, as the divergence times were directly inferred from the true tree, and the empirical datasets did not consist of several loci. Previous works employing both Bayesian approaches and treePL compared time estimates for specific taxa [59, 60], and their results are contrasting, with treePL leading either to older time estimates and narrower CIs than BEAST in angiosperm evolution [60], or younger node ages and wider CIs than BEAST in a flowering plant family [59]. In the present study, treePL CIs were narrower than Bayesian CIs for all datasets analyzed. This result is expected, because the bootstrap procedure leads to reduced parametric uncertainty as the number of sites increase, which is the case for phylogenomic data. Regarding time estimates, we found that treePL tended to produce older estimates than Bayesian analyses (Fig. 1a). This is in agreement with other works that have compared PL to Bayesian and non-Bayesian approaches [61–64]. It is already known that PL may provide overly ancient divergence time estimates when there is no calibration information to limit node ages near the root because of optimization issues [65]. The absence of efficient time constraints at deeper nodes was, in fact, common to all the analyses where older estimates were obtained (β > 1.1). For most of these datasets, treePL placed the age of the deep nodes exactly at or very close to the values provided as loosse maxima. Additionally, our findings corroborate Barba-Montoya et al. (2021), where TreePL was more impacted by small deviations from the molecular clock. This probably resulted in more asymmetrical distributions of \(\stackrel{-}{D}\) values for treePL, while RelTime presented lower asymmetry (Supporting information 2).
Comparisons between time estimates retrieved by the RFF and Bayesian methods have been carried out in several empirical studies [12, 22, 25, 42, 43, 66–68]. Mello et al. (2017) and Tao et al. (2020) employed phylogenomic datasets and found that RelTime produced reliable time estimates when compared to BEAST and MCMCTree. Here, we extended these findings to PhyloBayes software, which implements more sophisticated substitution models. Although MEGA does not provide the option to use the site-heterogeneous models implemented in PhyloBayes, times inferred employing the simpler models available in MEGA exhibited good correspondence to PhyloBayes estimates. The equivalence between timescales from simple and complex homogeneous substitution models was reported elsewhere [69]. We confirmed this finding and showed that it can be extended to site-heterogeneous substitution models.
If researchers need a faster alternative to Bayesian dating, our work demonstrated the good performance of the RelTime’s RFF when compared to treePL. Besides providing node ages closer to Bayesian estimates, RelTime infereed ages lied within Bayesian CIs more frequently. Recently, using simulated data, Barba-Montoya et al. (2021) also recovered a greater accuracy for RelTime when compared to other fast dating methods, particularly when autocorrelated rates were used. We showed that for empirical phylogenomic datasets, in which the true rate model is unknown, RelTime also performed better than treePL to approximate the standard Bayesian procedure.
Although Bayesian credibility intervals are not strictly comparable with confidence intervals produced by bootstrapping, empirical biologists use both metrics as measures of uncertainty of the estimated node ages when testing evolutionary scenarios. Therefore, we were prompted to contrast CI widths of Bayesian, RelTime and treePL estimates to compare the degree of uncertainty of the infereed times. On average, treePL CIs were 5 times narrower than Bayesian CIs, while RelTime produced CIs that were ca. 2 times wider than the Bayesian CIs. The greater precision of treePL when compared to Bayesian methods was also recovered using simulated data [47]. Simulations also have shown that RelTime CIs exhibit equivalent or greater coverage probabilities than Bayesian approaches [42]. Therefore, our analysis of empirical datasets confirmed that the uncertainty associated with RelTime estimates are closer to the Bayesian CIs.
Besides having good statistical proprieties, we expect fast dating methods to reduce computational time significantly. We demonstrated that, on average, RelTime was 60 times faster than treePL. On the age of big data, such speed-up makes large-scale biological hypotheses testing feasible. Moreover, previous works based on simulations that accessed PL performance against Bayesian approaches and RelTime found that it performed worse than these methods under various scenarios of heterogeneous rates [25, 70]. These findings, together with our results that certified the speed of RelTime, demonstrate the usefulness of the RRF to obtain biological timescale for large datasets.
The discrepancy between divergence time estimates from fast-dating and Bayesian methods was primarily influenced by the alignment length. Longer alignments resulted in larger differences between methods. This result is expected if methods rely on different modeling assumptions regarding parameters and evolutionary rate variation. Consequently, as sample size approaches infinity, estimates become significantly different. Although it seems that fast-dating and Bayesian methods are asymptotically different, even in the dataset with the longest alignment length (Ran18), the inferred timescales led to very similar biological interpretation of the scenario in which lineage diversification took place. For RelTime, calibration density significantly impacted the MSE of time estimates, implying that, besides alignment length, increasing the number of time constraints also makes the differences between methods more pronounced [47].
While previous work has advocated that RFF may not be suitable to infer divergence times for deep time datasets, leading to overly older time estimates [68], our analyses did not support this claim. Also, in contrast with a previous study [67], our results indicate that the strategy used by RelTime to calibrate timetrees [42] is as appropriate as the Bayesian calibration priors, yielding great correspondence between the timescales from both methods for most of the datasets (for ~ 78% of the datasets, β values deviated less than 0.2 from 1).
It is worth mentioning that larger differences between Bayesian analysis and RelTime may be retrieved at nodes connecting branches that have their lengths close to zero. Such lack of substitutions along branches cause RelTime to estimate more recent node ages. The fact that fast methods use branch lengths to estimate divergence times without relying on priors for node ages imply that, when some branches have near zero substitutions, they underestimate times when compared to Bayesian analysis. This occurs because divergence time priors assign lengths > 0 even when no substitutions are observed, as is the case of the coalescent prior [71]. This may also affect treePL estimates, as observed for the dataset of Fang18 (Supporting information 2), although treePL may also assign non-zero time values to branches in which the number of accumulated substitutions is effectively zero [40], leading to older inferred times than RelTime.
Our comparative analysis using a comprehensive empirical dataset has shown that fast dating methods are a viable alternative to time-consuming Bayesian methods to infer node ages for large-scale datasets. Additionally, we demonstrated that the RFF approach implemented in RelTime performed better, with a lower demand in computational times. Thus, we emphasize the efficacy of the RFF in establishing molecular timescales with excellent correspondence to those inferred by Bayesian approaches. Timescales from different dating frameworks were impacted by alignment length, suggesting that their asymptotic properties are different, although the biological meaning of the estimates did not change significantly. Furthermore, the quick estimation of confidence intervals of node ages allows for robust testing between several alternate evolutionary hypotheses, eliminating the computational burden brought forth by big data in biology.