DOI: 10.5061/dryad.rs449
title: Data from: The past sure is tense: on interpreting phylogenetic divergence time estimates

description: Divergence time estimation — the calibration of a phylogeny to geological
 time — is an integral first step in modelling the tempo of biological
 evolution (traits and lineages). However, despite increasingly
 sophisticated methods to infer divergence times from molecular genetic
 sequences, the estimated age of many nodes across the tree of life
 contrast significantly and consistently with timeframes conveyed by the
 fossil record. This is perhaps best exemplified by crown angiosperms,
 where molecular clock (Triassic) estimates predate the oldest (Early
 Cretaceous) undisputed angiosperm fossils by tens of millions of years or
 more. While the incompleteness of the fossil record is a common concern,
 issues of data limitation and model inadequacy are viable (if
 underexplored) alternative explanations. In this vein, Beaulieu et al.
 (2015) convincingly demonstrated how methods of divergence time inference
 can be misled by both (i) extreme state-dependent molecular substitution
 rate heterogeneity and (ii) biased sampling of representative major
 lineages. These results demonstrate the impact of (potentially common)
 model violations. Here, we suggest another potential challenge: that the
 configuration of the statistical inference problem (i.e., the parameters,
 their relationships, and associated priors) alone may preclude the
 reconstruction of the paleontological timeframe for the crown age of
 angiosperms. We demonstrate, through sampling from the joint prior (formed
 by combining the tree (diversification) prior with the calibration
 densities specified for fossil-calibrated nodes) that with no data present
 at all, that an Early Cretaceous crown angiosperms is rejected (i.e., has
 essentially zero probability). More worrisome, however, is that for the 24
 nodes calibrated by fossils, almost all have indistinguishable marginal
 prior and posterior age distributions when employing routine lognormal
 fossil calibration priors. These results indicate that there is inadequate
 information in the data to overrule the joint prior. Given that these
 calibrated nodes are strategically placed in disparate regions of the
 tree, they act to anchor the tree scaffold, and so the posterior inference
 for the tree as a whole is largely determined by the pseudo-data present
 in the (often arbitrary) calibration densities. We recommend, as for any
 Bayesian analysis, that marginal prior and posterior distributions be
 carefully compared, especially for parameters of direct interest. This
 recommendation is not novel. However, given how rarely such checks are
 carried out in evolutionary biology, it bears repeating. Ideally such
 practices will become customarily integrated into both the peer review
 process, as well as part of the standard workflow for conscientious
 scientists. Finally, we note that the results presented here do not refute
 the biological modelling concerns identified by Beaulieu et al. (2015).
 Both sets of issues remain apposite to the goals of accurate divergence
 time estimation, and only by considering them in tandem can we move
 forward more confidently.
description: Fig. S1: Crown
 angiosperm age traceFigure S1: Traces of the
 age of the crown angiosperm node across replicate analyses (burnin phase
 only) for Beaulieu et al. (2015) (top) and Magallo ́n et al. (2015)
 (bottom) data sets. Top: prior (lognormal priors), orange (n = 2);
 posterior (lognormal priors), blue (n = 3); prior (exponential priors),
 red (n = 2); posterior (exponential priors), green (n = 3). Bottom: prior
 (no angiosperm constraint), orange (n = 4); posterior (no angiosperm
 constraint), blue (n = 4); prior (all constraints), green (n = 4);
 posterior (all constraints), red (n = 3; note that this is mostly obscured
 by the green prior trace). All analyses were initialized with the age of
 crown angiosperms set at ∼140 Ma.FigS1.pdfPosterior-landPlants.4gene.original.lognormal.constraintsBEAST xml file to carry out the posterior analysis of angiosperm divergence times using the original lognormal fossil calibration priors.Prior-landPlants.4gene.original.lognormal.constraintsBEAST xml file to carry out the prior analysis of angiosperm divergence times using the original lognormal fossil calibration priors.Posterior-landPlants.4gene.extreme_exponential_constraintsBEAST xml file to carry out the posterior analysis of angiosperm divergence times using the extreme exponential fossil calibration priors.Posterior-landPlants.4gene.uniform_spermatophytesBEAST xml file to carry out the posterior analysis of angiosperm divergence times using the uniform fossil calibration priors.Prior-landPlants.4gene.uniform_spermatophytesBEAST xml file to carry out the prior analysis of angiosperm divergence times using the uniform fossil calibration priors.Prior-landPlants.4gene_extreme_exponential_constraintsBEAST xml file to carry out the prior analysis of angiosperm divergence times using the extreme exponential fossil calibration priors.