Data from: The past sure is tense: on interpreting phylogenetic divergence time estimates

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.分化时间估计（divergence time estimation）——即通过地质时间对系统发育（phylogeny）进行校准——是模拟生物演化（性状与演化支）节奏的核心首要步骤。然而，尽管从分子遗传序列推断分化时间的方法日趋精密，但生命之树中诸多节点的估算年龄，与化石记录所呈现的时间框架仍存在显著且一致的差异。其中以被子植物冠群（crown angiosperms）最为典型：分子钟（molecular clock）估算的三叠纪（Triassic）起源时间，比公认最早的被子植物化石（早白垩世（Early Cretaceous））早了数千万年甚至更久。尽管化石记录的不完整性是常见的解释，但数据限制与模型不足同样是合理（尽管尚未得到充分探索）的替代解释。对此，Beaulieu等人（2015）有力地证明了分化时间推断方法如何会被（i）极端的状态依赖型分子替换速率异质性，以及（ii）代表性大支系的有偏采样所误导。这些结果凸显了（可能普遍存在的）模型违反的影响。在此，我们提出另一项潜在挑战：仅统计推断问题的配置（即参数、参数间关系及相关先验），就可能无法重建被子植物冠群起源时间的古生物时间框架。我们通过联合先验（结合树（演化）先验与化石校准节点的校准密度所形成）的抽样证明：在完全无数据的情况下，早白垩世的被子植物冠群起源会被拒绝（即概率几乎为零）。但更令人担忧的是，对于24个经化石校准的节点，在使用常规对数正态化石校准先验时，几乎所有节点的边缘先验与后验年龄分布都难以区分。这些结果表明，数据中缺乏足够信息来推翻联合先验。鉴于这些校准节点被策略性地布置在系统发育树的各个迥异区域，它们起到了锚定树框架的作用，因此整个树的后验推断在很大程度上由（通常具有任意性的）校准密度中蕴含的伪数据所决定。与任何贝叶斯分析（Bayesian analysis）一样，我们建议应仔细比较边缘先验与后验分布，尤其是针对直接关注的参数。这一建议并非首创，但鉴于演化生物学领域中此类检查极少开展，仍有必要重申。理想情况下，此类实践应常规融入同行评审流程，以及严谨科学家的标准工作流程中。最后需指出，本文呈现的结果并未驳斥Beaulieu等人（2015）所指出的生物学建模顾虑。两类问题均与精准分化时间估计的研究目标息息相关，唯有同时兼顾二者，我们才能更有信心地推进研究。