Data from: Measuring stratigraphic congruence across trees, higher taxa, and time

The congruence between the order of cladistic branching and the first appearance dates of fossil lineages can be quantified using a variety of indices. Good matching is a prerequisite for the accurate time calibration of trees, while the distribution of congruence across large samples of cladograms has underpinned claims about temporal and taxonomic patterns of completeness in the fossil record. The most widely used stratigraphic congruence indices are the stratigraphic consistency index, the modified Manhattan stratigraphic measure, and the gap excess ratio (plus its derivatives; the topological gap excess ratio and the modified gap excess ratio). Many factors are believed to variously bias these indices, with several empirical and simulation studies addressing some subset of the putative interactions. This study combines both approaches to quantify the effects (on all five indices) of eight variables reasoned to constrain the distribution of possible values (the number of taxa, tree balance, tree resolution, range of first occurrence dates, center of gravity of first occurrence dates, the variability of first occurrence dates, percentage of extant taxa, and percentage of taxa with no fossil record). Our empirical data set comprised 647 published vertebrate and invertebrate cladograms spanning the entire Phanerozoic, and for these data we also modelled the effects of mean age of first occurrences (as a proxy for clade age), the taxonomic rank of the clade, and the higher taxonomic group to which it belonged. The center of gravity of first occurrence dates had not been investigated hitherto, and this was found to correlate most strongly with some measures of stratigraphic congruence in our empirical study (top-heavy clades had better congruence). The modified gap excess ratio was the index least susceptible to bias. We found significant differences across higher taxa for all indices; arthropods had lower congruence and tetrapods higher congruence. Stratigraphic congruence – however measured – also varied throughout the Phanerozoic, reflecting the taxonomic composition of our sample. Notably, periods containing a high proportion of arthropods had poorer congruence overall than those with higher proportions of tetrapods.分支系统学分支次序与化石谱系首次出现时间之间的一致性，可以通过多种指数进行量化。良好的匹配是对系统发育树进行精确时间校准的前提条件；而在大量分支图（cladogram）样本中呈现的一致性分布，则为有关化石记录完整性的时间与分类学模式的论断提供了支撑。目前应用最广泛的地层一致性指数（stratigraphic congruence indices）包括地层一致性指数（stratigraphic consistency index）、修正曼哈顿地层测度（modified Manhattan stratigraphic measure）以及缺口超额比（gap excess ratio）及其衍生形式：拓扑缺口超额比（topological gap excess ratio）与修正缺口超额比（modified gap excess ratio）。现有研究认为诸多因素会对这些指数产生不同程度的偏倚影响，已有多项实证与模拟研究针对这类假定的交互作用中的部分内容展开了探讨。本研究结合上述两类研究方法，对八种被认为会限制指数可能取值分布的变量（分别为分类单元数量、系统发育树平衡性、系统发育树分辨率、首次出现时间范围、首次出现时间重心、首次出现时间变异度、现生分类单元占比、无化石记录分类单元占比）对全部五种指数的影响进行了量化分析。本研究的实证数据集包含647篇已发表的、覆盖整个显生宙（Phanerozoic）的脊椎动物与无脊椎动物分支图；针对该数据集，我们还对首次出现平均年龄（作为演化支年龄的替代指标）、演化支的分类阶元以及其所属的高级分类群的影响进行了建模分析。首次出现时间重心这一变量此前尚未有相关研究涉及，而在本实证研究中，该变量与部分地层一致性指数的相关性最强；顶端偏向型演化支的一致性表现更佳。修正缺口超额比是受偏倚影响最小的指数。我们发现所有指数在不同高级分类群之间均存在显著差异：节肢动物的一致性表现较低，而四足动物则较高。无论采用何种方式衡量，地层一致性在整个显生宙期间均存在变化，这反映了本研究样本的分类学组成。值得注意的是，节肢动物占比高的时期，其整体一致性表现要低于四足动物占比更高的时期。