Measuring Stratigraphic Congruence Across Trees, Higher Taxa, and Time

Abstract

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 indices 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 (SCI), the modified Manhattan stratigraphic measure (MSM*), and the gap excess ratio (GER) (plus its derivatives; the topological GER and the modified GER). 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 (FO) dates, center of gravity of FO dates, the variability of FO dates, percentage of extant taxa, and percentage of taxa with no fossil record). Our empirical data set comprised 647 published animal and plant cladograms spanning the entire Phanerozoic, and for these data we also modeled the effects of mean age of FOs (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 FO 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 GER 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. [Fossil calibration; gap excess ratio; manhattan stratigraphic metric; molecular clocks; stratigraphic congruence.]