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.]
Highlights
Indices of stratigraphic congruence variously assess the difference between first occurrence dates in the fossil record and divergence times implied by the branching structure of a phylogeny (Norell and Novacek 1992; Huelsenbeck, 1994; Benton and Storrs, 1994; Siddall, 1996; Hitchin and Benton, 1997; Wills, 1999; Pol and Norell, 2001; Pol et al, 2004; Lelièvre et al, 2008; Wills et al, 2008; O’Connor et al, 2011; Bell and Lloyd, 2015)
Which indices have the widest utility? We address these questions in two ways: firstly using simulations for several contrived cases, and secondly using a large empirical data set of 647 published cladograms
We explored extremes of balance in our simulations since we have previously demonstrated that Gap excess ratio (GER), stratigraphic consistency index (SCI) and MSM* are all progressively depressed as tree balance increases (Wills et al 1998, 2008)
Summary
Indices of stratigraphic congruence variously assess the difference between first occurrence dates in the fossil record and divergence times implied by the branching structure of a phylogeny (Norell and Novacek 1992; Huelsenbeck, 1994; Benton and Storrs, 1994; Siddall, 1996; Hitchin and Benton, 1997; Wills, 1999; Pol and Norell, 2001; Pol et al, 2004; Lelièvre et al, 2008; Wills et al, 2008; O’Connor et al, 2011; Bell and Lloyd, 2015). A good fit between phylogenetic inferences and fossil dates can be regarded as mutually corroborative, and a prerequisite for using those same dates to time calibrate the tree. Developing stratigraphic congruence indices that can be interpreted straightforwardly and compared across trees is important for palaeontologists, but for all who seek to quantify evolutionary rates (Wiens, 2004; Jenner et al 2009; Clarke et al, 2011; Joyce et al, 2013; Legg et al 2013; Sansom and Wills, 2013; Wheeler, 2013). The stratigraphic distributions of fossils can be used to inform or constrain phylogenetic hypotheses (Wagner, 1995a, 1995b, 2005; Fisher, 2008), with tip dating (Pyron, 2011) and total evidence dating (Ronquist et al 2012) approaches being increasingly implemented (Lee and Palci, 2015; O’Reilly et al, 2015). The vast majority of cladograms are inferred from the distributions of morphological or molecular character states across taxa alone, and without reference to explicitly temporal data
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