Dinosaur diversity and the rock record
Paul M. Barrett, Alistair J. McGowan & Victoria Page
The following provides supplementary information on methodological procedures and results.
1. ADDITIONAL COMMENTS ON METHODOLOGY
(a) Diversity estimation
Various methodologies have been applied to palaeobiodiversity estimation, most of which can be described as either ‘taxic’ or ‘phylogenetic’. Taxic approaches rely on simple counts of the taxa present, or inferred to be present, within a series of time intervals; phylogenetic approaches utilise schemes of evolutionary relationship to count not only taxa, but also the presence of evolutionary lineages inferred from cladograms (Smith 1994). Both methodologies have some disadvantages due to the various assumptions they incorporate. Mosttaxic approaches make three major assumptions: that sampling is uniform in all intervals; that fossil preservation has been constant through time; and that taxonomists working on different groups classify organisms in a similar manner (Smith 2007). Pseudoextinctions, cases in which taxonomic practice assigns fossils from the same lineage to different taxa, are also a source of concern with the taxic approach. The phylogenetic method is not vulnerable to this problem (Smith 1994), but relies on accurate and stable phylogenetic hypotheses and assumes that the cladograms used to infer diversity estimates are correct. In addition, phylogenetic methods can only extend taxon originations backwards, and make the same assumption as the taxic method that the last known occurrence of a taxon represents its extinction. Finally, the phylogenetic method tends to inflate diversity due to the inclusion of inferred lineages. In both cases, the biasing effects of uneven sample sizes and differential sampling effort relative to palaeoenvironments and spatial distribution can be controlled using rarefaction (e.g. Gotteli & Colwell 2001; Alroy et al. 2001, 2008). Here, we use both taxic and phylogenetic approaches to estimate dinosaur diversity through time, focusing on the three major dinosaur clades: Ornithischia, Theropoda and Sauropodomorpha.
(b) Discrepancies between taxic (TDE) and phylogenetic (PDE) diversity estimates
In theory, the PDE should always be higher than the TDE in any particular timeslice as the former incorporates both standing diversity (the basis for the TDE) and the cryptic diversity predicted by the branching patterns of a cladogram. However, in practice, phylogenetic analyses rarely sample clades perfectly and dinosaurs were no exception to this. Exclusion of taxa from analyses results from a variety of factors, including specimen incompleteness and lack of adequate published descriptions (both of which lead to either errors or omissions in character scoring and thereby reduce resolution and/or support of the resulting cladogram). No phylogenetic analyses of dinosaurs contain all valid genera and this results in some cases where TDE are much higher than PDE: the number of valid taxa can considerably outweigh the number that can be included in an analysis. Total numbers of dinosaur taxa assigned to the clades studied herein and the number of those taxa included within the PDE are shown below:
1)Sauropodomorpha: 118 valid genera included, 54 sampled in phylogeny (45.7% of total).
2)Theropoda: 247 valid genera included, 121 sampled in phylogeny (48.9% of the total).
3)Ornithischia: 178 valid genera included, 112 sampled in phylogeny (62.9% of the total).
(c) Construction of cladograms
Source cladograms were obtained from the individual chapters in Weishampel et al. (2004) and combined to produce an informal supertree. Available supertrees (e.g. Lloyd et al. 2008) were avoided as these recover some sets of relationships not present in any of the source trees. As some taxa are present in more than cladogram (e.g. as part of the ingroup in one analysis and as part of theoutgroup in another) there is the potential for conflict. However, there were relatively few cases in which such conflicts occurred. Conflicts were resolved by taking the opinion of thoseauthors conducting the least inclusive analysis of a particular clade, as these analyses are those that are focused on specific ingroups and therefore have the more relevant lists ofcharacters. For example, the position of Barapasaurus varies between the basal sauropodomorph and sauropod analyses presented in Weishampel et al. (2004: Galton & Upchurch in this volume,versus Upchurch et al. in the same volume). In this case Barapasaurus was part of the ingroup of sauropods and the results of the ingroup analysis (that of Upchurch et al.) were followed herein. All conflicts within the cladograms could be resolved in this manner.
2. RESULTS OF STATISTICAL COMPARISONS AND ROCK-RECORD MODELLING
(a) Comparisons between TDE and PDE
Genus-level TDE and PDE obtained for the same clade are strongly positively correlated with each other (Table S1), suggesting that these diversity estimation methods are sampling the same underlying signal. Correlations between the ornithischian and theropod TDE and PDE are also strong (Table S2), while those between theropods and sauropodomorphs and ornithischians and sauropodomorphs are weaker.
Table S1. Results of correlation tests between TDE and PDE for each dinosaur clade (p < 0.01 in all cases).
Pearson's () / adjusted / Spearman's (rS) / Kendall's Ornithischia / 0.959 / 0.918 / 0.961 / 0.872
Theropoda / 0.715 / 0.505 / 0.757 / 0.605
Sauropodomorpha / 0.806 / 0.646 / 0.633 / 0.509
Table S2. Pearson’s product moment correlations () between the TDE and PDE diversity estimates for the three clades. Correlations between TDE lie above the diagonal; those for PDE lie below the diagonal (p > 0.01 in all cases except for the correlation between the PDE of ornithischians and sauropodomorphs, where p = 0.05).
Ornithischia / Theropoda / SauropodomorphaOrnithischia / –– / 0.893 / 0.429
Theropoda / 0.773 / –– / 0.421
Sauropodomorpha / 0.215 / 0.554 / ––
(b) Models
Table S3. Equations of the linear models describing TDE and PDE as a function of the number of DBF.
model (diversity~DBF)Ornithischia TDE / y = 0.1999x - 1.9892
Ornithischia PDE / y = 0.2660x - 1.3263
Theropoda TDE / y = 0.2877x - 2.5116
Theropoda PDE / y = 0.3251x - 7.4032
Sauropodomorpha TDE / y = 0.1192x - 0.6157
Sauropodomorpha PDE / y = 0.0977x - 2.033
(c) Modelling PDE and the rock record
The residuals of PDE from the modelled diversity estimates (MDE) are shown in Figure S1. Ornithischians show no notable residuals (figure S1a). Theropods show significant negative residuals during the Late Triassic and the Maastrichtian (figure S1b): both troughs probably result, in part, from under-representation of taxa from these intervals in the source phylogenies (see below). Finally, the sauropod residuals show a wide confidence limit (as explained in the text), but the PDE values also split into two phases, with higher than expected diversity during the Jurassic then lower than expected diversity during the Cretaceous (figure S1c). For ornithischians and sauropodomorphs, the pattern of residuals generated from the PDE/MDE is similar to that for the TDE/MDE residuals. More differences occur between the two sets of residuals generated for the theropod dataset, which may in part be due to taxon sampling within the phylogenetic analyses (see below).
Figure S1. Time-series of residuals of observed PDE from predicted MDE based on power-law models. Alternating grey/white bins mark durations of Standard International Stages (see Gradstein et al. 2004), starting with the Anisian stage of the Middle Triassic. Dashed lines mark 95% confidence limits. (a) Ornithischia. (b) Theropoda. (c) Sauropodomorpha. See text for further details.
(d) Potential artefacts
For theropods, residuals generated by subtracting PDE from MDE are exceptionally low for all three clades during the Late Triassic and Maastrichtian (figure S1). These may be partially artefactual, resulting from the relatively small number of taxa from each of these time intervals that were incorporated into the theropod cladogram (23/50 Maastrichtian genera and 3/15 Late Triassic genera, respectively). In addition, it is possible that the declines seen in the ornithischian and theropod residuals (generated from the PDE) prior to the K-P boundary may, in part, be an edge effect caused by the lack of lineages crossing into the Tertiary. However, the same trend is seen in the TDE, which would not be affected by this phenomenon. Moreover, it is noteworthy that the Maastrichtian has the highest number of opportunities to collect, yet witnessed a sharp decline in diversity, suggesting that the decline is a genuine biological signal.
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