two phylogenies that matched 95% of their taxa would not be considered redundant by our measure, since they do not have exactly the same taxon sample. This is likely to skew our results in unpredictable ways, depending on which taxa occur more frequently in the “group” under consideration. For instance, our sample of 655 dinosaur phylogenies has a total of 22,974 taxa (mean 35.1), but a recent evaluation of the PBDB revealed only 1,124 currently named dinosaur species (Starrfelt and Liow 2016). Consequently, each species is represented on average at least 20.4 times. Thus, additional work will be needed to better evaluate the question of redundancy and how best to deal with it. A. Correlations Overall, 1,989 of our 2,721 phylogenies exhibited statistically significant correlation (p < 0.05). That is well over a majority of the phylogenies (73.1%), but when we simultaneously consider the actual correlation coefficient (Spearman rho), the numbers change dramatically. We defined “high correlation” phylogenies as those with statistically significant correlations (p < 0.05) and a Spearman rho > 0.75. For the entire set of phylogenies, there are only 684 (25.1%) that are classified as high correlation. Considered stratigraphically, phylogenies that contain only Paleozoic taxa also have 25.1% that are highly correlated, but phylogenies that include Cenozoic taxa appear to have less frequent high correlations. In particular, only 12.3% of phylogenies that include only Cenozoic taxa are highly correlated. In contrast, phylogenies with only Mesozoic taxa have substantially more that are highly correlated (37.8%). Considered taxonomically, a surprisingly high fraction of high correlation phylogenies occurs among the sarcopterygians and “early” tetrapods (54.3% high correlation), non-mammalian synapsids (45.1% high correlation), and dinosaurs (31.1% high correlation). Should these correlations be considered paleontologically significant? While we could easily run a statistical test to determine if one set of correlations is significantly higher or lower than another set, several factors urge caution in interpreting these results. First, as we have mentioned, our dataset suffers from considerable redundancy, which must be addressed manually. Beyond that, though, we also see a significant correlation between the taxon sample size and the t-statistic by which the statistical significance of the Spearman rho is calculated (Fig. 3). For example, we observed that 37.8% of phylogenies that contained only Mesozoic taxa were high correlation, and those high correlation phylogenies had an average of 33.7 taxa. In contrast, the 12.3% of Cenozoic-only high correlation phylogenies had an average of only 27.6 taxa. If we are to compare different sets of phylogenies, we would either have to utilize samples with the same taxon sample sizes (unlikely) or in some manner adjust for differences in taxon sample size. B. Simulations We simulated rank correlations by randomly selecting data points from a distribution of points of specified correlation (Fig. 4). By using the same taxon sample sizes as in our set of phylogenies, any set of empirical correlations can be directly compared to a simulation. For all 2,721 phylogenies, the simulations only poorly match the empirical distribution of correlations. Above the median correlation, the empirical distribution of correlations fall between points drawn randomly from a population with a true correlation between 0.6 and 0.7. Below the median correlation, no single simulation best matches the empirical distribution of correlation coefficients. These results suggest that, at best, our set of 2,721 phylogenies represents a random sample from an approximately 65% correlation between the order of Figure 2. Number of phylogenies by each taxonomic group. MCGUIRE et al. Testing the order of the fossil record 2023 ICC 481
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