Estimating the diversity of dinosaurs

Results

Discussion

We estimate that 29% of discoverable dinosaur genera are now known. Other authors have estimated the percentage of known diversity for other fossil groups, but these studies have been at the species level and thus are not directly comparable with our estimate. However, 90% of dinosaur genera are monospecific (the mean number of species is 1.2, with 98.3% of genera having 3 or fewer species), so the percentage completeness at the species level is likely to be close to the generic figure of 29%. Using this figure, the dinosaur fossil record is less complete than that of North American fossil mammal species, of which 56–67% are estimated to be known (31–33). Considering the extensive history of exploration in North America and the more recent age of mammal fossils, it is not surprising that the mammal record is better known than that of dinosaurs. However, the dinosaur fossil record is substantially more complete than that of primate species in particular, of which Tavare et al. (10) estimated <7% are known. The primate fossil record is sparse, because primates (particularly early species) were likely small-bodied, had limited populations, and were arboreal, characteristics unfavorable to fossilization (10).

The dinosaur record also appears to be more complete than that of Phanerozoic marine invertebrate species as a whole, of which an estimated 12% are known (34). This overall figure of 12% combines soft-bodied groups whose fossil record is very sparse (e.g., ctenophores and nematodes) and well skeletonized taxa whose fossil record is relatively complete [e.g., crinoids, bivalves, brachiopods, and trilobites (31, 35)]. In general, marine ecosystems should be more conducive to fossilization than terrestrial ones, but the lack of hard parts of many invertebrates makes them less likely to fossilize than vertebrates such as dinosaurs. Moreover, although small animals often have larger population sizes, large animals such as dinosaurs may be more likely to be preserved because of taphonomic biases (36, 37).

Other studies have quantified the completeness of the fossil record for various groups [e.g., Phanerozoic marine invertebrates (35), Late Cretaceous mammals (38), Cretaceous tetrapods (13), and Phanerozoic animals and plants (39)]. These studies express their results as preservation rates per time interval (35, 38), the percentage of living families with fossil representatives (35), an index of completeness based on the prevalence of Lazarus taxa (13), and indices of congruence with published phylogenies (39). Because we calculate the percentage of genera that are known, our results and theirs cannot be compared directly.

Existing statistical methods for estimating diversity, including the ACE, assume random sampling of specimens. In reality, fossil discoveries are correlated in time and space depending on rock availability (see above) and numerous social and historical factors (40, 41). The dinosaur fossil record is especially patchy, because a substantial fraction of known diversity in some intervals derives from a single formation (e.g., Hell Creek, Morrison). No method yet exists to account for such temporal and spatial correlations, however, and authors disagree on how these correlations affect estimated diversity (42, 43). As a result, standard confidence intervals are likely to underestimate the true degree of uncertainty. We therefore do not attempt to calculate confidence intervals for our diversity estimates, because such intervals would be misleadingly narrow. For dinosaurs in particular, temporal and spatial correlations may cause the ACE, which assumes that undiscovered genera are inherently rare (see Methods), to underestimate diversity. Although many or even most undiscovered genera may in fact be rare, it is nonetheless probable that some abundant genera remain to be discovered, especially in time intervals or areas in which little terrestrial rock outcrop is available. If so, diversity would exceed our estimates.

Our estimate of 1,844 genera exceeds that of Dodson (2) by ≈50%, which is not surprising in light of recent growth in the rate of new genera being described, and is slightly over half of Russell's (3) estimate. The latter is not incompatible with our estimate, because it includes genera having no discoverable fossil record, whereas our estimate does not. If both our estimate and Russell's are correct, it would imply that 46% [(3,400–1,844)/3,400] of dinosaur genera have no discoverable fossil record.

It is an open question to what extent our estimates of discoverable genera mirror true original diversity. Our estimated diversity is surely a better proxy for true original diversity than is known diversity, because estimated diversity attempts to account for future discoveries. Furthermore, we posit that genera become undiscoverable primarily through initial failure to enter the fossil record (e.g., living in nondepositional environments) or subsequent loss of fossiliferous rock (e.g., subduction). (Other factors, such as size bias or erosion, might cause genera to be rare but not in principle undiscoverable.) If so, the issue of extrapolating to true original diversity from estimated diversity is analogous to inferring global diversity trends from a subset of localities, that is, showing that total richness mirrors alpha diversity. Research on marine invertebrates has shown that alpha diversity does in fact reflect global diversity (44–46). Furthermore, evidence suggests that dinosaur diversity trends at the formation level for well sampled formations (e.g., Morrison, Cloverly, Judith River) reflects global diversity trends (47). It is therefore plausible that estimated diversity reproduces the pattern of true original diversity in dinosaurs. This conclusion is strengthened by our results on rock availability bias: We expect that rock availability should have relatively little correlation with true original diversity, and its correlation with our estimated diversity is in fact low (Fig. 2b; R² = 12.8%).

Assuming that estimated diversity parallels true original diversity, Fig. 3 may provide additional insight into the correlation of known diversity and rock availability. The plots in Fig. 2 a and b can be thought of as corresponding to the left and right parts of the logistic accumulation curve, respectively. At the left part of the curve (Fig. 3 a or b), known diversity is low compared with the number of discoverable genera, and additional sampling is likely to yield new genera. Thus, known diversity and rock availability are expected to be correlated, because extraneous (e.g., geological, historical, or social) biases should have a relatively larger impact when our knowledge of the dinosaur record is incomplete. At the right part of the curve, known diversity and rock availability should not be highly correlated, because for that part of the curve, known diversity is close to estimated diversity (and therefore mirrors true original diversity). Over the next century or two, as we move rightward and upward on the curve and completeness of the dinosaur record improves, we should expect known diversity to become less correlated with rock availability. However, because we have not yet reached such a point on the curve, we thus find that current known diversity is correlated with rock availability.

In summary, we estimate that 71% of discoverable dinosaur genera remain unknown to science and that new genera will continue to be discovered for at least another century. We also find that the known dinosaur fossil record is biased by the availability of fossiliferous rock. Furthermore, contrary to the known fossil record, we find no evidence that diversity declined from the Campanian to the Maastrichtian. Previous studies (1, 48) have demonstrated that a literal reading of the fossil record can be misleading. Our analyses confirm that the incompleteness of the fossil record must be taken into account.

Methods

Numerous methods have been developed to estimate the diversity of a population including as-yet-undiscovered taxa (7, 8, 49–55). Here we used the ACE, a nonparametric statistical method (7, 8) based on abundance counts. The ACE has been shown to perform well in the statistics and ecology literature (49, 51, 53–55). Anderson et al. (52) used the ACE to estimate Triassic plant diversity, but to our knowledge, the method has not been applied to fossil animals. We used a variant of the ACE designed for populations in which taxon abundances vary widely (7), as is the case for dinosaurs. Because diagnosing dinosaur fossils at the species level is often problematic (2), we used the genus as our unit of analysis. As required by the ACE, we divided genera into groups of rare and abundant genera. We considered abundant genera to be those represented by >10 individuals, as recommended in the literature (8, 56). Only rare genera are used to estimate diversity, a procedure that has several advantages for dinosaurs. First, it is often difficult to determine the exact number of individuals of very abundant genera. For example, in a large bonebed, we may be able to determine only that there are approximately several hundred individuals. Using only rare genera avoids the need for precise counts of abundant genera. Second, finds of very abundant genera are less likely to be collected or reported in the literature. For example, a new find of a rare genus such as Neuquenraptor (known from only one individual) is more likely to be reported than a new find of a common genus such as Protoceratops (known from nearly 100 individuals). Third, rare genera provide the best information about undiscovered genera. Undiscovered genera are inherently rare and would likely be represented by only a few individuals if discovered, so only similarly rare known genera are relevant to estimating the number of undiscovered genera.

The ACE uses the number of known rare genera to estimate “coverage,” defined as the total relative abundance of all known genera. Stated mathematically, suppose there are a total of K known and unknown genera, with p_i denoting the probability that a fossil find (i.e., individual) belongs to genus i for i = 1, 2, …, K. Coverage is defined as the sum of the p_i values for the known genera. This quantity can be estimated from fossil abundance data and is a function of the number of genera known from only a single individual (7). A high coverage suggests that few unknown genera remain to be found, whereas a low coverage suggests that many unknown genera remain to be found. Estimated diversity is then calculated as follows:

Here,

is a measure of the heterogeneity of the p_i values (reflecting the dominance or evenness of the relative abundance distribution), D_abun is the number of known abundant genera, D_rare is the number of known rare genera, Ĉ_rare = 1 − f₁/n_rare is the coverage estimated from rare genera, f_i is the number of genera known from exactly i individuals, n_rare is the number of individuals among rare genera, and the index i in the definition of γ̃²rare ranges from 1 to 10 (the cutoff for rare vs. abundant genera). Raw data needed to calculate these quantities are given in Data Set 1, which is published as supporting information on the PNAS web site. See refs. 7 and 8 for details on the ACE methodology. All calculations were performed by using code written by S.C.W. for the statistical software R (www.r-project.org).

Supplementary Material