We thank J.D. Archibald for his comment on our study (Fastovsky et al., 2004) because his misunderstanding of our work provides the opportunity to clarify ideas that may have similarly confused other readers.
The raw data show high abundance in the late Campanian, decreased abundance in the early–middle Maastrichtian, and increased abundance in the late Maastrichtian. Given the stunning overall increase in dinosaur generic richness toward the end of the Mesozoic, there are clearly concerns about artifacts of sampling and, as acknowledged by Archibald, interpretation is required. Our view is that the significance of any change in diversity (in this case, that from the Campanian to the Maastrichtian) can be assessed only in the context of the magnitude of other diversity fluctuations in the time interval under study (in this case, the Late Cretaceous). It was thus never a question of whether we did or did not “accept (our) results”; it was only about constructing a context in which to be able to intelligently interpret them.
That context was developed by the use of total generic richness and statistically tested via rarefaction. Total generic richness is analogous to ecological sampling (counts per unit area), and was necessary for quantitative treatment of the data. Thus, we do not accept Archibald's preemptory assertion that “the groupings are not relevant to questions of taxonomic diversity through time.”
The citations in our manuscript indicate “which of the many forms” of rarefaction we used. The one we applied to this problem was developed by Sanders (1968) and corrected by Hurlbert (1971) and Simberloff (1972). Thus,Heck et al. (1975) gave the formula of var(Šn) for estimating the variance of the expected number of species in a sample of size n.
Archibald's suggestion that comparison of the taxonomically richest units from Campanian and Maastrichtian (Dinosaur Park Formation and Lance Formation, respectively) is “more ecologically meaningful” is absurd. There is no reason to suppose that the richest formations of each time interval are spatially equivalent or preserve faunas with equal fidelity. That is why we undertook the analyses presented in Fastovsky et al. (2004).
Archibald constructed his own database from our original source (Weishampel et al., 2004), inviting “readers to examine these data for themselves.” Having done so, we are reassured that Archibald's data and ours are generally in agreement. The late Maastrichtian has fewer taxa recorded than the Late Campanian, but it also has more taxa than any other interval in the Mesozoic. We again see the apparent decline in generic richness from the Campanian to the Maastrichtian, which we clearly acknowledged before (Tables 4 and 7, and accompanying text), and we again see the apparent increase in diversity between the early and late Maastrichtian. So we again ask ourselves, as we did when we wrote our manuscript, are these fluctuations significant or are they due to sampling? And again we conclude that the only way to assess their significance is to consider them in the context of other generic diversity fluctuations throughout the Late Cretaceous. When that is done, it cannot be shown that the drop from late Campanian to late Maastrichtian is remarkable. And that, of course, is the conclusion reached in Fastovsky et al. (2004).