Because the fossil record has long been known to be incomplete (50, 51), it is possible that the observed slowdown and downturn are byproducts of undersampling. This assumption would imply that there is a systematic downward bias in the phylogeny toward recent times, which would be counter to the usual expectation for poor sampling (50, 51). Here, to test the effect of such biases, we fitted additional models with appropriate covariates, including stage-level formation counts (because formation count is widely reported to be associated with sampling bias) (9, 10, 12, 35, 44, 52, 53), taxon-specific formation counts (the number of formations in which a taxon is found), taxon-specific collection count (the number of fossil collections in which a taxon is represented), cladewise valid taxa counts (the known underrepresentation in the phylogeny) (54), fossil quality scores (state of preservation) (55), and body size (smaller taxa are less likely to be preserved) (56).
As an indirect measure of the influence of geography on speciation dynamics, such as segregation by geographic barriers (30), we used Mesozoic eustatic sea-level reconstructions (34) as an additional covariate in our models (mean sea-level value along each terminal branch). We also tested the ecological limit on clade diversification or the possible effects of niche saturation by adding a measure of intraclade diversity taken as the number of contemporary branches (including internal branches) for each taxon (the number of tips in time-sliced trees) (48). All data files are available in Datasets S1–S13.
There was a slow-down in speciation rates prior to the K-Pg, see:
Sakamoto, M.; Benton, M. J. & Venditti, C.
Dinosaurs in decline tens of millions of years before their final extinction
Proceedings of the National Academy of Sciences, 2016, 113, 5036-5040
https://www.pnas.org/content/early/2016/04/13/1521478113.abstract