Background
The authors write that "understanding the controls on biodiversity is a central goal in biology," and in this regard they note that "most studies examining climate-diversity hypotheses use present-day observations or conceptual models." However, they indicate that "a growing number of studies have turned to the fossil record, trading space for time," but they say that "most of these studies do not distinguish between the effects of atmospheric CO2 and temperature," due to the fact that "CO2 and temperature correlate broadly with one another on geologic timescales," which "makes differentiating their influence on biodiversity patterns difficult."

What was done
Royer and Chernoff analyzed "how atmospheric CO2 and temperature relate to an angiosperm-dominated record of plant diversity," based on the specific types and proportions of pollen found in central Colombia and western Venezuela that dated back to the Palaeogene and early Neogene (65-20 Ma), where the knowledge of pollen morphospecies richness came from Jaramillo et al. (2006) - who had analyzed a total of 1060 samples - while atmospheric CO2 data came from the compilation of Beerling and Royer (2011), together with subsequent updates provided by Pagani et al. (2011) and Grein et al. (2011), and where benthic δ¹⁸O data came from the compilation of Zachos et al. (2008).

What was learned
The two U.S. researchers report that "pollen morphospecies richness from the neotropics of Colombia and Venezuela is more strongly correlated with atmospheric CO2 than it is with temperature," and they say that their interpreted patterns hold "whether or not the data are transformed by their first difference and whether or not the data are analyzed univariately or multivariately." In fact, they state that "atmospheric CO2 is the only dataset that mirrors [1] the low richness values at the beginning (Palaeocene) and end (Miocene) of the time series, [2] sustained high values during the mid-Eocene, and [3] a short-term spike in the late Palaeocene."

What it means
Once again quoting the scientists who performed the work, "because the diversity correlations to temperature are always weaker than those to CO2, it is possible that temperature is simply secondarily related." Hence, it would appear that irrespective of all else, if the air's CO2 content continues to rise, so also should the diversity of neotropical wet forests rise right along with it.

References
Beerling, D.J. and Royer, D.L. 2011. Convergent Cenozoic CO2 history. Nature Geoscience 4: 418-420.

Grein, M., Konrad, W., Wilde, V., Utescher, T. and Roth-Nebelsick, A. 2011. Reconstruction of atmospheric CO2 during the early Middle Eocene by application of a gas exchange model to fossil plants from the Messel Formation, Germany. Paleogeography, Paleoclimatology, Paleoecology 309: 383-391.

Jaramillo, C., Rueda, M.J. and Mora, G. 2006. Cenozoic plant diversity in the Neotropics. Science 311: 1893-1896.

Pagani, M., Huber, M., Liu, Z., Bohaty, S.M., Hendriks, J., Sijp, W., Krishnan, S. and DeConto, R.M. 2011. The role of carbon dioxide during the onset of Antarctic glaciation. Science 334: 1261-1264.

Zachos, J.C., Dickens, G.R. and Zeebe, R.E. 2008. An early Cenozoic perspective on greenhouse warming and carbon-cycle dynamics. Nature 451: 279-283.