What was done
The authors studied 49 ground ant assemblages from 1994-1997, including two from South America, six from Central America, and 41 from North America.  They used standard protocols to estimate both ground ant abundance and site net primary productivity (NPP), after which they regressed the log₁₀-transformed ant abundance upon the similarly transformed site NPP.

What was learned
With site net primary productivity varying over three orders of magnitude and ant abundance varying over two orders of magnitude, the authors found that ant abundance rose with increasing site NPP, and that NPP alone accounted for 56% of the variation in ant abundance, with the next best predictor explaining only 8% of the variation.

What it means
Ants are ectotherms; and ectotherms represent most of the world's animal biomass and biodiversity (Wilson, 1993).  Consequently, as the authors state, "understanding the mechanisms that regulate ectotherm abundance is key to predicting the impacts of climate change."

In this regard, the authors further note that "this study is the first we know of that explores factors regulating the abundance of a taxon over the terrestrial productivity gradient;" and what they found clearly demonstrates that a site's net primary productivity is the primary determinant of ectotherm abundance.  Hence, based on the fact that atmospheric CO2 enrichment invariably leads to increases in ecosystem NPP, we can confidently say that the ongoing rise in the air's CO2 content should prove to be extremely beneficial for the vast majority of earth's animal life in terms of both its abundance and diversity.

Reference
Wilson, E.O.  1993.  The Diversity of Life.  W.W. Norton & Co., New York, NY.