Here's the abstract:
"Many palaeobiological analyses have concluded that modern birds (Neornithes) radiated no earlier than the Maastrichtian, whereas molecular clock studies have argued for a much earlier origination. Here, we assess the quality of the fossil record of Mesozoic avian species, using a recently proposed character completeness metric which calculates the percentage of phylogenetic characters that can be scored for each taxon. Estimates of fossil record quality are plotted against geological time and compared to estimates of species level diversity, sea level, and depositional environment. Geographical controls on the avian fossil record are investigated by comparing the completeness scores of species in different continental regions and latitudinal bins. Avian fossil record quality varies greatly with peaks during the Tithonian-early Berriasian, Aptian, and Coniacian–Santonian, and troughs during the Albian-Turonian and the Maastrichtian. The completeness metric correlates more strongly with a ‘sampling corrected’ residual diversity curve of avian species than with the raw taxic diversity curve, suggesting that the abundance and diversity of birds might influence the probability of high quality specimens being preserved. There is no correlation between avian completeness and sea level, the number of fluviolacustrine localities or a recently constructed character completeness metric of sauropodomorph dinosaurs. Comparisons between the completeness of Mesozoic birds and sauropodomorphs suggest that small delicate vertebrate skeletons are more easily destroyed by taphonomic processes, but more easily preserved whole. Lagerstätten deposits might therefore have a stronger impact on reconstructions of diversity of smaller organisms relative to more robust forms. The relatively poor quality of the avian fossil record in the Late Cretaceous combined with very patchy regional sampling means that it is possible neornithine lineages were present throughout this interval but have not yet been sampled or are difficult to identify because of the fragmentary nature of the specimens."
It's an extensive paper with quite a bit of information regarding discovery bias. If you're interested in fossil birds and the origins of modern avian diversity, this is a must-read (and open access!)
The manuscript does not discuss flight much (as that's not really the topic at hand), but there is one mention that I thought might be worth discussing here. The authors note that: "Avian species today, and in the past, are typically small-bodied and lightly built because of the constraints imposed by powered flight."
Overall, this is almost certainly true: birds are (both historically and today) overwhelmingly represented by small species, and flight certainly adds constraints to body size and build. I am curious, though, whether birds are actually more skewed in their body size distribution than other, non-flying animals. Most mammals are small, for example (about half of all the mammal species are rodents, and these are mostly quite small). Squamates and amphibians are also overwhelmingly represented by small forms. Now, that said, these groups also include some giant forms, and most of the large birds have historically been flightless. However, some of the larger flying birds (the largest pseudodontorns and teratorns, for example) were reasonably large, all considered. Argentavis may have tipped the scales at 75-80 kg, and while that's not huge, it's well within the body size range of larger mammalian predators alive today (it's more massive than a leopard by a fair margin, for example).
This is not to say that the body size distribution of birds is not skewed by their volancy, but rather than I'm not sure this has been rigorously demonstrated. Many supposedly "obvious" facts go untested because they seem to intuitive. Perhaps this is another one worth a serious look.
(2012) The Completeness of the Fossil Record of Mesozoic Birds: Implications for Early Avian Evolution. PLoS ONE 7(6): e39056. doi:10.1371/journal.pone.0039056