The result was obtained through modelling of the data using an approach which allowed us to repeat the calculations millions of time, using different assumptions about uncertainties each time, to see whether the analysis converged on a single result. In this case, we modelled uncertainties in the phylogeny, in geological dating, and in sampling, and tried every variant of the data, and the result was robust. We can now say categorically: for their final 40m years on Earth, the dinosaurs were in decline - their rate of species extinction was on average consistently higher than their rate of forming new and distinct species (speciation).
But what we cannot yet explain is why this was so. We found correlation of our speciation dynamics data with sea level, but a more detailed exploration is needed of the impact of cooling climates and their interactions with other species such as mammals. Whatever the driver, dinosaurs were declining. They went out with a long, protracted whimper … followed by that almighty meteoric bang.