Multi-variate models are essential for understanding vertebrate diversification in deep time

Statistical models are helping palaeontologists to elucidate the history of biodiversity. Sampling standardization has been extensively applied to remedy the effects of uneven sampling in large datasets of fossil invertebrates. However, many vertebrate datasets are smaller, and the issue of uneven sampling has commonly been ignored, or approached using pairwise comparisons with a numerical proxy for sampling effort. Although most authors find a strong correlation between palaeodiversity and sampling proxies, weak correlation is recorded in some datasets. This has led several authors to conclude that uneven sampling does not influence our view of vertebrate macroevolution. We demonstrate thatmulti-variate regression models incorporating a model of underlying biological diversification, as well as a sampling proxy, fit observed sauropodomorph dinosaur palaeodiversity best. This bivariate model is a better fit than separate univariate models, and illustrates that observed palaeodiversity is a composite pattern, representing a biological signal overprinted by variation in sampling effort. Multivariate models and other approaches that consider sampling as an essential component of palaeodiversity are central to gaining a more complete understanding of deep time vertebrate diversification.