Estimating diversity through time using molecular phylogenies: old and species-poor frog families are the remnants of a diverse past.

Estimating how the number of species in a given group varied in the deep past is of key interest to evolutionary biologists. However, current phylogenetic approaches for obtaining such estimates have limitations, such as providing unrealistic diversity estimates at the origin of the group. Here we develop a robust probabilistic approach for estimating Diversity-Through-Time (DTT) curves and uncertainty around these estimates from phylogenetic data. We show with simulations that under various realistic scenarios of diversification, this approach performs better than previously proposed approaches. We also characterize the effect of tree size and undersampling on the performance of the approach. We apply our method to understand patterns of species diversity in anurans (frogs and toads). We find that Archaeobatrachia -- a species-poor group of old frog clades often found in temperate regions -- formerly had much higher diversity and net diversification rate, but the group declined in dive...