Supplementary text, figures and Additional material from Diversity-dependent evolutionary rates in early Palaeozoic zooplankton.

The extent to which biological diversity affects rates of diversification is central to understanding macroevolutionary dynamics, yet no consensus has emerged on the importance of diversity-dependence of evolutionary rates. Here, we analyse the species-level fossil record of early Palaeozoic graptoloids, documented with high temporal resolution, to test directly whether rates of diversification were influenced by levels of standing diversity within this major clade of marine zooplankton. To circumvent the statistical regression-to-the-mean artefact, whereby higher- and lower-than-average values of diversity tend to be followed by negative and positive diversification rates, we construct a non-parametric, empirically scaled, diversity-independent null model by randomizing the observed diversification rates with respect to time. Comparing observed correlations between diversity and diversification rate to those expected from this diversity-independent model, we find evidence for negative diversity-dependence, accounting for up to 12% of the variance in diversification rate, with maximal correlation at a temporal lag of approximately 1 Myr. Diversity-dependence persists throughout the Ordovician and Silurian, despite a major increase in the strength and frequency of extinction and speciation pulses in the Silurian. By contrast to some previous work, we find that diversity-dependence affects rates of speciation and extinction nearly equally on average, although subtle differences emerge when we compare the Ordovician and Silurian.