DIVERSITY-DEPENDENT DIVERSIFICATION IN ORDOVICIAN–SILURIAN GRAPTOLOIDS

The extent to which biological diversity affects rates of diversification is central to macroevolutionary dynamics, yet no consensus has emerged on the importance of diversity-dependence of evolutionary rates. Here we analyze the species-level fossil record of early Paleozoic graptoloids, documented with high temporal resolution, to test whether rates of diversification were influenced by levels of standing diversity. We adopt a direct approach, tabulating diversity at the start of a series of 0.25-Myr-long time intervals and diversification rate during each interval, and asking whether diversity and diversification rate are negatively correlated, as predicted by the hypothesis of diversity-dependence. This direct comparison is complicated, however, because basic properties of random walks imply that even a random time series of diversification rates will produce a diversity history that appears, spuriously, to reflect diversity-dependence: standing diversity will be negatively correlated with diversification rate even if diversity in fact has no effect on this rate. We therefore developed a null expectation for the cross-correlation between diversity and diversification rate by generating an ensemble of empirically scaled, synthetic diversity histories in which, by construction, diversification rate is completely unaffected by diversity. Only if the observed cross-correlation lies outside the null distribution do we infer that diversification rate in fact depended on diversity. Comparing observed correlations to this null model, we find evidence for significant diversity-dependence, which is maximally strong at a lag of about 1 Myr. The lag between changes in diversity and in diversification rate may reflect diachroneity: the fact that species take time to spread throughout their geographic range and to contract from their maximal range. 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. In 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.