1. Department of Earth and Planetary Science, University of California, Berkeley, California 94720-4767, USA

Correspondence to: Correspondence and requests for materials should be addressed to the author (e-mail: Email: kirchner@seismo.berkeley.edu).

The dynamics of extinction and diversification determine the long-term effects of extinction episodes¹. If rapid bursts of extinction are offset by equally rapid bursts of diversification, their biodiversity consequences will be transient. But if diversification rates cannot accelerate rapidly enough, pulses of extinction will lead to long-lasting depletion of biodiversity^{2, 3}. Here I use spectral analysis of the fossil record to test whether diversification rates can accelerate as much as extinction rates, over both short and long spans of geological time. I show that although the long-wavelength variability of diversification rates equals or exceeds that of extinctions, diversification rates are markedly less variable than extinction rates at wavelengths shorter than roughly 25 million years. This implies that there are intrinsic speed limits that constrain how rapidly diversification rates can accelerate in response to pulses of extinction.