The Fossil Record 2 database gives a stratigraphic range of most known animal and plant families. We have used it to plot the number of families extant through time and argue for an exponential fit, rather than a logistic one, on the basis of power spectra of the residuals from the exponential. The times of origins and extinctions, when plotted for all families of marine and terrestrial organisms over the last 600 Myr, reveal different origination and extinction peaks. This suggests that patterns of biological evolution are driven by its own internal dynamics as well as responding to upsets from external causes. Spectral analysis shows that the residuals from the exponential model of the marine system are more consistent with 1/f noise suggesting that self–organized criticality phenomena may be involved.