  Recent Fourier analyses of fossil extinction data have indicated that the
power spectrum of extinction during the Phanerozoic may take the form of 1/f
noise, a result which, it has been suggested, could be indicative of the
presence of "critical dynamics" in the processes giving rise to extinction. In
this paper we examine extinction power spectra in some detail, using
family-level data from a variety of different sources. We find that although
the average form of the power spectrum roughly obeys the 1/f law, the spectrum
can be represented more accurately by dividing it into two regimes: a
low-frequency one which is well fit by an exponential, and a high-frequency one
in which it follows a power law with a 1/f^2 form. We give explanations for the
occurrence of each of these behaviours and for the position of the cross-over
between them.
