  We have examined the Fourier power spectrum as well as the Hurst exponent of
extinction, origination, and total biodiversity in the marine fossil record,
using a recently improved geologic timescale. We find all of them strongly
inconsistent with past claims of self-similarity as well as inconsistent with
random walk behavior. Instead, they are dominated by low-frequency power, with
approximate f^-2 power over one decade in frequency. The spectrum turns over at
about 10^8 y, lending plausibility to connections with galactic dynamics. Even
in the background of this low-frequency dominance, a previously noted 62 My
biodiversity cycle stands out with better than 99% confidence above the noise
level, accounting for about 35% of the total variance in the fossil
biodiversity record.
