Fossil Biodiversity: Red Noise Plus Signal
  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. 
Adrian L. Melott and Bruce S. Lieberman (University of Kansas)