Fossil Biodiversity: Red Noise

We have examined the Fourier power spectrum of extinction, origination, and total biodiversity in the marine fossil record. We find them inconsistent with self-similarity as well as random walk behavior, but instead dominated by low-frequency power. Even in the background of this low-frequency dominance, the 62 My biodiversity cycle is predominant. A recent analysis 1 of fossil biodiversity found a 99%-significant 62 My periodicity against permuted random walk Monte Carlo simulations, based on a large database of marine genera 2 with improved dating 3. Earlier studies have claimed self-similarity in extinction 4 or little inconsistency with random walk behavior 5. We reexamine some of these issues with additional analysis of the newer data. Fourier analysis of detrended biodiversity, origination, and extinction produces power spectra P strongly declining with frequency, which is inconsistent with random walk behavior. Analysis of autocorrelations shows them approaching zero at lag 20 My 5 but with considerable structure at larger lag, best studied with spectra. Power spectra of extinction based on improved dating are different from earlier work 4 showing far more fluctuation and no power-law behavior. Earlier smooth power-law results may be a sampling artifact 6. The Hurst Exponent H can characterize processes with " memory ". It is defined by R/σ α n H , where R is the range of the data, σ is the sample standard deviation, and n is the number of steps; H=0.5 for a pure random walk 7. Although we do not find a single power law over the whole domain of n, we find that a best fit for extinction, expressed as number or fraction of genera, detrended or not, is H~0.7, again inconsistent with pure random walk behavior. Power spectra of origination and total biodiversity approach P α k-2 , marginally consistent with self-similarity and with the use of the Hurst Exponent; this shows H~1, very far from a random walk. Our analysis of origination, extinction, and biodiversity as a function of geological (sub)stage, rather than time also shows behavior inconsistent with a random walk. All exhibit evidence of long-range memory using both spectral and range analysis.