Scaling of power spectrum of extinction events in the fossil record

The fast Fourier transform, maximum entropy method, Lomb’s method of spectral analysis and rescaled range analysis are applied to the study of extinction patterns. Using a database of marine families from mid-Permian to Pleistocene, it is shown that a long-range correlation is present. Since the data record is non-stationary and unevenly spaced, linear interpolation is carried out for obtaining evenly spaced data. The data are also de-trended from their mean to obtain a stationary time series. Scaling behavior is observed in both interpolated and detrended unevenly spaced data. Application of the randomization test on both interpolated and de-trended data revealed that the interpolated data lost the randomness of the original record due to a smoothing effect, while the de-trended data retained the randomness property and hence are reliable for drawing information. The most popular method, the fast Fourier transform spectral method based on stationarity assumption, yields a contradictory result, and is independent of the interpolation technique used to fill gaps in the discontinuous fossil record.