Comment on ``Scaling of power spectrum of extinction events

Fossil extinction power spectra, recently published by Dimri and Prakash [1], appear to exhibit power-law scaling in which spectral power is inversely proportional to frequency. Dimri and Prakash interpret their results as demonstrating a fractal pattern in the fossil record, with longrange correlations that suggest self-organized critical dynamics. Here I point out that their methods are vulnerable to biases and artifacts, and I show that their conclusions are based on power spectra that have been plotted upside-down. Dimri and Prakash analyze marine family extinction data [2] using rescaled-range (R/S) analysis and three di¡erent spectral techniques: the fast Fourier transform (FFT), the maximum entropy method (MEM), and the Lomb^Scargle Fourier transform (LSFT). Their use of R/S analysis overlooks the fact that particularly with small data sets like theirs, R/S analysis exhibits `very large bias' [3], often yielding results similar to their ¢gures 3d and 4d whether or not the underlying data are fractal. Similarly, their use of interpolated time series (in their ¢gures 1b,d, 2a,b, 3a,b, and 4) overlooks previous work showing that interpolation can introduce signi¢cant artifactual correlation, yielding apparent fractal behavior even when the underlying data are random white noise [4]. Dimri and Prakash correctly point out that the LSFT [5,6] o¡ers signi¢cant advantages over conventional spectral methods, because it can be used on unevenly spaced data. Previous studies have used the LSFT to calculate fossil extinction power spectra [7] and autocorrelation functions [8], as well as cross-correlations between extinction and origination rates [9]. However, this previous body of work contradicts Dimri and Prakash's conclusion that fossil extinction rates are fractal. Analyses of four di¡erent extinction metrics and three di¡erent fossil data sets (including a longer and more complete version of the data used by Dimri and Prakash) using the LSFT show that fossil extinction rates do not exhibit fractal scaling [7], and are not signi¢cantly correlated over timescales longer than 5 Myr [8]. In contrast to this previous work, Dimri and Prakash present no statistical tests of their ¢nding of fractal structure in the fossil record. That is, they do not show that the fossil record yields signi¢cantly di¡erent results than would be obtained from appropriate null hypotheses (such as random re-shu¥es of the original data), when subjected to the same pre-processing and analysis. What, then, is Dimri and Prakash's evidence, and how do they arrive at it? Their R/S analysis