Self-similarity of extinction statistics in the fossil record

Abstract

The dynamical processes underlying evolution over geological timescales remain unclear¹,². Analyses of time series of the fossil record have highlighted the possible signature of periodicity in mass extinctions³,⁴, perhaps owing to external influences such as meteorite impacts. More recently the fluctuations in the evolutionary record have been proposed to result from intrinsic nonlinear dynamics for which self-organized criticality provides an appropriate theoretical framework^5,6,7. A consequence of this controversial⁸ conjecture is that the fluctuations should be self-similar, exhibiting scaling behaviour like that seen in other biological⁹ and socioeconomic¹⁰,¹¹ systems. The self-similar character is described by a 1/f power spectrum P(f), which measures the contributions of each frequency f to the overall time series. If self-similarity is present, then P(f) ≈ f^{− β} with 0 < β <2. This idea has not been sufficiently tested, however, owing to a lack of adequate data. Here we explore the statistical fluctuation structure of several time series obtained from available palaeontological data bases, particularly the new ‘Fossil Record 2’¹⁸. We find that these data indeed show self-similar fluctuations characterized by a 1/f spectrum. These findings support the idea that a nonlinear response of the biosphere to perturbations provides the main mechanism for the distribution of extinction events.