Letters to Nature

Nature 388, 764-767 (21 August 1997) |

Self-similarity of extinction statistics in the fossil record

Ricard V. Solé1,2, Susanna C. Manrubia1, Michael Benton3 and Per Bak4,2

  1. Department of Physics FEN, Universitat Politècnica de Catalunya, Campus Nord, Mòdul B4, 08034 Barcelona, Spain
  2. Santa Fe Institute, 1399 Hyde Park Road, New Mexico 87501, USA
  3. Department of Geology, University of Bristol, Bristol BS8 1RJ, UK
  4. The Niels Bohr Institute, Biegdamsvej 17, DK-2100 Copenhagen, Denmark

Correspondence to: Ricard V. Solé1,2 Correspondence and requests for materials should be addressed to R.V.S. (e-mail: Email: sole@santafe.edu).

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 framework5, 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) approximately f - beta with 0 < beta <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.