SELF-SIMILARITY OF EXTINCTION STATISTICS IN THE FOSSIL RECORD

The dynamical processes underlying evolution over geological timescale s remain unclear(1,2). Analyses of time series of the fossil record ha ve highlighted the possible signature of periodicity in mass extinctio ns(3,4), perhaps owing to external influences such as meteorite impact s, More recently the fluctuations in the evolutionary record have been proposed to result from intrinsic nonlinear dynamics for which self-o rganized criticality provides an appropriate theoretical framework(5-7 ). A consequence of this controversial(8) conjecture is that the fluct uations should be self-similar, exhibiting scaling behaviour like that seen in other biological(9) and socioeconomic(10,11) systems. The sel f-similar character is described by a 1/f power spectrum P(f), which m easures the contributions of each frequency f to the overall time seri es. If self-similarity is present, then P(f) approximate to f(-beta) w ith 0 < beta < 2, This idea has not been sufficiently tested, however, owing to a lack of adequate data, Here we explore the statistical flu ctuation structure of several time series obtained from available pala eontological data bases, particularly the new 'Fossil Record 2'(18). W e find that these data indeed show self-similar fluctuations character ized by a 1/f spectrum. These findings support the idea that a nonline ar response of the biosphere to perturbations provides the main mechan ism for the distribution of extinction events.