Fluctuations in models of biological macroevolution (Invited Paper)

Fluctuations in diversity and extinction sizes are discussed and compared for two dierent, individual-basedmodels of biological coevolution. Both models display power-law distributions for various quantities of evolu-tionary interest, such as the lifetimes of individual species, the quiet periods between evolutionary upheavalslarger than a given cuto, and the sizes of extinction ev ents. Time series of the diversity and measures of thesize of extinctions give rise to ”icker noise. Surprisingly, the power-law behaviors of the probability densities ofquiet periods in the two models dier, while the distributions of the lifetimes of individual species are the same.Keywords: Biological evolution, Coevolution, Flicker noise, Fluctuations, Power-law distributions 1. INTRODUCTION Biological evolution presents many problems concerning highly nonlinear, nonequilibrium systems of interactingentities that are well suited for study by methods from statistical mechanics. An excellent review of this rapidlygrowing “eld is found in Ref. 1. Among these problems are those concerned with coevolution :thesimulta-neous evolution of many species, whose mutual interactions produce a constantly changing Þtness landscape .Throughout this process, new species are created and old species go extinct. A question that is still debated inevolutionary biology is whether evolu tion on the macroscaleproceeds gradually or in “ts and starts, as suggestedby Eldredge and Gould.