A multiplicative multifractal model for originations and extinctions

Abstract

Recent works have suggested that the fossil record exhibits a fractal structure; i.e., that processes, such as extinction, follow a power-law size distribution and their time series show a 1/f power spectrum. This structure has been used as evidence that evolutionary dynamics are an example of a self-organized critical (SOC) process. We have reexamined this claim by analyzing a detailed record of marine genus-level extinctions and originations. Our results indicate that neither extinctions nor origination metrics show the power-law size distribution or a 1/f power spectrum characteristic of SOC and related models. We also believe that the underlying assumptions of SOC are incompatible with our understanding of the processes controlling macroevolutionary patterns.Statistical analyses of the data sets are compatible, however, with the presence of multifractal self-similarity in both records, consistent with a hierarchical and multiplicative generating process. This model assumes that multiple causal mechanisms, acting over many spatial and temporal scales, interact to promote or inhibit originations and extinctions. In this view, the same event can have quite different impacts depending on the state of the biotic or physical system at the time that it occurs. This may at least partially explain such phenomena as the imperfect correlation between eustatic sea-level changes and macroevolutionary processes and the apparent nonlinear response of biotic systems to bolide impacts.