Sensitivity to Initial Conditions and Nonextensivity in Biological Evolution

TL;DR

This paper explores how biological evolution modeled by Bak and Sneppen's framework exhibits power-law sensitivity to initial conditions and relates it to nonextensive thermostatistics, drawing parallels with chaos theory.

Contribution

It demonstrates power-law sensitivity and connects it to nonextensive statistics within the Bak and Sneppen evolution model, highlighting a novel link between biological evolution and complex systems theory.

Findings

Power-law sensitivity to initial conditions at critical state

Calculated sensitivity exponent and related it to nonextensive thermostatistics

Determined the dynamical exponent z

Abstract

We consider biological evolution as described within the Bak and Sneppen 1993 model. We exhibit, at the self-organized critical state, a power-law sensitivity to the initial conditions, calculate the associated exponent, and relate it to the recently introduced nonextensive thermostatistics. The scenario which here emerges without tuning strongly reminds that of the tuned onset of chaos in say logistic-like onedimensional maps. We also calculate the dynamical exponent z.