Fitness fluctuations in the Bak-Sneppen model
Abha Singh, Rahul Chhimpa, Avinash Chand Yadav
Abstract
We study the one-dimensional Bak-Sneppen model for the evolution of species in an ecosystem. Of particular interest are the temporal fluctuations in fitness variables. We numerically compute the power spectral density and apply the finite-size scaling method to get data collapse. A clear signature of $1/{f}^{\ensuremath{\alpha}}$ noise with $\ensuremath{\alpha}\ensuremath{\approx}1.2$ (long-time correlations) emerges for both local and global (or average) fitness noises. The limiting value of the spectral exponent, 0 or 2, corresponds to no interaction or a random neighbor version of the model, respectively. The local power spectra are spatially uncorrelated and also show an additional scaling, $\ensuremath{\sim}1/L$, in the frequency regime ${L}^{\ensuremath{-}\ensuremath{\lambda}}\ensuremath{\ll}f\ensuremath{\ll}1/2$, where $L$ is the linear extent of the system.