Asymptotic fitness distribution in the Bak-Sneppen model of biological evolution with four species

TL;DR

This paper introduces a novel method to compute the long-term fitness distribution in the Bak-Sneppen model, successfully deriving explicit results for models with four and five species, advancing understanding of evolutionary dynamics.

Contribution

A new computational approach for asymptotic fitness distribution in the Bak-Sneppen model, with explicit solutions for four species and recurrence relations for five species.

Findings

Derived the full asymptotic distribution for four species

Established a recurrence relation for five species

Enhanced analytical understanding of the Bak-Sneppen model

Abstract

We suggest a new method to compute the asymptotic fitness distribution in the Bak-Sneppen model of biological evolution. As applications we derive the full asymptotic distribution in the four-species model, and give an explicit linear recurrence relation for a set of coefficients determining the asymptotic distribution in the five-species model.