title: A differential equation for the asymptotic fitness distribution in the Bak-Sneppen model with five species.
abstract: The Bak-Sneppen model is an abstract representation of a biological system that evolves according to the Darwinian principles of random mutation and selection. The species in the system are characterized by a numerical fitness value between zero and one. We show that in the case of five species the steady-state fitness distribution can be obtained as a solution to a linear differential equation of order five with hypergeometric coefficients. Similar representations for the asymptotic fitness distribution in larger systems may help pave the way towards a resolution of the question of whether or not, in the limit of infinitely many species, the fitness is asymptotically uniformly distributed on the interval [fc, 1] with fc ≳ 2/3.
authors.affiliation: University College London Medical School, Gower Street, London WC1E 6BT, United Kingdom. Electronic address: eckhard.schlemm.13@ucl.ac.uk.
authors.forename: Eckhard
authors.initials: E
authors.lastname: Schlemm
mesh_terms: D005075:Biological Evolution; D049810:Genetic Speciation; D016014:Linear Models; D055641:Mathematical Concepts; D008957:Models, Genetic; D009154:Mutation; D012641:Selection, Genetic
keywords: Bak–Sneppen model; Evolutionary biology; Hypergeometric function; Markov chain; Steady-state distribution