  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 [f,1] with f approximately equal to 2/3.
