  We study the backwards Markov chain for the Bak-Sneppen model of biological
evolution and derive its corresponding reversibility equations. We show that,
in contrast to the forwards Markov chain, the dynamics of the backwards chain
explicitly involve the stationary distribution of the model, and from this we
derive a functional equation that the stationary distribution must satisfy. We
use this functional equation to derive differential equations for the
stationary distribution of Bak-Sneppen models in which all but one or all but
two of the fitnesses are replaced at each step. This gives a unified way of
deriving Schlemm's expressions for the stationary distributions of the
isotropic four-species model, the isotropic five-species model, and the
anisotropic three-species model.
