  We show that evolutionary computation can be implemented as standard
Markov-chain Monte-Carlo (MCMC) sampling. With some care, `genetic algorithms'
can be constructed that are reversible Markov chains that satisfy detailed
balance; it follows that the stationary distribution of populations is a Gibbs
distribution in a simple factorised form. For some standard and popular
nonparametric probability models, we exhibit Gibbs-sampling procedures that are
plausible genetic algorithms. At mutation-selection equilibrium, a population
of genomes is analogous to a sample from a Bayesian posterior, and the genomes
are analogous to latent variables. We suggest this is a general, tractable, and
insightful formulation of evolutionary computation in terms of standard machine
learning concepts and techniques.
  In addition, we show that evolutionary processes in which selection acts by
differences in fecundity are not reversible, and also that it is not possible
to construct reversible evolutionary models in which each child is produced by
only two parents.
