  We study the equilibrium behaviour of a deterministic four-state
mutation-selection model as a model for the evolution of a population of
nucleotide sequences in sequence space. The mutation model is the Kimura 3ST
mutation scheme, and the selection scheme is assumed to be invariant under
permutation of sites. Considering the evolution process both forward and
backward in time, we use the ancestral distribution as the stationary state of
the backward process to derive an expression for the mutational loss (as the
difference between ancestral and population mean fitness), and we prove a
maximum principle that determines the population mean fitness in
mutation-selection balance.
