  Selection, mutation and random drift affect the dynamics of allele
frequencies and consequently of quantitative traits. While the macroscopic
dynamics of quantitative traits can be measured, the underlying allele
frequencies are typically unobserved. Can we understand how the macroscopic
observables evolve without following these microscopic processes? The problem
has previously been studied by analogy with statistical mechanics: the allele
frequency distribution at each time is approximated by the stationary form,
which maximizes entropy. We explore the limitations of this method when
mutation is small ($4N\!\mu<1$) so that populations are typically close to
fixation and we extend the theory in this regime to account for changes in
mutation strength. We consider a single diallelic locus under either
directional selection, or with over-dominance, and then generalise to multiple
unlinked biallelic loci with unequal effects. We find that the maximum entropy
approximation is remarkably accurate, even when mutation and selection change
rapidly.
