Optimality principles in evolutionary genetics

A population evolves due to changes in its gene frequencies arising due to mutations, natural selection, random genetic drifts and migrations, Svirezh ev introduced an integral variational principle, in analogy with the least- action principle of classical mechanics, by defining a Lagrangian which rem ained stationary on the trajectory followed by the population undergoing se lection, This principle can also be extended to multiple loci in some simpl e cases. However, in a two-locus model or more general models, there is not straightforward extension of this principle if linkage and epistasis are p resent. The local optimality principle can be geometrically formulated in a Riemannian metric space of gene frequencies: so that, under evolutionary p ressures, the population trajectory moves in that direction along which the increment of the mean fitness is maximum.