  We study the evolution of sexual and asexual populations in general fitness
landscapes. We find deep relations between the mathematics of biological
evolution and the formalism of quantum mechanics. We give the general structure
of the evolution of populations which is in general an off-equilibrium process
that can be expressed by path integrals over phylogenies. These phylogenies are
sums of linear lineages for asexual populations. For sexual populations
instead, each lineage is a tree of branching ratio two and the path integral
describing the evolving population is given by a sum over these trees. Finally,
we show that the Bose-Einstein and the Fermi-Dirac distributions describe the
stationary state of biological populations in simple cases.
