  We investigate the profound relation between the equations of biological
evolution and quantum mechanics by writing a biologically inspired equation for
the stochastic dynamics of an ensemble of particles. Interesting behavior is
observed which is related to a new type of stochastic quantization. We find
that the probability distribution of the ensemble of particles can be
decomposed into eigenfunctions associated to a discrete spectrum of
eigenvalues. In absence of interactions between the particles, the
out-of-equilibrium dynamics asymptotically relaxes towards the fundamental
state. This phenomenon can be related with the Fisher theorem in biology. On
the contrary, in presence of scattering processes the evolution reaches a
steady state in which the distribution of the ensemble of particles is
characterized by a Bose-Einstein statistics. In order to show a concrete
example of this stochastic quantization we have solved explicitly the case in
which the potential energy has the harmonic oscillator form.
