Evolution is a quest for innovation: organisms adapt to changing natural
selection by evolving new phenotypes. At the molecular level, adaptive
evolution takes place in a sea of stochasticity generated by random new
mutations and fluctuations in reproduction. The irreversibility of adaptive
evolution can be measured by a quantity called fitness flux. This talk
addresses the statistical foundation of molecular evolution, which is
provided by a fitness flux theorem. The theorem reconciles opposing classic
views of molecular evolution expressed by R.A. Fisher's fundamental theorem
of natural selection and by S. Wright's dynamics in fitness landscapes. It
shows that evolutionary dynamics and modern nonequilibrium thermodynamics
obey strikingly analogous statistical principles which, in turn, can be
traced back to Feynman's quantum mechanics. We will discuss how fitness flux
can be measured and the theorem can be tested by evolution experiments and
by analysis of genome sequences.