  Phenotypic evolution implies sequential fixations of new genomic sequences.
The speed at which these mutations fixate depends, in part, on the relative
fitness (selection coefficient) of the mutant vs. the ancestor. Using a simple
population dynamics model we show that the relative fitness in dynamical
environments is not equal to the fitness averaged over individual environments.
Instead it includes a term that explicitly depends on the sequence of the
environments. This term is geometric in nature and depends only on the oriented
area enclosed by the trajectory taken by the system in the environment state
space. It is related to the well-studied geometric phases in classical and
quantum physical systems. We discuss possible biological implications of these
observations, focusing on evolution of novel metabolic or stress-resistant
functions.
