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

Fitness in time-dependent environments includes a geometric contribution