Mathematics and Computation in Phenotypic Switching

Phenotypic switching is the property of cultures of some bacteria and other microbes, including yeast, to change aspects of their phenotypes in response to environmental perturbation. This has been framed as a kind of "bet-hedging." Mathematical models of phenotypic switching assume that the two phenotypes can be represented as genes whose fitnesses change cyclically or randomly. The rate of mutation between these genes evolves in response to the changes in fitnesses. We derive mathematical representations for the evolution of the mutation rate in cyclic environments and show how the stable mutation rate depends on symmetry assumptions on the fluctuating fitnesses. Computer analyses show fascinating complexities with asymmetric selection.