Exact dynamics for a mutator gene model
We investigate the dynamics of a molecular evolution model related to the mutator gene phenomenon. Here mutation in one gene drastically changes the properties of the whole genome. We investigated the Crow-Kimura version of the model, which can be mapped into a Hamilton-Jacobi equation. For the symmetric fitness landscape, we calculated the dynamics of the maximum of the total population distribution. We found two phases in the dynamics: a simple one when the maximum of distribution moves along a characteristics, and more involved one when the maximum jumps to another characteristic at some turnout point T.