Fitness potentials and qualitative properties of the Wright-Fisher dynamics. (14th November 2018) - Chalub, Fabio A.C.C.; Souza, Max O.
Highlights: We introduce a mechanistic formalism for evolutionary processes valid in the diffusive regime. A monomorphic state reachable with minimum internal work is most likely to fixate. A heuristic graphical analysis provides significant insight on the dynamics. We developed and presented further numerical generalisations of the formalism. Abstract: We present a mechanistic formalism for the study of evolutionary dynamics models based on the diffusion approximation described by the Kimura Equation. In this formalism, the central component is the fitness potential, from which we obtain an expression for the amount of work necessary for a given type to reach fixation. In particular, within this interpretation, we develop a graphical analysis — similar to the one used in classical mechanics — providing the basic tool for a simple heuristic that describes both the short and long term dynamics. As a by-product, we provide a new definition of an evolutionary stable state in finite populations that includes the case of mixed populations. We finish by showing that our theory – rigorous for two types evolution without mutations– is also consistent with the multi-type case, and with the inclusion of rare mutations.