Escape from infinite adaptive peak

Abstract

We study the transition time between different meta-stable states in the continuous Wright-Fisher (diffusion) model. We construct an adaptive landscape for describing the system both qualitatively and quantitatively. When strong genetic drift and weak mutation generate infinite adaptive peaks, we calculate the expected time to escape from such peak states. We find a new way to analytically approximate the escape time, which extends the application of Kramer's classical formulae to the cases of non-Gaussian equilibrium distribution and bridges previous results in two limits. Our adaptive landscape, compared to the classical fitness landscape or other scalar functions, is directly related to system's middle-and-long-term dynamics and is self-consistent in the whole parameter space. Our work provides a complete description for the bi-stabilities in the present model.