Hamiltonian model for multidimensional epistasis

We propose and solve a Hamiltonian model for multidimensional epistatic interactions between beneficial mutations. The model gives rise to either a phase transition between two equilibrium states, without any coexistence, or exhibits a state where hybrid species coexist, with gradual passage from one wild type to another. The transition takes place as a function of the tolerance of the environment, which we defined as the amount of noise in the system.