Funnel landscape and mutational robustness as a result of evolution under thermal noise.

Using a statistical-mechanical model of spins, the evolution of phenotype dynamics is studied. Configurations of spins and their interaction J represent the phenotype and genotype, respectively. The fitness for selection of J is given by the equilibrium spin configurations determined by a Hamiltonian with J under thermal noise. The genotype J evolves through mutational changes under selection pressure to raise its fitness value. From Monte Carlo simulations we find that the frustration around the target spins disappears for J evolved under temperature beyond a certain threshold. The evolved Js give the funnel-like dynamics, which is robust to noise and also to mutation.