Relaxation of Evolutionary Dynamics on the Bethe Lattice

Realistic evolutionary systems are generally structured and are in infinite dimensions. We study the relaxation behavior of evolutionary dynamics on a Bethe lattice, which concerns the invasion of mutants into a population of wild-type individuals. Since the boundary effect plays a significant role in a finite system, with proper approximation we propose an effective method to characterize the evolutionary dynamics. The relaxation behavior of the invasion process is analytically investigated, which is confirmed by extensive simulations. This work is the first systematical investigation on evolutionary dynamics in an infinitely dimensional lattice.