Selection via flatness as a dynamical effect in evolution models with finite population

We investigate the phenomenon of selection via flatness. In the static case, the finiteness of the population does not seriously influence the increase of mean fitness of population due to flatness around a peak. The effect is proportional to 1/square root(L), where L is the genome length. We investigated the two peak model (high peak and a flat peak). We find that the selection of flatness for long genome lengths occurs as a dynamic phenomenon in the case of evolution with small populations. We found that two factors are crucial to define the role of flatness: special initial distribution (the population is located at centers of peaks) allows flat peak to attract more population, and the large value of mutations per population per virus life cycle sometimes also increases the role of flatness. We suggested simple criteria to identify the phenomenon of dynamical arresting of population around flat peak by experiment. We infer that selection via robustness is possible in evolution as a nonequilibrium phenomenon.