On the evolution of hypercycles

In this study, we examine the process of fitness landscape evolution of the hypercycle system. We assume that the parameters that define the fitness landscape change in order to maximize the mean fitness of the system. The environmental influence is expressed as resource limitation: we formalize it as a restriction on the fitness matrix coefficients. We show that this process of adaptation leads to a system that is sustainable in the presence of parasites. Even if the parasites are harmful to the classical hypercycle, the persistence of the population develops under fitness landscape evolution. One of the central results presented in this paper is the existence of a phase transition similar to the "error threshold" in the Eigen model: starting from some time moment the mean fitness value increase to a plateau and the hypercycle structure changes. The evolutionary parameters that define the fitness landscape and the mean fitness value tend to stabilize.