Open quasispecies systems: New approach to evolutionary adaptation

Chinese Journal of Physics. 2021. P. 1–27.

Samokhin I., Yakushkina T., Bratus A.

Consider a mathematical model of evolutionary adaptation of fitness landscape and mutation matrix as a reaction to population changes. As a basis, we use an open quasispecies model, which is modified to include explicit death flow. We assume that evolutionary parameters of mutation and selection processes vary in a way to maximize the mean fitness of the system. From this standpoint, Fisher’s theorem of natural selection is being rethought and discussed. Another assumption is that system dynamics has two significant timescales. According to our central hypothesis, major evolutionary transitions happen in the steady-state of the corresponding dynamical system, so the evolutionary time is much slower than the one of internal dynamics. For the specific cases of quasispecies systems, we show how our premises form the fitness landscape adaptation process.

Keywords: evolutionary modeling, non-linear partial differential equations, модели эволюции, replicator systems, репликаторные системы