Evolutionary dynamics of a polymorphic self-replicator population with a finite population size and hyper mutation rate

• Published in: Journal of theoretical biology Vol. 382; pp. 298 - 308
• Main Authors: Aita, Takuyo, Yomo, Tetsuya
• Format: Journal Article
• Language: English
• Published: England Elsevier Ltd 07.10.2015
• Subjects: Biological Evolution; Computer Simulation; Evolvability; Experimental evolution; Fitness landscape; In vitro evolution; Kinetics; Models, Genetic; Mutation; Mutation Rate; NK model; Population Density; Probability; Selection, Genetic; Time Factors; NK model; Experimental evolution; Fitness landscape; Evolvability; In vitro evolution
• ISSN: 0022-5193; 1095-8541; 1095-8541
• DOI: 10.1016/j.jtbi.2015.07.007

Self-replicating biomolecules, subject to experimental evolution, exhibit hyper mutation rates where the genotypes of most offspring have at least a one point mutation. Thus, we formulated the evolutionary dynamics of an asexual self-replicator population with a finite population size and hyper mutation rate, based on the probability density of fitnesses (fitness distribution) for the evolving population. As a case study, we used a Kauffman׳s “NK fitness landscape”. We deduced recurrence relations for the first three cumulants of the fitness distribution and compared them with the results of computer simulations. We found that the evolutionary dynamics is classified in terms of two modes of selection: the “radical mode” and the “gentle mode”. In the radical mode, only a small number of genotypes with the highest or near highest fitness values can leave offspring. In the gentle mode, genotypes with moderate fitness values can leave offspring. We clarified how the evolutionary equilibrium and climbing rate depend on given parameters such as gradient and ruggedness of the landscape, mutation rate and population size, in terms of the two modes of selection. Roughly, the radical mode conducts the fast climbing but attains to the stationary states with low fitness, while the gentle mode conducts the slow climbing but attains to the stationary states with high fitness. •We analyzed the evolutionary dynamics of an asexual self-replicator population.•The Kauffman׳s NK model was used as a model of the fitness landscape.•The dynamics was considered based on the local fitness distribution on the landscape.•The first three cumulants of fitnesses in the evolving population were formulated.•We examined how the dynamics depends on several parameters.