Molecular Evolution under Macro-Perturbation Barrier and the Fixation Process of Polyploidization

Abstract

The Neutral Theory in molecular evolution mainly addresses the allele frequency change of individual loci, postulating that the fixation process of a mutant is independent of other loci. For instance, the basic formula of molecular evolution claims that the rate of molecular evolution ({lambda}) is determined by the mutation rate (v), the coefficient of selection (s) and the effective population size (Ne), asserting the basic rule of molecular evolution: {lambda}>v if s>0 (positive selection), {lambda}=v if s=0 (neutrality) or {lambda}<v if s<0 (negative selection). However, many studies have indicated that this independent assumption should be examined carefully. This paper studies focused on the effect of major-perturbation barrier on molecular evolution, which refers to a rare, randomly occurred major genetic, epigenetic or environmental event that virtually stopped the fixation process of a mutation, resulting in loss of the mutation. A special diffusion model called KAC model was invoked, which allows the stochastic trajectory of gene frequency toward fixation can be randomly stopped at any time with a certain rate. The analytical form of the rate of molecular evolution showed that a strictly neutral mutant would evolve more slowly than the mutation rate due to the macro-perturbation barrier. A further quasi-neutrality analysis (the rate of molecular evolution equals to the mutation rate) was carried out, based upon the balance between the selection advantage of the mutant and the macro-perturbation barrier. Finally, the theory of macro-perturbation barrier was illustrated by the fixation process of polyploidization, as the outcome of the short-term selective advantages and the genome instability.