Evolutionary advantage via common action of recombination and neutrality

Abstract

We investigate evolution models with recombination and neutrality. We consider the Crow-Kimura (parallel) mutation-selection model with the neutral fitness landscape, in which there is a central peak with high fitness A, and some of 1-point mutants have the same high fitness A, while the fitness of other sequences is 0. We find that the effect of recombination and neutrality depends on the concrete version of both neutrality and recombination. We consider three versions of neutrality: (a) all the nearest neighbor sequences of the peak sequence have the same high fitness A; (b) all the l-point mutations in a piece of genome of length l≥1 are neutral; (c) the neutral sequences are randomly distributed among the nearest neighbors of the peak sequences. We also consider three versions of recombination: (I) the simple horizontal gene transfer (HGT) of one nucleotide; (II) the exchange of a piece of genome of length l, HGT-l; (III) two-point crossover recombination (2CR). For the case of (a), the 2CR gives a rather strong contribution to the mean fitness, much stronger than that of HGT for a large genome length L. For the random distribution of neutral sequences there is a critical degree of neutrality ν(c), and for μ<μ(c) and (μ(c)-μ) is not large, the 2CR suppresses the mean fitness while HGT increases it; for ν much larger than ν(c), the 2CR and HGT-l increase the mean fitness larger than that of the HGT. We also consider the recombination in the case of smooth fitness landscapes. The recombination gives some advantage in the evolutionary dynamics, where recombination distinguishes clearly the mean-field-like evolutionary factors from the fluctuation-like ones. By contrast, mutations affect the mean-field-like and fluctuation-like factors similarly. Consequently, recombination can accelerate the non-mean-field (fluctuation) type dynamics without considerably affecting the mean-field-like factors.

Punctuated equilibrium and shock waves in molecular models of biological evolution

“…[3,14] with asexual biological evolution models. For example, we can extend the study of this paper to the finite-population problem [49] or the sexual biological evolution model with an approximate neutral fitness function [17]. It will be interesting to apply our findings to cancer, relating them with different stages of tumor progression [46].…”

“…Applications of the methods of statistical physics to the study of the molecular models of biological evolution [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and the origin of life [1,18] have attracted much attention in recent decades. In this paper, we use the methods of statistical physics to study punctuated equilibria [19][20][21]: a well-known phenomenon of biological evolution during long geological time scales, related to the the life tree [22].…”

“…An important concept in the modern molecular theory of genetics and biological evolution is epistasis, which means that different genes or mutations are not independent. Epistasis is positive (negative) when the second derivative of the fitness with respect to the number of mutations is positive, i.e., g (n) > 0 [negative, i.e., g (n) < 0] [17]. In positive (negative) epistasis, the effects of two mutations is larger (smaller) than the effects of the addition of two separate mutations.…”

“…In the usual statistical physical models of biological evolution, the genome of length L is considered as a collection of L alleles of two types: +1 and −1 [1,3,13,14,17], and there are 2…”

Modularity enhances the rate of evolution in a rugged fitness landscape

“…Nonetheless, nearly all analytical theoretical treatments assume a smooth fitness landscape with a dependence only on Hamming distance from a most-fit sequence [11], a linear or multiplicative fitness landscape for dynamical analysis of horizontal gene transfer [12,13], or an uncorrelated random energy model [14,15]. Horizontal gene transfer processes on more general, but still smooth, landscapes have been analyzed [16][17][18][19][20]. Here we provide, to our knowledge, the first analytical treatment of a finite-population Markov model of evolution showing how horizontal gene transfer couples to modularity in the fitness landscape.…”