Neutral evolution of mutational robustness

Abstract

We introduce and analyze a general model of a population evolving over a network of selectively neutral genotypes. We show that the population's limit distribution on the neutral network is solely determined by the network topology and given by the principal eigenvector of the network's adjacency matrix. Moreover, the average number of neutral mutant neighbors per individual is given by the matrix spectral radius. These results quantify the extent to which populations evolve mutational robustness-the insensitivity of the phenotype to mutations-and thus reduce genetic load. Because the average neutrality is independent of evolutionary parameters-such as mutation rate, population size, and selective advantage-one can infer global statistics of neutral network topology by using simple population data available from in vitro or in vivo evolution. Populations evolving on neutral networks of RNA secondary structures show excellent agreement with our theoretical predictions.Kimura's (1) contention that a majority of genotypic change in evolution is selectively neutral has gained renewed attention with the recent analysis of evolutionary optimization methods (2, 3) and the discovery of neutral networks in genotypephenotype models for RNA secondary structure (4-6) and protein structure (7). It was found that collections of mutually neutral genotypes, which are connected via single mutational steps, form extended networks that permeate large regions of genotype space. Intuitively, a large degeneracy in genotypephenotype maps, when combined with the high connectivity of (high-dimensional) genotype spaces, readily leads to such extended neutral networks. This intuition is now supported by recent theoretical results (8,9).In evolution of ribozymes in vitro, mutations responsible for an increase in fitness are only a small minority of the total number of accepted mutations (10). This fact indicates that, even in adaptive evolution, the majority of point mutations is neutral. The fact that only a minority of loci is conserved in sequences evolved from a single ancestor similarly indicates a high degeneracy in ribozymal genotype-phenotype maps (11). Neutrality is also implicated in experiments where RNA sequences evolve a given structure starting from a range of different initial genotypes (12). More generally, neutrality in RNA and protein genotype-phenotype maps is indicated by the observation that their structures are much better conserved during evolution than their sequences (13,14).Given the presence of neutral networks that preserve structure or function in sequence space, one asks, how does an evolving population distribute itself over a neutral network? Can we detect and analyze structural properties of neutral networks from data on biological or in vitro populations? To what extent does a population evolve toward highly connected parts of the network, resulting in sequences that are relatively insensitive to mutations? Such mutational robustness has been observed in biological RNA structures (15) and in simula...

Robustness, Evolvability, and Accessibility in Linear Genetic Programming

“…We are particularly interested in analyzing population diffusions throughout genotype and phenotype networks [23], under mutational and recombinative variation operators, to understand how robustness and evolvability change as a function of phenotypic distance to the target.…”

Modelling ‘evo‐devo’ with RNA

“…interconnected regions. (68) Thus, a selection/mutation balance on a neutral network automatically yields phenotypes that are relatively robust to mutations. (68) Second, evolution requires the hereditary transmission of a phenotype rather than any particular genotype.…”

Critical mutation rate has an exponential dependence on population size

“…In addition, evolution of mutational robustness has been observed in simulated RNA evolution (van Nimwegan et al, 1999) and in laboratory protein evolution experiments (Bloom et al, 2007). Both van Nimwegan et al (1999) and Bloom et al (2007) place an emphasis on the degree of polymorphism in the population, suggesting that highly polymorphic populations are more likely to spread across many nodes of a neutral network (each corresponding to a genotype), concentrating at highly connected parts; individuals at highly connected nodes have greater robustness to mutation, which they pass on to the next generation. Robustness will evolve in any population where the product of the population size and frequency of mutation per sequence per generation is sufficiently large (>1).…”