| Mutations introduce novelty in the evolutionary process by modifying the genetically transmitted information (genotype). Natural selection acts on differences that arise through the expression of this information, that is on phenotypes. The genotype-phenotype map is therefore central to an understanding of evolution. We embed all genotypes on a high-dimensional hypercube, such that adjacent genotypes differ only by a single mutation. The genotype-phenotype map then induces 'neutral networks' that contain all genotypes with a particular phenotype. In many systems studied to date, the distribution of neutral network sizes is heavy-tailed: most networks are small, but some phenotypes are realized by very large numbers of genotypes. Here, we study the evolutionary implications of this skewed distribution using a simple mean-field description. Our findings confirm the intuition that frequent phenotypes are discovered earlier and are produced more often than rare ones and imply that the mutational accessibility of a phenotype is of paramount importance for its potential fixation in a population. Through extensive numerical simulations, we show a striking departure from the mean-field predictions for all but the most abundant phenotypes; the effect is due to the slow exploration of neutral spaces and can be interpreted as a reduction of the population size, similar to an effective temperature in out-of-equilibrium systems with slow relaxation. Our results underline the importance of the network structure induced by the genotype-phenotype map, and raise important questions about the possibility of coarse-grained descriptions of evolutionary dynamics. |
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