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. 1999 Aug 17;96(17):9716-20.
doi: 10.1073/pnas.96.17.9716.

Neutral evolution of mutational robustness

E van Nimwegen  1 , J P Crutchfield, M Huynen
Affiliations

Neutral evolution of mutational robustness

E van Nimwegen et al. Proc Natl Acad Sci U S A. .

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.

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Figures

Figure 1
Figure 1
The target RNA secondary structure.
Figure 2
Figure 2
The evolution of RNA mutational robustness: convergence of the population’s average neutrality to the theoretical value, ⟨d⟩ = ρ ≈ 15.7, predicted by the spectral radius of G (upper dashed line). The network’s average neutrality d̄ is represented by the lower dashed line. Simulations used a population size of M = 104 and mutation rates of μ = 0.5 and μ = 0.1 per sequence. Simulations were started at sequences with either a relatively large number of neutral neighbors (ds = 24) (upper curves for each mutation rate) or a small number (ds = 5) (lower curves).
Figure 3
Figure 3
Dependence of the population neutrality on mutation rate μ and population size M. Simulations used three mutation rates, μ∈ {0.5, 0.1, 0.01}, and a range of population sizes, M∈ {10,000, 5,000, 1,000, 500, 250, 100, 50, 20}. The results show that the evolved neutrality in the population depends on the product Mμ of population size and mutation rate. Neutrality increases with increasing Mμ and saturates when Mμ > 500. When Mμ < 1 population neutrality approximates G’s average neutrality d̄ ≈ 12.0. When Mμ > 500, population neutrality converges to the spectral radius of the network’s adjacency matrix, ρ ≈ 15.7.
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