doi:10.1016/j.mbs.2008.03.010 
Copyright © 2008 Elsevier Inc. All rights reserved.
The effect of recombination on the neutral evolution of genetic robustness
aBiological Physics Department, Eötvös University, H-1117, Budapest, Hungary
Received 26 February 2008;
revised 25 March 2008;
accepted 29 March 2008.
Available online 6 April 2008.
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Abstract
Conventional population genetics considers the evolution of a limited number of genotypes corresponding to phenotypes with different fitness. As model phenotypes, in particular RNA secondary structure, have become computationally tractable, however, it has become apparent that the context dependent effect of mutations and the many-to-one nature inherent in these genotype–phenotype maps can have fundamental evolutionary consequences. It has previously been demonstrated that populations of genotypes evolving on the neutral networks corresponding to all genotypes with the same secondary structure only through neutral mutations can evolve mutational robustness [E. van Nimwegen, J.P. Crutchfield, M. Huynen, Neutral evolution of mutational robustness, Proc. Natl. Acad. Sci. USA 96(17), 9716–9720 (1999)], by concentrating the population on regions of high neutrality. Introducing recombination we demonstrate, through numerically calculating the stationary distribution of an infinite population on ensembles of random neutral networks that mutational robustness is significantly enhanced and further that the magnitude of this enhancement is sensitive to details of the neutral network topology. Through the simulation of finite populations of genotypes evolving on random neutral networks and a scaled down microRNA neutral network, we show that even in finite populations recombination will still act to focus the population on regions of locally high neutrality.
Keywords: Mutational robustness; Recombination; Population dynamics; Neutral networks
Fig. 1. Histograms of the entropy H and mutational robustness enhancement D/D0 for different values of r. Numerically calculating the stationary distribution of the population on 105 neutral networks M=200 genotypes of length L=20 randomly drawn from the uniform attachment ensemble (a and b) and preferential attachment ensembles (b and c) indicated that recombination leads to significant enhancement of mutational robustness under very general conditions. Comparison of the results for the two ensembles suggests that preferential attachment networks, where genotypes of higher centrality are more neutral, evolve higher levels of mutational robustness.
Fig. 2. Simulations on a random uniform attachment network with M=200, L=20 with different values of μN show that the extent to which mutational robustness is evolved increases as μN becomes larger. (a–c) snapshots of the time evolution of mutational robustness enhancement D/D0 in a population evolving on the same random uniform attachment network with different values of μN, time is indicated in units of 2N generations. Recombination was turned on at t=30 (indicated by the arrow). (d) mutational robustness enhancement D/D0 as a function of μN for the same network with r=10 as calculated from 100 simulations with random initial conditions, where the population was allowed to evolve for 100×2N generations, the error bars indicate the variance in the time averages over runs with random initial conditions. The dashed line indicates the value of the mutational robustness enhancement D/D0 in the N→∞ limit, throughout.
Fig. 3. To investigate a more realistic neutral network we performed simulations using a scaled down analog of microRNA stem-loop hairpin structures (a) consisting of a 7 nucleotide long loop and a 3 nucleotide long stem region. (b) The extent of mutational robustness was found to be higher in the presence of recombination (r=10) then without it (r=0) for all values of μN. Simulations for different values of μN were performed for a set of 20 random initial conditions starting from which the population was allowed to evolve for 100×2N generations, the error bars indicate the variance in the time averages over runs with random initial conditions. The dashed line indicates the value of D0 throughout.
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