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Effects of ploidy and recombination on evolution of robustness in a model of the segment polarity network.

Kim KJ, Fernandes VM - PLoS Comput. Biol. (2009)

Bottom Line: Robustness was measured by simulating a mutation in the network and measuring the effect on the engrailed and wingless patterns; higher robustness corresponded to insensitivity of this pattern to perturbation.We compared robustness in diploid and haploid populations, with either asexual or sexual reproduction.In all cases, robustness increased, and the greatest increase was in diploid sexual populations; diploidy and sex synergized to evolve greater robustness than either acting alone.

View Article: PubMed Central - PubMed

Affiliation: Center for Cell Dynamics, Friday Harbor Labs, University of Washington, Friday Harbor, Washington, USA. kjkim@u.washington.edu

ABSTRACT
Many genetic networks are astonishingly robust to quantitative variation, allowing these networks to continue functioning in the face of mutation and environmental perturbation. However, the evolution of such robustness remains poorly understood for real genetic networks. Here we explore whether and how ploidy and recombination affect the evolution of robustness in a detailed computational model of the segment polarity network. We introduce a novel computational method that predicts the quantitative values of biochemical parameters from bit sequences representing genotype, allowing our model to bridge genotype to phenotype. Using this, we simulate 2,000 generations of evolution in a population of individuals under stabilizing and truncation selection, selecting for individuals that could sharpen the initial pattern of engrailed and wingless expression. Robustness was measured by simulating a mutation in the network and measuring the effect on the engrailed and wingless patterns; higher robustness corresponded to insensitivity of this pattern to perturbation. We compared robustness in diploid and haploid populations, with either asexual or sexual reproduction. In all cases, robustness increased, and the greatest increase was in diploid sexual populations; diploidy and sex synergized to evolve greater robustness than either acting alone. Diploidy conferred increased robustness by allowing most deleterious mutations to be rescued by a working allele. Sex (recombination) conferred a robustness advantage through "survival of the compatible": those alleles that can work with a wide variety of genetically diverse partners persist, and this selects for robust alleles.

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Diploid sexual populations evolve mutational robustness at lower                            mutation rate.Plots show results of 38 simulations to 5,000 generations with                            μ = 0.005, smoothed with a                            sliding window of 100 generations. (A) Robustness to point mutations                            shows diploid sexual populations evolve greater robustness, while                            diploid asexual populations have a transient decrease in robustness. (B)                            Symmetric double mutations were simulated the same as Figure 5D and                            eliminated most of the diploid robustness advantage. (C) Fraction of                            mutated individuals that were viable during evolutionary simulation. (D)                            Fitness load calculated according to Equation 16.
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pcbi-1000296-g009: Diploid sexual populations evolve mutational robustness at lower mutation rate.Plots show results of 38 simulations to 5,000 generations with μ = 0.005, smoothed with a sliding window of 100 generations. (A) Robustness to point mutations shows diploid sexual populations evolve greater robustness, while diploid asexual populations have a transient decrease in robustness. (B) Symmetric double mutations were simulated the same as Figure 5D and eliminated most of the diploid robustness advantage. (C) Fraction of mutated individuals that were viable during evolutionary simulation. (D) Fitness load calculated according to Equation 16.

Mentions: In the previous simulations, mutational robustness was expected to evolve due to the high mutation rate. Theory predicts such robustness should evolve when there is substantial genetic diversity, specifically when μN>1. Sex may allow selection for robustness at lower mutation rates, and this has been shown in randomly-wired transcriptional networks [35]. To test whether this holds in our network, we ran simulations with μ = 1/N = 0.005. Figure 9 shows the results of this simulation for 38 founders. We observed little robustness evolution in haploid populations, with no significant increase in robustness by generation 5,000. In contrast, diploid sexual populations evolved higher mutational robustness, while asexual diploid populations showed a transient decrease in robustness that stabilized by generation 1,000. As before, symmetric double mutations eliminated the diploid robustness advantage, indicating the diploid advantage was due to dominance of functional alleles. Again, recombination resulted in a greater fitness penalty in diploid populations compared to haploid (Figure 9C), and diploid sexual populations had the highest fitness load (Figure 9D). Thus, diploid sexual populations still experience the strongest selection for robustness when μN = 1.


Effects of ploidy and recombination on evolution of robustness in a model of the segment polarity network.

Kim KJ, Fernandes VM - PLoS Comput. Biol. (2009)

Diploid sexual populations evolve mutational robustness at lower                            mutation rate.Plots show results of 38 simulations to 5,000 generations with                            μ = 0.005, smoothed with a                            sliding window of 100 generations. (A) Robustness to point mutations                            shows diploid sexual populations evolve greater robustness, while                            diploid asexual populations have a transient decrease in robustness. (B)                            Symmetric double mutations were simulated the same as Figure 5D and                            eliminated most of the diploid robustness advantage. (C) Fraction of                            mutated individuals that were viable during evolutionary simulation. (D)                            Fitness load calculated according to Equation 16.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2637435&req=5

pcbi-1000296-g009: Diploid sexual populations evolve mutational robustness at lower mutation rate.Plots show results of 38 simulations to 5,000 generations with μ = 0.005, smoothed with a sliding window of 100 generations. (A) Robustness to point mutations shows diploid sexual populations evolve greater robustness, while diploid asexual populations have a transient decrease in robustness. (B) Symmetric double mutations were simulated the same as Figure 5D and eliminated most of the diploid robustness advantage. (C) Fraction of mutated individuals that were viable during evolutionary simulation. (D) Fitness load calculated according to Equation 16.
Mentions: In the previous simulations, mutational robustness was expected to evolve due to the high mutation rate. Theory predicts such robustness should evolve when there is substantial genetic diversity, specifically when μN>1. Sex may allow selection for robustness at lower mutation rates, and this has been shown in randomly-wired transcriptional networks [35]. To test whether this holds in our network, we ran simulations with μ = 1/N = 0.005. Figure 9 shows the results of this simulation for 38 founders. We observed little robustness evolution in haploid populations, with no significant increase in robustness by generation 5,000. In contrast, diploid sexual populations evolved higher mutational robustness, while asexual diploid populations showed a transient decrease in robustness that stabilized by generation 1,000. As before, symmetric double mutations eliminated the diploid robustness advantage, indicating the diploid advantage was due to dominance of functional alleles. Again, recombination resulted in a greater fitness penalty in diploid populations compared to haploid (Figure 9C), and diploid sexual populations had the highest fitness load (Figure 9D). Thus, diploid sexual populations still experience the strongest selection for robustness when μN = 1.

Bottom Line: Robustness was measured by simulating a mutation in the network and measuring the effect on the engrailed and wingless patterns; higher robustness corresponded to insensitivity of this pattern to perturbation.We compared robustness in diploid and haploid populations, with either asexual or sexual reproduction.In all cases, robustness increased, and the greatest increase was in diploid sexual populations; diploidy and sex synergized to evolve greater robustness than either acting alone.

View Article: PubMed Central - PubMed

Affiliation: Center for Cell Dynamics, Friday Harbor Labs, University of Washington, Friday Harbor, Washington, USA. kjkim@u.washington.edu

ABSTRACT
Many genetic networks are astonishingly robust to quantitative variation, allowing these networks to continue functioning in the face of mutation and environmental perturbation. However, the evolution of such robustness remains poorly understood for real genetic networks. Here we explore whether and how ploidy and recombination affect the evolution of robustness in a detailed computational model of the segment polarity network. We introduce a novel computational method that predicts the quantitative values of biochemical parameters from bit sequences representing genotype, allowing our model to bridge genotype to phenotype. Using this, we simulate 2,000 generations of evolution in a population of individuals under stabilizing and truncation selection, selecting for individuals that could sharpen the initial pattern of engrailed and wingless expression. Robustness was measured by simulating a mutation in the network and measuring the effect on the engrailed and wingless patterns; higher robustness corresponded to insensitivity of this pattern to perturbation. We compared robustness in diploid and haploid populations, with either asexual or sexual reproduction. In all cases, robustness increased, and the greatest increase was in diploid sexual populations; diploidy and sex synergized to evolve greater robustness than either acting alone. Diploidy conferred increased robustness by allowing most deleterious mutations to be rescued by a working allele. Sex (recombination) conferred a robustness advantage through "survival of the compatible": those alleles that can work with a wide variety of genetically diverse partners persist, and this selects for robust alleles.

Show MeSH