Effects of Ploidy and Recombination on Evolution of Robustness in a Model of the Segment Polarity Network

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.

Author Summary

Most so-called “higher organisms” are diploid (have two copies of each gene) and reproduce sexually. Diploidy may be advantageous if one functional copy can mask the effects of a mutation in the other copy; however, it is a liability if most mutations are dominant. Sex can increase genetic diversity and the rate of evolution by creating new combinations of alleles that might function better together but can also disrupt working combinations. Given these trade-offs, why are sex and diploidy so common, and why do they occur so often together? We hypothesize that sex and diploidy allow gene networks to evolve to function more robustly in the face of genetic and environmental variation. This robustness would be advantageous because organisms are exposed to constantly changing environments and all genes undergo mutation. To test this hypothesis, we simulated evolution in a model of the segment polarity network, a well-studied group of genes essential for proper development in many organisms. We compared the robustness of haploid and diploid populations that reproduced either sexually or asexually. Sexually reproducing diploid populations evolved the greatest robustness, suggesting an explanation for the selective advantage of diploid sexual reproduction.