Heterosis of fitness and phenotypic variance in the evolution of a diploid gene regulatory network

Heterosis describes the phenomenon, whereby a hybrid population has higher fitness than an inbred population, which has previously been explained by either Mendelian dominance or overdominance under the general assumption of a simple genotype–phenotype relationship. However, recent studies have demonstrated that genes interact through a complex gene regulatory network (GRN). Furthermore, phenotypic variance is reportedly lower for heterozygotes, and the origin of such variance-related heterosis remains elusive. Therefore, a theoretical analysis linking heterosis to GRN evolution and stochastic gene expression dynamics is required. Here, we investigated heterosis related to fitness and phenotypic variance in a system with interacting genes by numerically evolving diploid GRNs. According to the results, the heterozygote population exhibited higher fitness than the homozygote population, indicating fitness-related heterosis resulting from evolution. In addition, the heterozygote population exhibited lower noise-related phenotypic variance in expression levels than the homozygous population, implying that the heterozygote population is more robust to noise. Furthermore, the distribution of the ratio of heterozygote phenotypic variance to homozygote phenotypic variance exhibited quantitative similarity with previous experimental results. By applying dominance and differential gene expression rather than only a single gene expression model, we confirmed the correlation between heterosis and differential gene expression. We explain our results by proposing that the convex high-fitness region is evolutionarily shaped in the genetic space to gain noise robustness under genetic mixing through sexual reproduction. These results provide new insights into the effects of GRNs on variance-related heterosis and differential gene expression.