Fitness landscapes of simple regulatory genetic interactions show pervasive heterozygote advantage and support stable polymorphism.

Although the regulation of gene expression is a fundamental link between genotype, phenotype, and fitness, little is known about how natural selection drives its evolution. To address this gap, we used a biophysical (thermodynamic) model of molecular interactions between allelic variants of transcription factors (TFs) and their cis-regulatory binding sites. We generated diploid genotype-phenotype maps for gene expression. We then applied a Gaussian fitness function to these maps, where the environment determines optimal expression level. The corresponding genotype-fitness landscapes are characterized by high ridges of heterozygote superiority. Heterozygote advantage occurs whenever the environmentally determined phenotypic optimum lies between the phenotypes of the two homozygotes. To determine whether this superiority could lead to stable polymorphism, for each of 201 optimal expression levels we determined frequency-fitness landscapes (allele frequency vs. fitness) for all allelic combinations; maximized their population mean fitnesses; identified combinations with globally maximal mean fitness; and found their equilibrium allele frequencies. Globally stable polymorphisms occurred whenever the phenotypic optimum laid between the phenotypes of the best two homozygotes. Stable polymorphisms occupied 49-75% of the range of optimal expression levels, depending on biophysical and fitness parameters. Virtually all included TF polymorphism, with binding site co-polymorphisms across 33-55% of the range. Neutral polymorphisms were also widely distributed. Neither molecular complexity of the TF-cis interaction nor pleiotropic constraint had qualitative effects on polymorphism. However, genetic load was negatively correlated with molecular complexity, suggesting that reducing genetic load may be an important mechanism for increasing the complexity of regulatory genetic interactions. While this analysis assumes environmental homogeneity, the results suggest that this phenomenon may enhance the role of environmental heterogeneity in maintaining regulatory polymorphism. Selection favors the maintenance of polymorphism not just because different homozygotes have higher fitness in different environments, but also because heterozygote advantage can act as a 'storage effect' by promoting regulatory polymorphism during the transitions between environmental states. We use the model to make predictions about future evolutionary trajectories in a well-documented case of regulatory heterozygote advantage involving flower color in an Alpine orchid. More empirical research on the extent and maintenance of regulatory polymorphism within populations is needed.