The fitness landscape is a critical concept in evolutionary biology and genetics that depicts fitness in the genotype space and visualizes the relationship between genotype and fitness. However, the fitness landscape is challenging to characterize because the quantitative relationships between genotype and phenotype and their association to fitness has not been comprehensively well described. To address this challenge, we adopted gene regulatory networks to determine gene expression dynamics. We analyzed how phenotype and fitness are shaped by the genotype in two-gene networks. A two-by-two matrix provided the two-gene regulatory network in which a vector with two angle values (Θ) was introduced to characterize the genotype. Mapping from this angle vector to phenotypes allowed for the classification of steady-state expression patterns of genes into seven types. We then studied all possible fitness functions given by the Boolean output from the on/off expression of the two genes. The possible fitness landscapes were obtained as a function of the genetic parameters Θ. Finally, the evolution of the population distribution under sexual reproduction was investigated in the obtained landscape. We found that the distribution was restricted to a convex region within the landscape, resulting in the branching of population distribution, including the speciation process.
