A family of fitness landscapes modeled through gene regulatory networks

Over 100 years, Fitness landscapes have been a powerful metaphor for understanding the evolution of biological systems. These landscapes describe how genotypes are connected to each other and are related according to relative fitness. Despite the high dimensionality of such real-world landscapes, empirical studies are often limited in their ability to quantify the fitness of different genotypes beyond point mutations, while theoretical works attempt statistical/mechanistic models to reason the overall landscape structure. However, most classical fitness landscape models overlook an instinctive constraint that genotypes leading to the same phenotype almost certainly share the same fitness value, since the information of genotype-phenotype mapping is rarely incorporated. Here, we investigate fitness landscape models through the lens of Gene Regulatory Networks (GRNs), where the regulatory products are computed from multiple genes and collectively treated as the phenotypes. With the assumption that regulatory mediators/products exhibit binary states, we prove topographical features of GRN fitness landscape models such as accessibility and connectivity insensitive to the choice of the fitness function. Furthermore, using graph theory, we deduce a mesoscopic structure underlying GRN fitness landscape models that retains necessary information for evolutionary dynamics with minimal complexity. We also propose an algorithm to construct such a mesoscopic backbone which is more efficient than the brute-force approach. Combined, this work provides mathematical implications for fitness landscape models with high-dimensional genotype-phenotype mapping, yielding the potential to elucidate empirical landscapes and their resulting evolutionary processes in a manner complementary to existing computational studies.