Bipartite Networks Show the Genotype-to-Phenotype Relationship in Biological Systems Models: A Study of the Robustness, Evolvability, and Accessibility in Linear Cellular Automata

In biological organisms, a single genotype may map to several phenotypes and vice-versa. This many-to-many relationship is believed to be a major drive of the phenotypic robustness and genotypic evolvability found in all life forms. Given the inherent complexity of the genotype-to-phenotype (G2P) mappings, we use cellular automata (CAs) as rudimentary proxies for biological organisms. CA models have the same many-to-many G2P mappings, and their sensitivity to initial conditions allows the same genotype to differentiate into different phenotypes. We use a bipartite network to study the G2P landscape, and its projections in either space. The degree distributions of the network and its projections are all heavy-tailed, denoting the presence of highly connected hubs, implying that increased robustness is supported by the network structure. We also show a strong correlation between the phenotype’s complexity and its robustness. We analyze the relationships between the robustness and the evolvability both at the genotypic and phenotypic level. Although we use different computational models, our results agree with those of previous similar studies, and with observations in biological organisms.