Phenotype-genotype relation in Wagner's canalization model.

Theoretical works have shed light on the impact of natural selection in shaping phenotypes and genotypes. Wagner's canalization model (Wagner, 1996) is one of the well-established models which describe emergent properties of evolving gene networks. In this paper, we propose a deeper theoretical understanding of this well-studied model and we extend its conclusions by characterizing new emergent properties of evolving networks. We start with the review of the Wagner model and its applications to robustness of gene networks, gene duplication and evolution of sexual reproduction. Then, we perform a mathematical analysis to gain a better understanding of the model evolutionary dynamics. Doing so paves the way to study systematically the impact of mutation rates on compatibility of genotypes, variability of phenotypes and viability of offspring in evolving populations. Finally, we derive new observations concerning two emergent properties concerning evolved genomes robustness. First, we show that selecting for development towards a specific phenotype also contributes to enhance the stability of other alternative phenotypes which can be revealed under stress. Second, we find that this generalized canalization also renders gene networks more robust towards gene deletion, loss of interactions, perturbations of regulation activity and mutations. Therefore, not only evolution selects for individuals robust to types of perturbation they have faced in previous generations, but also robust to types of perturbations they have never experienced.