Fig. 1

Mutational robustness and phenotypic similarity after mutations before and after gene duplication. a Mutational robustness before and after duplication. Each dot represents a GRN in our random sample; its position along the horizontal and vertical axes reflects the network’s \(R_\mu\) before and after gene duplication, respectively. Light blue points represent duplication-resistant GRNs and the dark ones duplication-susceptible GRNs. The continuous line is the identity line; points above and below such line indicate, respectively, GRNs that increased or decreased \(R_\mu\) after duplication. b Phenotypic similarity after mutations. The similarity to the original phenotype of the phenotypes that mutation produces is significantly greater after adding a duplicate gene in duplication-resistant GRNs but not after adding a non-duplicate regulator gene in addition-resistant GRNs. The panel includes data for 1,000 GRNs before adding a new gene, 588 duplication-resistant GRNs and 413 addition-resistant GRNs. We note that duplication-resistance and addition-resistance are not mutually exclusive categories