Understanding the complex interaction between genotype and phenotype is a major challenge of Evolutionary Developmental Biology. One important facet of this complex interaction has been called "Developmental System Drift" (DSD). DSD occurs when a similar phenotype, which is homologous across a group of related species, is produced by different genes or gene expression patterns in each of these related species. We constructed a mathematical model to explore the developmental and evolutionary dynamics of DSD in the gene network underlying wing polyphenism in ants. Wing polyphenism in ants is the ability of an embryo to develop into a winged queen or a wingless worker in response to an environmental cue. Although wing polyphenism is homologous across all ants, the gene network that underlies wing polyphenism has evolved. In winged ant castes, our simulations reproduced the conserved gene expression patterns observed in the network that controls wing development in holometabolous insects. In wingless ant castes, we simulated the suppression of wings by interrupting (up- or downregulating) the expression of genes in the network. Our simulations uncovered the existence of four groups of genes that have similar effects on target gene expression and growth. Although each group is comprised of genes occupying different positions in the network, their interruption produces vestigial discs that are similar in size and shape. The implications of our results for understanding the origin, evolution, and dissociation of the gene network underlying wing polyphenism in ants are discussed.