Although numerous investigators assume that the global features of genetic networks are moulded by natural selection, there has been no formal demonstration of the adaptive origin of any genetic network. This Analysis shows that many of the qualitative features of known transcriptional networks can arise readily through the non-adaptive processes of genetic drift, mutation and recombination, raising questions about whether natural selection is necessary or even sufficient for the origin of many aspects of gene-network topologies. The widespread reliance on computational procedures that are devoid of population-genetic details to generate hypotheses for the evolution of network configurations seems to be unjustified.