Several proposals are made to explain the apparent increase in complexity of certain lineages during evolution. The proposals (not made in this order) are: (1) that gene number is a valid measure of biological complexity; (2) that gene number has not increased continuously during evolution, but has risen in discrete steps; (3) that two of the biggest steps occurred at the transition from prokaryotes to eukaryotes and the transition from invertebrates to vertebrates; (4) that these steps were made possible by 'systemic' changes in the way that genetic information is managed in the genome; (5) that the ability to silence inappropriate promoters is the primary limitation on gene number; (6) that the invention of nucleosomes (and perhaps the nuclear membrane) facilitated the evolution of eukaryotes from prokaryotic ancestors; (7) that the spread of low density methylation throughout the genome facilitated the evolution of vertebrates from invertebrate ancestors.