Cell proliferation involves duplication of all cell constituents and their more-or-less equal segregation to daughter cells. It seems probable that the performance of primitive cell-like structures would have been dogged by poor duplication and segregation fidelity, and by parasitism. This favoured evolution of the genome and with it the distinction between `genomic' components like chromosomes whose synthesis is periodic and most other `functional' components whose synthesis is continuous. Eukaryotic cells evolved from bacterial ancestors whose fused genome was replicated from a single origin and whose means of segregating sister chromatids depended on fixing their identity at replication. Evolution of an endo- or cytoskeleton, initially as means of consuming other bacteria, eventually enabled evolution of the mitotic spindle and a new means of segregating sister chromatids whose replication could be initiated from multiple origins. In this primitive eukaryotic cell, S and M phases might have been triggered by activation of a single cyclin-dependent kinase whose destruction along with that of other proteins would have triggered anaphase. Mitotic non-disjunction would have greatly facilitated genomic expansion, now possible due to multiple origins, and thereby accelerated the tempo of evolution when permitted by environmental conditions.