Frank, S. A. 2004. Commentary: Mathematical models of cancer progression and epidemiology in the age of high throughput genomics. International Journal of Epidemiology 33:1179-1181.

The major principles of genetics and evolution were developed before the structure of DNA was discovered in 1953. Darwin got pretty much everything right about evolution, despite his mistaken views on genetics. After the rediscovery of Mendel’s theory, Fisher, Wright, and Haldane worked out the mathematical principles of mutation, selection, and evolutionary genetics during the first half of the 20th century. The spectacular accomplishments of modern molecular biology have greatly enriched understanding of genetics and evolution. However, the foundational principles of evolution and adaptation from the pre-molecular era remain the guidelines by which we interpret why biology appears as it does.

Perhaps Armitage and Doll’s paper marks the same sort of divide in cancer research. Their paper laid out foundational principles of cancer progression and epidemiology in mathematical form long before we knew about the molecular basis of somatic mutation and the key roles of genes such as p53 and APC.

The puzzle faced by Armitage and Doll was set out by Fisher and Hollomon and Nordling, who used epidemiological data to infer that cancer incidence increases with approximately the sixth power of age. The pioneers of genetics and evolution faced the same sort of problem: how can one use easily observed patterns in populations to infer the underlying dynamical processes that give rise to those patterns? In the case of cancer, what can be said about the dynamical processes of progression within individuals that would explain the aggregate patterns of epidemiology observed in populations?