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Despite the many successes of cancer research, we lack the framework necessary to predict the ratio of familial (inherited) to sporadic (non-inherited) cancers. An evolutionary model of multistage carcinogenesis provides this framework by demonstrating that the number of tumour suppressor loci (TSLs) preventing cancer in a given tissue is expected to depend upon the tissue's vulnerability to pre-reproductive somatic mutation. Since this vulnerability increases with tissue size, single gene control of human cancer may be restricted to retinoblastoma, a cancer of the tiny embryonic retina. The model is used to estimate the frequency of mutant alleles causing inherited cancers, based on the population genetics of the mutation-selection balance between new mutations arising and selection that eliminates them. For each specific cancer, this balance is determined by the effectiveness with which pre-reproductive cancer is suppressed in the non-mutant genotype characteristic of that population. Effectiveness depends on an interaction between the number of TSLs suppressing the cancer and factors determining the tissue-wide somatic mutation rate, such as tissue size and number of pre-reproductive cell divisions. The model predicts that the commonest pre-reproductive cancers will have the lowest proportion of familial cases, and that cancers associated with the most TSLs will have the highest post-reproductive incidence but no elevated pre-reproductive risk (a pattern seen in human epithelial cancers).