In general, it is presumed that colonic epithelial stem cells are the principal cell type at risk of incurring the series of somatic mutations leading to carcinoma, since all other epithelial cell types are short-lived. Mutant stem cell clonal expansion increases the risk for subsequent mutations and is therefore a potentially important step in carcinogenesis. The stem cells reside in colonic crypts, simple tubular foldings of the epithelium, and thus counting crypts provides an indirect means to determine stem cell numbers. The normal crypt population is known to expand through a process of crypt replication and this is thought to result in a corresponding expansion of the epithelial stem cell population. A simple mathematical model of the population dynamics of normal and mutant crypts (crypts containing mutant stem cells) is developed and used to estimate a lower bound on the relative rate of expansion of the mutant stem cell population. The model predicts that if mutant and normal crypt populations expand at the same rate, and if the mutation rate is small relative to the rate of growth, then the fraction of clusters of mutant crypts composed of only a single mutant crypt should steadily decrease with age towards one-half. Aberrant crypts are easily recognizable lesions in human colon which have frequently been shown to contain cells with K-ras and occasionally APC gene mutations. Application of the model to recent counts of aberrant crypt cluster sizes indicate that the aberrant crypt population, and the contained mutant stem cell population, is expanding substantially faster than normal.