Fig 7. A simple model of cell replacement structure in epithelial crypts of the small intestine, based on results of [41] and [45].

A small number of stem cells (N _↑ ∼ 5) residing at the bottom of the intestinal crypt and are replaced at rate d _↑ ∼ 0.1 per stem cell per day. Empirical results [41, 45] suggest a cycle structure for stem cells. To achieve the correct replacement rate we set e _ij = 0.05/day for each neighboring pair. Stem cells in an individual crypt replace a much larger number of progenitor and differentiated cells (∼ 250; [46]). These downstream progenitor and differentiated cells are replaced about every day [46]. The hierarchical organization of intestinal crypts, combined with the low turnover rate of stem cells, limits the rate of neutral genetic substitutions ($\tilde{K}\approx 0.1u$ substitutions per day), since only mutations that arise in stem cells can fix.