The predominantly hexagonal cell pattern of simple epithelia was noted in the earliest microscopic analyses of animal tissues¹, a topology commonly thought to reflect cell sorting into optimally packed honeycomb arrays². Here we use a discrete Markov model validated by time-lapse microscopy and clonal analysis to demonstrate that the distribution of polygonal cell types in epithelia is not a result of cell packing, but rather a direct mathematical consequence of cell proliferation. On the basis of in vivo analysis of mitotic cell junction dynamics in Drosophila imaginal discs, we mathematically predict the convergence of epithelial topology to a fixed equilibrium distribution of cellular polygons. This distribution is empirically confirmed in tissue samples from vertebrate, arthropod and cnidarian organisms, suggesting that a similar proliferation-dependent cell pattern underlies pattern formation and morphogenesis throughout the metazoa.

1. Department of Genetics and Howard Hughes Medical Institute, Harvard Medical School, Boston, Massachusetts 02115, USA
2. Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
3. †Present address: Stowers Institute for Medical Research, 1000 East 50th Street, Kansas City, Missouri 64110, USA
4. *These authors contributed equally to this work

Correspondence to: Matthew C. Gibson^1,3,4 Correspondence and requests for materials should be addressed to M.C.G. (Email: mgx@stowers-institute.org) or R.N. (Email: rad@eecs.harvard.edu).

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