Estimation of directional division frequencies in vascular cambium and in marginal meristematic cells of plants

Using simple arithmetical formulae, it is shown that, when the meristematic initial cells of a growing plant organ are arranged in a ring, the cellular dimensions predict the relative frequencies of anticlinal and periclinal divisions which these cells undergo. The pattern of cell file branching which appears during the course of development, and which is predicted by this mathematical model, is validated using data pertaining to the numbers and dimensions of initial cells within the secondary vascular cambium of hybrid aspen trees. Data pertaining to a second, simpler set of initial cells which comprises the outer cellular ring of the thallus of the alga Coleochaete orbicularis, and from which all the radial cell files of the circular disc-like thallus are descended, have also been used for model validation. Combining the mathematical approach to division frequencies with data of actual cell sizes permits inferences about the course of the increase of the number of cell files (generated by the anticlinal divisions) and the number of cells within each file (generated by the periclinal divisions) during the earlier stages of secondary tissue or thallus development, and also about how they will develop at future stages. The question whether or not cell division patterns conform to the geometry of the system in which the cells are embedded is also discussed.