A stochastic approach to phyllotactic patterns analysis.

A statistical method is presented to characterize the degree of order in phyllotactic systems. We developed equations allowing the theoretical estimation of the number of leaves regularly distributed (spiral or verticillate) in a partially random phyllotactic system. The equations are simple and accurate enough to make quantitative predictions concerning the organization of different phyllotactic patterns (verticillate, distichous, spiral and random). This method can bring out patterns that are not visible a priori on a planar representation of the shoot apex. As a case study, the method was applied to the quantitative analysis of the sho mutants recently produced by Itoh et al. [2000. SHOOT ORGANIZATION genes regulate shoot apical meristem organization and the pattern of leaf primordium initiation in Rice. Plant Cell 12, 2161-2174]. By using our method, it was possible to predict the number of leaves distributed in distichous or random patterns on these phyllotactic mutants.