Statistical recognition of random and regular phyllotactic patterns

AIMS: A statistical method used in ecology is adapted to characterize the degree of order in phyllotactic systems. SCOPE: The test consists of subdividing a planar projection of the stem apical meristem into 16 sectors and counting the number of primordia appearing in each. By dividing the sum of squared deviations by the mean number of primordia per sector the chi-square (chi2) is obtained. When there are a total number of 20 primordia, if the chi2 is less than 6.26, the phyllotaxis is spiral; if it is between 6.26 and 27.5 the phyllotaxis is random; and if it is greater than 27.5, the phyllotaxis is distichous or whorled (level of significance alpha = 5 %). It is also possible to remove one or more sectors. If there are k sectors, the two critical values delimiting the random zone will be found in a chi2 table for k - 1 degrees of freedom. CONCLUSIONS: The method is applied to the analysis of sho mutants described by Itoh et al. in 2000 (Plant Cell 12: 2161-2174). The results obtained are in agreement with the theoretical analysis showing that a whorled or spiral phyllotactic system may contain a certain number of randomly distributed elements without losing its regular global structure.