SIMULATIONS OF TRANSITIONS FROM REGULAR TO STOCHASTIC PHYLLOTACTIC PATTERNS

Abstract

The paper deals with a statistical method to analyze irregular phyllotactic patterns. To characterize the degree of order in phyllotactic systems, we determine the variation of the angle of divergence of a given leaf with regard to the preceding one. By knowing the range of uncertainty of the angle of divergence, it is possible to determine from which leaves rank a system becomes completely disorganized. We show that there is a quantitative link between the degree of uncertainty of the angle of divergence, and the number of regularly and randomly distributed leaves. To quantify this relationship, we deduced a formula from numerical simulations involving different ranges of uncertainty that can be observed in the angle of divergence in three different phyllotactic patterns: distichous (two orthostichies), opposite-decussate (four orthostichies) and spiral (137°). A χ2statistical test allows us to determine the threshold of transition between ordered and disordered phyllotactic patterns with a fixed level of confidence. By using the sho mutants described by Itoh et al.1as a case study, we show that this formula is useful mainly for analyzing the degree of order in phyllotactic mutants from two complementary points of view: the number of regularly distributed leaves and the degree of uncertainty of the divergence angle.