Phyllotaxis: Its quantitative expression and relation to growth in the apex

Abstract

Current methods of classifying the phyllotaxis patterns found at stem apices are discussed, and it is concluded that the numerical measures employed do not characterize solely the arrangement or positioning of the primordia, but are partially determined also by primordial shape. A method of phyllotaxis assessment is proposed that is free from this ambiguity. For a complete description three parameters are necessary, namely, the angle of the cone tangential to the apex in the region under consideration, the divergence angle, and the plastochrone ratio, i.e. the ratio of the radial distances of two successive primordia from the central axis. For assessment of the transverse component of the system the two last parameters are alone required. Of these three characteristics the plastochrone ratio is the most useful, and from it a ‘phyllotaxis index’ may be calculated that immediately conveys the most essential information relating to the primordial arrangement. Since this index is a continuously varying function, phyllotaxis assessment is no longer confined to a few discrete recognized systems, and it becomes possible to compare quantitatively with one another phyllotaxis arrangements of very diverse kinds. The relationship between the index and primordial pattern is presented for all important divergence angles, and also for those systems wherein more than one leaf appears at each node. The phyllotaxis index is rigidly related to the ratio of the transverse components of two areas, that of the central apex and that of the newly initiated primordium; a simple extension enables a similar relationship to be determined on the actual apical surface, opening the way for a practical adaptation of the older theoretical concept of ‘ bulk ratio'.