Two algorithms of determining the middle point of the shoot apex by surrounding organ primordia positions and their usage for computer measurements of divergence angles

Abstract

The measurements of the divergence angle between organ primordia in magnolia floral apices and vegetative apices (embryonic shoots) of coniferous trees were performed, using computer application Phyl for IRIX. It appears that the values of the angle are strongly affected by the position of the apex centre, which was calculated by the program on a base of input positions of surrounding primordia. Two algorithms were used to determine the centre position: in program version Phyl 1 it was calculated as the gravity centre whereas in Phyl 2 version as a geometrical midpoint. The both methods differ in resulting centre position. This is dependent on such apex features as: proportions between its size and the size of primordia (expression of phyllotaxis), the angular distances between succesive primordia (quality of phyllotaxis), radial distances between primordia of different age (profile of the apical dome), the number of recorded primordia. The accuracy and reliability of both algorithms for determination of the centre position and, consequently, the reliability of divergence measurements were verified by applying them to ideal, computer simulated spiral phyllotactic systems with divergence given arbitrarily by the user. The conclusions from the results of simulations are that there is a possibility of selecting more suitable algorithm for particular apex with regard to specific parameters of its phyllotactic system.

Keywords

• phyllotaxis
• apex
• geometrical centre
• gravity centre
• divergence angle
• computer simulation