Systematic variations in divergence angle

TL;DR

This paper presents methods for analyzing the divergence angles of leafy organs in plants, confirming their constancy with high precision and identifying systematic variations as primary causes of apparent fluctuations.

Contribution

It introduces practical analysis techniques and demonstrates that divergence angle variations are mainly systematic rather than random, challenging previous assumptions.

Findings

Divergence angle remains constant within less than one degree.

Apparent fluctuations are mainly due to systematic variations.

Random fluctuations are minor in divergence angle measurements.

Abstract

Practical methods for quantitative analysis of radial and angular coordinates of leafy organs of vascular plants are presented and applied to published phyllotactic patterns of various real systems from young leaves on a shoot tip to florets on a flower head. The constancy of divergence angle is borne out with accuracy of less than a degree. It is shown that apparent fluctuations in divergence angle are in large part systematic variations caused by the invalid assumption of a fixed center and/or by secondary deformations, while random fluctuations are of minor importance.