A geometrical model of Phyllotaxis

Abstract

A geometrical model of phyllotaxis which simulates the requirements of the next-available-space theory is developed and is shown to reproduce the spiral systems of nature. It also models the evolution of high-order from low-order members of the same type of system and the devolutionary processes that are characteristic of composite capituli. It is shown that all systems which arise de novo from a bare apex are likely to belong to the series m : m+l. This implies that high-order Fibonacci systems do not arise de novo but evolve from 1 : 2 or 2 : 3 systems. It is suggested that the development of whorled systems requires the intervention of secondary constraints that permit the initiation of more than one primordium at each node. Finally, the results are interpreted as showing that the Fibonacci and related limiting divergence angles that are approximated in nature are inevitable consequences of the packing of the primordia as they arise on the edge of the apical dome.

The shoot apices of higher plants are seen as hierarchical systems and the phenomena of phyllotaxis as relating to their higher levels. Systems theory suggests that causal mechanisms should be sought in the next lower level, rather than more remotely.