Application of Two Mathematical Models to the Araceae, a Family of Plants with Enigmatic Phyllotaxis

Abstract

In this paper we show that two mathematical models can be of great help in the analysis of observational data, in this case the difficult and little studied phyllotactic phenomena that occur in the Araceae family. We apply the Fundamental Theorem of Phyllotaxis, together with an explanatory model of phyllotaxis, to plant specimens of this family, to obtain phyllotactic parameters and information that cannot be otherwise obtained. Most significant is the fact that the two models show evidence of regularities in the overwhelming diversity of the patterns observed in the Araceae (essentiallyDracontium and Anthurium) characterized by discontinuous transitions. In particular, this work reveals the regularity of the behaviour of the divergence angle in the specimens analysed. Features of the inflorescences ofDracontium , especially the presence of whorls, are compared to those observed in inflorescences ofAnthurium (characterized by the absence of whorls), and in the capitulae of Compositae (characterized by continuous transition). We question the possible meaning at the genetic level of the diversity of patterns observed at the macroscopic level.