A new mathematical model of phyllotaxis to solve the genuine puzzle spiromonostichy

The view is widely accepted that the inhibitory effect of existing leaf primordia on new primordium formation determines phyllotactic patterning. Previous studies have shown that mathematical models based on such inhibitory effect can generate most of phyllotactic patterns. However, a few types of phyllotaxis still remain unaddressed. A notable example is costoid phyllotaxis showing spiromonostichy, which is characterized by a steep spiral with a small divergence angle and is unique to Costaceae plants. Costoid phyllotaxis has been called a "genuine puzzle" because it seems to disagree with the inhibitory effect-based mechanism. In an attempt to produce a steep spiral pattern, we developed a new mathematical model assuming that each leaf primordium emits not only the inhibitory effect but also some inductive effect. Computer simulations with the new model successfully generated a steep spiral pattern when these two effects met a certain relationship. The obtained steep spiral matched the real costoid phyllotaxis observed with Costus megalobractea. We also found by the mathematical model analysis that the early phyllotactic transition in the seedlings of this plant can be explained by the SAM enlargement.