Two-step mechanism of spiral phyllotaxis

Fibonacci numbers such as 5, 8, and 13 occur in the spiral arrangement of lateral organs at shoot tips in plants. While the cone scales of conifers are normally arranged in 5 and 8 (or 8 and 13) curved rows in opposite directions, other numbers such as 4 and 7 (or 7 and 11) are found anomalously. The observed numbers still obey the Fibonacci rule, with the next number being the sum of the preceding two. Although these observations have been made for centuries, the underlying mechanisms of the numerical relationship have not been investigated. Here, we show that this phenomenon is caused by a two-step mechanism: (1) maintenance of a constant angle between consecutive lateral organs and (2) strong canalization of this angle to a specific value. The first step of the mechanism precedes the second step of the mechanism because the Fibonacci-rule pattern is due to the first step, while the second step distinguishes normal, anomalous and unobserved types. The current dominance of the normal type is a result of the evolutionary process of the second step.