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.

斐波那契数（例如5、8和13）出现在植物芽尖上的侧部器官的螺旋排列中。针叶树的圆锥鳞片通常以相反的方向排列在5和8（或8和13）个弯曲的行中，但异常地发现了其他数字，例如4和7（或7和11）。观察到的数字仍然服从斐波那契定律，下一个数字是前两个数字的和。尽管这些观察已经进行了数百年，但尚未研究数值关系的潜在机理。在这里，我们表明此现象是由两步机制引起的：（1）连续的侧向器官之间保持恒定的角度，（2）将该角度的强力根管化为特定值。该机制的第一步先于该机制的第二步，因为斐波那契规则模式是由于第一步引起的，而第二步则区分正常，异常和未观察到的类型。普通类型的当前优势是第二步进化过程的结果。