The spiral arrangement (phyllotaxis) of leaves is a shared morphology in land plants, and exhibits diversity constrained to the Fibonacci sequence. Phyllotaxis in vascular plants is produced at a multicellular meristem, whereas bryophyte phyllotaxis emerges from a single apical stem cell (AC) that is embedded in a growing tip of the gametophyte. An AC is asymmetrically divided into itself and a single ‘merophyte’, producing a future leaf and a portion of the stem. Although it has been suggested that the arrangement of merophytes is regulated by a rotation of the division plane of an AC, the quantitative description of the merophyte arrangement and its regulatory mechanism remain unclear. To clarify them, we examined three moss species, Tetraphis pellucida, Physcomitrium patens, and Niphotrichum japonicum, which exhibit 1/3, 2/5, and 3/8 spiral phyllotaxis, respectively. We measured the angle between the centroids of adjacent merophytes relative to the AC centroid on cross-transverse sections. At the outer merophytes, this divergence angle converged to nearly 120\(^\circ\) in T. pellucida, 136\(^\circ\) in N. japonicum, and 141\(^\circ\) in P. patens, which was nearly consistent with phyllotaxis, whereas the divergence angle deviated from the converged angle at the inner merophytes near an AC. A mathematical model, which assumes scaling growth of AC and merophytes and a constant angle of division plane rotation, quantitatively reproduced the sequence of the divergence angles. This model showed that successive relocations of the centroid position of an AC upon its division inevitably result in the transient deviation of the divergence angle. As a result, the converged divergence angle was equal to the rotation angle, predicting that the latter is a major regulator of the spiral phyllotaxis diversity in mosses.

叶子的螺旋排列（叶序）是陆生植物共有的形态，表现出受斐波那契数列限制的多样性。维管植物中的叶序是在多细胞分生组织中产生的，而苔藓植物的叶序则是从嵌入配子体生长尖端的单个顶端干细胞 (AC) 中产生的。一个 AC 不对称地分成它自己和一个单一的“分生植物”，产生一个未来的叶子和一部分茎。虽然有人提出分生植物的排列受AC分割平面的旋转调节，但对分生植物排列及其调控机制的定量描述仍不清楚。为了澄清它们，我们检查了三种苔藓，即Tetraphis pellucida、Physcomitrium patens和Niphotrichum japonicum，分别表现出 1/ 3、2 /5 和 3/8 螺旋叶序。我们测量了相邻分生植物的质心相对于交叉横截面上的 AC 质心之间的角度。在外部的分生植物，这个发散角在T. pellucida 中收敛到接近 120 \(^\circ\)，在N. japonicum 中收敛到136 \(^\circ\)，在P. patens 中收敛到141 \(^\circ\)，这几乎与叶序一致，而发散角偏离了 AC 附近内部分生植物的会聚角。一个数学模型，假设 AC 和分枝植物的比例增长和分割平面旋转的恒定角度，定量地再现了发散角的序列。该模型表明，AC 的质心位置在其分割时的连续重定位不可避免地导致发散角的瞬态偏差。结果，收敛的发散角等于旋转角，预测后者是苔藓螺旋叶序多样性的主要调节因子。