Data from: A lognormal distribution of the lengths of terminal twigs on self-similar branches of elm trees

Lognormal distributions and self-similarity are characteristics associated with a wide range of biological systems. The sequential breakage model has established a link between lognormal distributions and self-similarity and has been used to explain species abundance distributions. To date, however, there has been no similar evidence in studies of multicellular organismal forms. We tested the hypotheses that the distribution of the lengths of terminal stems of Japanese elm trees (Ulmus davidiana), the end products of a self-similar branching process, approaches a lognormal distribution. We measured the length of the stem segments of three elm branches and obtained the following results: (i) each occurrence of branching caused variations or errors in the lengths of the child stems relative to their parent stems; (ii) the branches showed statistical self-similarity; the observed error distributions were similar at all scales within each branch and (iii) the multiplicative effect of these errors generated variations of the lengths of terminal twigs that were well approximated by a lognormal distribution, although some statistically significant deviations from strict lognormality were observed for one branch. Our results provide the first empirical evidence that statistical self-similarity of an organismal form generates a lognormal distribution of organ sizes.对数正态分布（lognormal distribution）与自相似性（self-similarity）是诸多生物系统共有的典型特征。连续断裂模型（sequential breakage model）已证实对数正态分布与自相似性之间存在内在关联，并被广泛用于解释物种多度分布。然而迄今为止，在多细胞生物体形态的相关研究中，尚无此类实证依据。我们针对下述假说展开验证：作为自相似分枝过程的最终产物，日本榆（Ulmus davidiana）的末端茎干长度分布趋近于对数正态分布。我们对3根榆树枝的茎段长度进行了测量，得到如下结果：(i) 每一次分枝事件都会导致子茎相对于母茎的长度出现偏差或误差；(ii) 受试枝条呈现统计意义上的自相似性，且各枝条在所有尺度下观测到的误差分布均保持一致；(iii) 尽管其中一根枝条与严格的对数正态分布存在统计学意义上的显著偏离，但这些误差的累积倍增效应所产生的末端细枝长度变异，可通过对数正态分布得到较好拟合。本研究首次通过实证证实，生物体形态的统计自相似性可催生器官尺寸的对数正态分布。