A lognormal distribution of the lengths of terminal twigs on self-similar branches of elm trees
A lognormal distribution of the lengths of terminal twigs on self-similar branches of elm trees
复制标题
榆树自相似枝顶枝长度的对数正态分布
DOI：
10.1098/rspb.2016.2395
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
and M. Ushio
中科院分区：
文献类型：
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作者：
K. Koyama;K. Yamamoto;and M. Ushio
对数正态分布和自相似性是与广泛的生物系统相关的特征。连续破碎模型建立了对数正态分布和自相似性之间的联系，并已被用来解释物种丰度分布。然而，到目前为止，在多细胞生物形式的研究中还没有类似的证据。我们测试的假设，日本榆树（Ulmus davidiana），一个自相似的分支过程的最终产品的终端茎的长度的分布，接近对数正态分布。我们测量了三个榆树枝条的茎段长度，结果表明：（1）每一次分枝都引起子茎长度相对于母茎的变异或误差，（2）枝条具有统计自相似性;观察到的误差分布在每个分支内的所有尺度上都是相似的，以及（iii）这些误差的乘法效应产生了末端树枝长度的变化，其很好地近似于对数正态分布，尽管对于一个分支观察到与严格对数正态性的一些统计学显著偏差。我们的研究结果提供了第一个经验证据，统计自相似性的有机体形式产生的器官大小的对数正态分布。
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.