title: A lognormal distribution of the lengths of terminal twigs on self-similar branches of elm trees.
abstract: 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.
authors.affiliation: Department of Life Science and Agriculture, Obihiro University of Agriculture and Veterinary Medicine, Inada-cho, Obihiro 080-8555, Japan koyama@obihiro.ac.jp.
authors.forename: Kohei
authors.identifier: 0000-0001-6707-3130
authors.initials: K
authors.lastname: Koyama
authors.affiliation: Department of Physics, Faculty of Science and Engineering, Chuo University, Bunkyo, Tokyo 112-8551, Japan.
authors.forename: Ken
authors.initials: K
authors.lastname: Yamamoto
authors.affiliation: Department of Environmental Solution Technology, Faculty of Science and Technology, Ryukoku University, 1-5 Yokotani, Seta Oe-cho, Otsu 520-2194, Japan.|Joint Research Center for Science and Technology, Ryukoku University, 1-5 Yokotani, Seta Oe-cho, Otsu 520-2194, Japan.
authors.forename: Masayuki
authors.identifier: 0000-0003-4831-7181
authors.initials: M
authors.lastname: Ushio
mesh_terms: D018547:Plant Stems / Q000254:growth & development*; D014197:Trees / Q000254:growth & development; D034403:Ulmus / Q000254:growth & development*
keywords: WBE theory; allometry; fractal; phenotypic plasticity; shoot size; stochastic process