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.