{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T12:42:55Z","timestamp":1776429775977,"version":"3.51.2"},"reference-count":38,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,8,19]],"date-time":"2021-08-19T00:00:00Z","timestamp":1629331200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Many plant species produce ovate leaves, but there is no general parametric model for describing this shape. Here, we used two empirical nonlinear equations, the beta and Lobry\u2013Rosso\u2013Flandrois (LRF) equations, and their modified forms (referred to as the Mbeta and MLRF equations for convenience), to generate bilaterally symmetrical curves along the x-axis to form ovate leaf shapes. In order to evaluate which of these four equations best describes the ovate leaf shape, we used 14 leaves from 7 Neocinnamomum species (Lauraceae) and 72 leaves from Chimonanthus praecox (Calycanthaceae). Using the AIC and adjusted root mean square error to compare the fitted results, the modified equations fitted the leaf shapes better than the unmodified equations. However, the MLRF equation provided the best overall fit. As the parameters of the MLRF equation represent leaf length, maximum leaf width, and the distance from leaf apex to the point associated with the maximum leaf width along the leaf length axis, these findings are potentially valuable for studying the influence of environmental factors on leaf shape, differences in leaf shape among closely related plant species with ovate leaf shapes, and the extent to which leaves are bilaterally symmetrical. This is the first work in which temperature-dependent developmental equations to describe the ovate leaf shape have been employed, as previous studies lacked similar leaf shape models. In addition, prior work seldom attempted to describe real ovate leaf shapes. Our work bridges the gap between theoretical leaf shape models and empirical leaf shape indices that cannot predict leaf shape profiles.<\/jats:p>","DOI":"10.3390\/sym13081524","type":"journal-article","created":{"date-parts":[[2021,8,19]],"date-time":"2021-08-19T09:58:06Z","timestamp":1629367086000},"page":"1524","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["A General Model for Describing the Ovate Leaf Shape"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4696-0130","authenticated-orcid":false,"given":"Peijian","family":"Shi","sequence":"first","affiliation":[{"name":"Co-Innovation Centre for Sustainable Forestry in Southern China, Bamboo Research Institute, College of Biology and the Environment, Nanjing Forestry University, Nanjing 210037, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kexin","family":"Yu","sequence":"additional","affiliation":[{"name":"Co-Innovation Centre for Sustainable Forestry in Southern China, Bamboo Research Institute, College of Biology and the Environment, Nanjing Forestry University, Nanjing 210037, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3491-1286","authenticated-orcid":false,"given":"Karl J.","family":"Niklas","sequence":"additional","affiliation":[{"name":"Plant Biology Section, School of Integrative Plant Science, Cornell University, Ithaca, NY 14853, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8392-211X","authenticated-orcid":false,"given":"Julian","family":"Schrader","sequence":"additional","affiliation":[{"name":"Department of Biological Sciences, Macquarie University, Sydney, NSW 2109, Australia"},{"name":"Department of Biodiversity, Macroecology & Biogeography, University of Goettingen, 37077 Goettingen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2123-934X","authenticated-orcid":false,"given":"Yu","family":"Song","sequence":"additional","affiliation":[{"name":"Center for Integrative Conservation, Xishuangbanna Tropical Botanical Garden, Chinese Academy of Sciences, Mengla 666303, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Renbin","family":"Zhu","sequence":"additional","affiliation":[{"name":"Center for Integrative Conservation, Xishuangbanna Tropical Botanical Garden, Chinese Academy of Sciences, Mengla 666303, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hailin","family":"Wei","sequence":"additional","affiliation":[{"name":"Hunan Academy of Forestry, Changsha 410004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7514-3570","authenticated-orcid":false,"given":"David A.","family":"Ratkowsky","sequence":"additional","affiliation":[{"name":"Tasmanian Institute of Agriculture, University of Tasmania, Private Bag 98, Hobart, TAS 7001, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Shi, P., Ratkowsky, D.A., Li, Y., Zhang, L., Lin, S., and Gielis, J. 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