A General Model for Describing the Ovate Leaf Shape

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–Rosso–Flandrois (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.

[1]  D. Inzé,et al.  LEAF-E: a tool to analyze grass leaf growth using function fitting , 2014, Plant Methods.

[2]  I. Wright,et al.  Leaf size estimation based on leaf length, width and shape. , 2021, Annals of botany.

[4]  D. Ratkowsky,et al.  Empirical Model With Excellent Statistical Properties for Describing Temperature-Dependent Developmental Rates of Insects and Mites , 2017, Annals of the Entomological Society of America.

[5]  K. Niklas,et al.  Lamina shape does not correlate with lamina surface area: An analysis based on the simplified Gielis equation , 2019, Global Ecology and Conservation.

[6]  P. Lootens,et al.  A flexible geometric model for leaf shape descriptions with high accuracy , 2018 .

[7]  J. Gielis A generic geometric transformation that unifies a wide range of natural and abstract shapes. , 2003, American journal of botany.

[8]  Li Zhang,et al.  A geometrical model for testing bilateral symmetry of bamboo leaf with a simplified Gielis equation , 2016, Ecology and evolution.

[9]  Sean C. Thomas,et al.  Elevated CO2 and leaf shape: Are dandelions getting toothier? , 1996 .

[10]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[11]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[12]  Bruno Andrieu,et al.  A comparative analysis of leaf shape of wheat, barley and maize using an empirical shape model. , 2011, Annals of botany.

[13]  D. Adams,et al.  Leaf shape and size track habitat transitions across forest–grassland boundaries in the grass family (Poaceae) , 2019, Evolution; international journal of organic evolution.

[14]  Tom Ross,et al.  Unifying temperature effects on the growth rate of bacteria and the stability of globular proteins. , 2005, Journal of theoretical biology.

[15]  Ülo Niinemets,et al.  Leaf shape and venation pattern alter the support investments within leaf lamina in temperate species: a neglected source of leaf physiological differentiation? , 2007 .

[16]  David A. Ratkowsky,et al.  Nonlinear regression modeling : a unified practical approach , 1984 .

[17]  D. Ruppert The Elements of Statistical Learning: Data Mining, Inference, and Prediction , 2004 .

[18]  A. N. Stokes,et al.  Model for bacterial culture growth rate throughout the entire biokinetic temperature range , 1983, Journal of bacteriology.

[19]  L. Santiago,et al.  Correlated Evolution of Leaf Shape and Physiology in the Woody Sonchus Alliance (Asteraceae: Sonchinae) in Macaronesia , 2009, International Journal of Plant Sciences.

[20]  Ü. Niinemets Adjustment of foliage structure and function to a canopy light gradient in two co-existing deciduous trees. Variability in leaf inclination angles in relation to petiole morphology , 1998, Trees.

[21]  J. Gielis,et al.  Comparison of dwarf bamboos (Indocalamus sp.) leaf parameters to determine relationship between spatial density of plants and total leaf area per plant , 2015, Ecology and evolution.

[22]  J. Pierre,et al.  A Novel Rate Model of Temperature-Dependent Development for Arthropods , 1999 .

[23]  D. Ratkowsky,et al.  Comparison of two ontogenetic growth equations for animals and plants , 2017 .

[24]  D. Royer,et al.  Why Do Toothed Leaves Correlate with Cold Climates? Gas Exchange at Leaf Margins Provides New Insights into a Classic Paleotemperature Proxy , 2006, International Journal of Plant Sciences.

[25]  A. Samal,et al.  Plant species identification using Elliptic Fourier leaf shape analysis , 2006 .

[26]  D. Ratkowsky,et al.  A General Leaf Area Geometric Formula Exists for Plants—Evidence from the Simplified Gielis Equation , 2018, Forests.

[27]  Dwight T. Kincaid,et al.  Quantification of leaf shape with a microcomputer and Fourier transform , 1983 .

[28]  R. Craigen,et al.  Improved Rate Model of Temperature-Dependent Development by Arthropods , 1995 .

[29]  Panayiotis A. Nektarios,et al.  Allometric Individual Leaf Area Estimation in Chrysanthemum , 2021, Agronomy.

[30]  Nathan J B Kraft,et al.  Sensitivity of leaf size and shape to climate: global patterns and paleoclimatic applications. , 2011, The New phytologist.

[31]  Y. Si,et al.  Apex structures enhance water drainage on leaves , 2020, Proceedings of the National Academy of Sciences.

[32]  Johan Gielis,et al.  The Generalized Gielis Geometric Equation and Its Application , 2020, Symmetry.

[33]  J P Flandrois,et al.  An unexpected correlation between cardinal temperatures of microbial growth highlighted by a new model. , 1993, Journal of theoretical biology.

[34]  P. Sharpe,et al.  Non-linear regression of biological temperature-dependent rate models based on absolute reaction-rate theory. , 1981, Journal of theoretical biology.

[35]  Andrej-Nikolai Spiess,et al.  An evaluation of R2 as an inadequate measure for nonlinear models in pharmacological and biochemical research: a Monte Carlo approach , 2010, BMC pharmacology.

[36]  P. Sharpe,et al.  Reaction kinetics of poikilotherm development. , 1977, Journal of theoretical biology.

[37]  Xinyou Yin,et al.  A nonlinear model for crop development as a function of temperature , 1995 .