Intra- and inter-specific scaling laws of plants and animals

• Published in: Acta mechanica Sinica 2021-02, Vol.37 (2), p.321-330
• Main Authors: Li, Jiahang, Wu, Hao, Kassab, Ghassan S., Tan, Wenchang, Huo, Yunlong
• Format: Article
• Language: English
• Subjects: Animals; Asymmetry; Classical and Continuum Physics; Computational Intelligence; Diameters; Engineering; Engineering Fluid Dynamics; Fractal geometry; Fractal models; Fractals; Metabolism; Research Paper; Scaling laws; Theoretical and Applied Mechanics; Trees
• ISSN: 0567-7718; 1614-3116
• DOI: 10.1007/s10409-020-01013-7

The allometric scaling laws of metabolism in 447 animal and 1200 plant species showed convex and concave curvatures between mass and metabolic rate, respectively. The objective of the study is to explain the difference of curvatures between animals and plants based on fractal models. Several intraspecific scaling laws were derived from an asymmetric vascular tree with the fractal dimension (i.e., a in k 1 a + k 2 a + ⋯ = 1 , where k i refers to the ratio of daughter to mother diameters). Based on the intraspecific scaling laws, the allometric scaling exponent of metabolism (i.e., an interspecific scaling law) was shown to be equal to one-third of fractal dimension. Moreover, a novel piecewise-defined function in conjunction with the intraspecific scaling laws was proposed to explain the diverse metabolic scaling in animals and plants. The intraspecific and interspecific scaling laws showed good agreement with morphometric measurements. The experimentally-validated scaling models predict the diversity of intraspecific and interspecific scaling seen in nature. To our knowledge, this is the first study to use fractal models to explain the convex and concave forms of metabolic scaling in animals and plants. The study resolves the long-term controversies to use the resource-transport network models for explanation of the allometric scaling law of metabolism. Graphic Abstract This study validated intraspecific scaling laws of asymmetric vascular trees instead of idealized symmetric trees. The fractal dimension was found to greatly affect the scaling exponents. Based on the intraspecific scaling laws, the allometric scaling exponent of metabolism was shown to be equal to one-third of fractal dimension. The piecewise-defined asymmetric vascular tree was further proposed to accurately explain convex and concave curvatures in metabolic scaling of animals and plants, respectively.