A general simple theory for the interspecific allometric scaling is developed in the $d+1$-dimensional space ($d$ biological lengths and a physiological time) of metabolic states of organisms. It is assumed that natural selection shaped the metabolic states in such a way that the mass and energy $d+1$-densities are size-invariant quantities (independent of body mass). The different metabolic states (basal and maximum) are described by considering that the biological lengths and the physiological time are related by different transport processes of energy and mass. In the basal metabolism, transportation occurs by ballistic and diffusion processes. In $d=3$, the 3/4 law occurs if the ballistic movement is the dominant process, while the 2/3 law appears when both transport processes are equivalent. Accelerated movement during the biological time is related to the maximum aerobic sustained metabolism, which is characterized by the scaling exponent $2d/(2d+1)$ (6/7 in $d=3$). The results are in good agreement with empirical data and a verifiable empirical prediction about the aorta blood velocity in maximum metabolic rate conditions is made.
A Model for Self-Organized Growth, Branching, and Allometric Scaling of the Planarian Gut
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Department of Tissue Dynamics and Regeneration, Max Planck Institute for Multidisciplinary Sciences（马克斯·普朗克多学科科学研究所组织动力学与再生系）；Faculty of Biology and Psychology, University of Göttingen（哥廷根大学生物学与心理学院）；Center for Systems Biology, Dresden（德累斯顿系统生物学中心）；Cluster of Excellence Physics of Life, Technische Universität Dresden（德累斯顿工业大学生命物理学卓越集群）
Metabolic scaling, von Bertalanffy growth and an exponent equation
Institute of Measurement Science, Slovak Academy of Sciences（斯洛伐克科学院测量科学研究所）；Institute of the Science of Complex Systems, Center for Medical Data Science, Medical University of Vienna（维也纳医科大学复杂系统科学与医学数据中心研究所）；Complexity Science Hub（复杂性科学中心）；Neurolinx Research Institute（Neurolinx 研究所）；Silliman University Angelo King Center for Research & Environmental Management（锡利曼大学安杰洛·金研究与环境管理中心）
Physical Approaches to Metabolic Scaling in Living Systems
Aix-Marseille Université（艾克斯-马赛大学）；INSERM（法国国家健康与医学研究院）；DyNaMo（动态建模中心）；Turing Centre for Living Systems（图灵生命系统中心）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Case Western Reserve University（凯斯西储大学）；Cluster of Excellence Physics of Life (PoL)（生命物理学卓越集群）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）
A multiscale theory based on metabolic scaling connects forest dynamics to tree-size distributions
University of Padova（帕多瓦大学）；Department TESAF, University of Padova（帕多瓦大学TESAF系）；National Biodiversity Future Center（国家生物多样性未来中心）；Laboratory of Interdisciplinary Physics, Department of Physics and Astronomy “G. Galilei”, University of Padova（帕多瓦大学伽利略物理与天文学系跨学科物理实验室）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Department of Civil, Environmental and Architectural Engineering, University of Padova（帕多瓦大学土木、环境与建筑工程系）；CMCC Centro Euro-Mediterraneo sui Cambiamenti Climatici（欧洲地中海气候变化研究中心）
