Metabolic theory aims to tackle ecological and evolutionary problems by explicitly including physical principles of energy and mass exchange, thereby increasing generality and deductive power. Individual growth models (IGMs) are the fundamental basis of metabolic theory because they represent the organisational level at which energy and mass exchange processes are most tightly integrated and from which scaling patterns emerge. Unfortunately, IGMs remain a topic of great confusion and controversy about the origins of the ideas, their domain and breadth of application, their logical consistency and whether they can sufficiently capture reality. It is now 100 years since the first theoretical model of individual growth was put forward by Pütter. His insights were deep, but his model ended up being attributed to von Bertalanffy and his ideas largely forgotten. Here I review Pütter's ideas and trace their influence on existing theoretical models for growth and other aspects of metabolism, including those of von Bertalanffy, the Dynamic Energy Budget (DEB) theory, the Gill-Oxygen Limitation Theory (GOLT) and the Ontogenetic Growth Model (OGM). I show that the von Bertalanffy and GOLT models are minor modifications of Pütter's original model. I then synthesise, compare and critique the ideas of the two most-developed theories, DEB theory and the OGM, in relation to Pütter's original ideas. I formulate the Pütter, DEB and OGM models in the same structure and with the same notation to illustrate the major similarities and differences among them. I trace the confusion and controversy regarding these theories to the notions of anabolism, catabolism, assimilation and maintenance, the connections to respiration rate, and the number of parameters and state variables their models require. The OGM model has significant inconsistencies that stem from the interpretation of growth as the difference between anabolism and maintenance, and these issues seriously challenge its ability to incorporate development, reproduction and assimilation. The DEB theory is a direct extension of Pütter's ideas but with growth being the difference between assimilation and maintenance rather than anabolism and catabolism. The DEB theory makes the dynamics of Pütter's 'nutritive material' explicit as well as extending the scheme to include reproduction and development. I discuss how these three major theories for individual growth have been used to explain 'macrometabolic' patterns including the scaling of respiration, the temperature-size rule (first modelled by Pütter), and the connection to life history. Future research on the connections between theory and data in these macrometabolic topics have the greatest potential to advance the status of metabolic theory and its value for pure and applied problems in ecology and evolution.

中文翻译：

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在 Pütter 发明 von B ertalanffy 生长曲线一个世纪后，代谢理论的地位如何？

代谢理论旨在通过明确包含能量和质量交换的物理原理来解决生态和进化问题，从而提高普遍性和演绎能力。个体增长模型 (IGM) 是代谢理论的基本基础，因为它们代表了能量和质量交换过程最紧密集成的组织级别，并且从该级别出现了缩放模式。不幸的是，IGM 仍然是一个关于思想起源、应用领域和广度、逻辑一致性以及它们是否能够充分捕捉现实的巨大混乱和争议的话题。距离 Pütter 提出第一个个人成长理论模型至今已有 100 年。他的见解很深刻，但他的模型最终被归功于 von Bertalanffy，而他的想法在很大程度上被遗忘了。在这里，我回顾了 Pütter 的想法，并追溯了它们对现有生长和新陈代谢其他方面的理论模型的影响，包括 von Bertalanffy、动态能量收支 (DEB) 理论、Gill-Oxygen 限制理论 (GOLT) 和个体发育生长模型（OGM）。我表明 von Bertalanffy 和 GOLT 模型是对 Pütter 原始模型的微小修改。然后，我结合 Pütter 的原始思想，综合、比较和批判了两个最发达的理论，DEB 理论和 OGM 的思想。我用相同的结构和相同的符号制定了 Pütter、DEB 和 OGM 模型，以说明它们之间的主要相似之处和不同之处。我将这些理论的混乱和争议追溯到合成代谢、分解代谢、同化和维持的概念、与呼吸速率的联系以及模型所需的参数和状态变量的数量。OGM 模型因将生长解释为合成代谢和维持之间的差异而存在显着不一致，这些问题严重挑战了其整合发育、繁殖和同化的能力。DEB 理论是 Pütter 思想的直接延伸，但增长是同化和维持之间的区别，而不是合成代谢和分解代谢之间的区别。DEB 理论明确了 Pütter 的“营养物质”的动力学，并将该方案扩展到包括繁殖和发育。我讨论了这三个关于个人成长的主要理论是如何被用来解释“大代谢”模式的，包括呼吸的比例、温度大小规则（首先由 Pütter 建模）以及与生命史的联系。未来对这些宏观代谢主题中理论与数据之间联系的研究最有可能推动代谢理论的地位及其对生态学和进化中纯粹和应用问题的价值。