The temperature-size rule is one of the universal rules in ecology and states that ectotherms in warmer waters will grow faster as juveniles, mature at smaller sizes and younger ages, and reach smaller maximum body sizes. Many models have unsuccessfully attempted to reproduce temperature-size rule-consistent life histories by using two-term (anabolism and catabolism) Pütter-type growth models, such as the von Bertalanffy. Here, we present a physiologically structured individual growth model, which incorporates an energy budget and optimizes energy allocation to growth, reproduction, and reserves. Growth, maturation, and reproductive output emerge as a result of life-history optimization to specific physiological rates and mortality conditions. To assess which processes can lead to temperature-size rule-type life histories, we simulate 42 scenarios that differ in temperature and body size dependencies of intake, metabolism, and mortality rates. Results show that the temperature-size rule can emerge in two ways. The first way requires both intake and metabolism to increase with temperature, but the temperature-body size interaction of the two rates must lead to relatively faster intake increase in small individuals and relatively larger metabolism increase in large ones. The second way requires only higher temperature-driven natural mortality and faster intake rates in early life (no change in metabolic rates is needed). This selects for faster life histories with earlier maturation and increased reproductive output. Our model provides a novel mechanistic and evolutionary framework for identifying the conditions necessary for the temperature-size rule. It shows that the temperature-size rule is likely to reflect both physiological changes and life-history optimization and that use of von Bertalanffy-type models, which do not include reproduction processes, can hinder our ability to understand and predict ectotherm responses to climate change.

中文翻译：

---

机械温度大小规则解释应调和生理和死亡率对温度的反应

温度大小规则是生态学中的普遍规则之一，指出变温动物在较温暖的水域中作为幼体会生长得更快，在较小的尺寸和较年轻的年龄成熟，并达到较小的最大体型。许多模型试图通过使用两项（合成代谢和分解代谢）Pütter 型生长模型（例如 von Bertalanffy）来重现温度大小规则一致的生命史，但没有成功。在这里，我们提出了一个生理结构的个体生长模型，该模型结合了能量预算并优化了生长、繁殖和储备的能量分配。生长、成熟和生殖输出是针对特定生理率和死亡率条件的生命史优化的结果。为了评估哪些过程可以导致温度大小规则类型的生命史，我们模拟了 42 种情景，这些情景在温度和体型对摄入量、新陈代谢和死亡率的依赖性方面有所不同。结果表明，温度大小规则可以通过两种方式出现。第一种方式要求摄入量和新陈代谢都随着温度的升高而增加，但这两种速率的温度-体型相互作用必然导致小个体的摄入量增加相对较快，而大个体的代谢增加相对较大。第二种方式只需要更高的温度驱动的自然死亡率和生命早期更快的摄入率（不需要改变代谢率）。这选择了具有较早成熟和增加的繁殖输出的更快的生活史。我们的模型提供了一种新颖的机制和进化框架，用于识别温度大小规则所需的条件。