Both oxygen and temperature are fundamental factors determining metabolic performance, fitness, ecological niches, and responses of many aquatic organisms to climate change. Despite the importance of physical and physiological constraints on oxygen supply affecting aerobic metabolism of aquatic ectotherms, ecological theories such as the metabolic theory of ecology have focused on the effects of temperature rather than oxygen. This gap currently impedes mechanistic models from accurately predicting metabolic rates (i.e., oxygen consumption rates) of aquatic organisms and restricts predictions to resting metabolism, which is less affected by oxygen limitation. Here, we expand on models of metabolic scaling by accounting for the role of oxygen availability and temperature on both resting and active metabolic rates. Our model predicts that oxygen limitation is more likely to constrain metabolism in larger, warmer, and active fish. Consequently, active metabolic rates are less responsive to temperature than are resting metabolic rates, and metabolism scales to body size with a smaller exponent whenever temperatures or activity levels are higher. Results from a metaanalysis of fish metabolic rates are consistent with our model predictions. The observed interactive effects of temperature, oxygen availability, and body size predict that global warming will limit the aerobic scope of aquatic ectotherms and may place a greater metabolic burden on larger individuals, impairing their physiological performance in the future. Our model reconciles the metabolic theory with empirical observations of oxygen limitation and provides a formal, quantitative framework for predicting both resting and active metabolic rate and hence aerobic scope of aquatic ectotherms.

氧气和温度都是决定代谢性能，适应性，生态位和许多水生生物对气候变化的反应的基本因素。尽管物理和生理学上的限制因素对氧气的供应有影响，影响了水生等温线的有氧代谢，但是诸如生态学的代谢理论之类的生态学理论却侧重于温度而不是氧气的影响。这种差距目前阻碍了机械模型准确预测水生生物的代谢速率（即氧气消耗速率），并将预测限制在静息代谢中，后者受氧气限制的影响较小。在这里，我们通过考虑氧气的可用性和温度对静止和活跃代谢率的作用，扩展了代谢缩放模型。我们的模型预测，氧气的限制更可能限制大型，温暖和活跃鱼类的新陈代谢。因此，活跃的代谢速率对温度的响应要比静止的代谢速率低，并且只要温度或活动水平较高，新陈代谢就会以较小的指数缩放到人体大小。对鱼类代谢率的荟萃分析结果与我们的模型预测一致。观察到的温度，氧气供应和身体大小的相互作用影响预测，全球变暖将限制水生等温线的有氧范围，并可能给较大的个体带来更大的代谢负担，从而损害其未来的生理机能。我们的模型将代谢理论与氧气限制的经验性观察相吻合，并提供了正式的，