Testing mechanistic theories must be based on correct interpretations

Journal of Experimental Biology has recently published a number of studies that critically discussed the Gill-Oxygen Limitation Theory (GOLT, see Pauly, 2021), and Lonthair et al. (2024) is the latest contribution to the current debate. We welcome the increasing interest in this theory, especially by physiologists who examine the link between increasing temperatures and the growth of fishes. However, testing a theory must be based on its actual premises and hypotheses, and we have to conclude that the model of Lonthair et al. (2024) does not correspond to any of the GOLT's assumptions and instead, its results are entirely predicted by this theory, as we show here.As Lonthair et al. (2024) find, higher temperatures reduce the growth of Arctic char (Salvelinus fontinalis) while the increase of its gill surface area and metabolic rate scale with similar slopes. The authors interpret this observation as contradictory to the GOLT. However, the similarity in slopes between metabolic rate and gill surface area is actually an inherent component of the GOLT, as explicitly stated (Pauly, 2019, 2021).Central to the arguments presented by Lonthair et al. (2024) is a parameter introduced by Scheuffele et al. (2021), which these authors believe to be derived from the GOLT: the parameter bS, i.e. the difference between the scaling exponents of metabolic rate (bMR) and that of gill surface area (bGSA). Thus:(1)As both Scheuffele et al. (2021) and Lonthair et al. (2024) assert, in order for the GOLT to apply, bS should be ≤0. Therefore, the authors conclude, values of bS>0 would refute this theory, since the allometric slopes of the GSA would make it increase faster than MR with increasing body size. However, the GOLT always assumed bGSA and bMR to have about the same values (see Pauly, 2019, pp. 36–37), where bGSA and bMR are referred to a ‘dG’ and ‘dQ,’ respectively, and are used as substitute for one another. Thus, Lonthair et al.’s interpretation overlooks the fundamental assumptions of the GOLT. The theory has always presumed that the scaling exponents of gill surface area and metabolic rate are approximately equal (Pauly, 2019). Random deviations from this balance, whether positive or negative, are not inherently contradictory to the theory. Instead, consistent deviations from this equilibrium would indeed challenge the validity of the GOLT.Furthermore, the interpretation put forth by Scheuffele et al. (2021) and Lonthair et al. (2024) suggests that the GOLT implies that fish continue to grow until their vital functions are on the verge of collapse due to oxygen limitation, which is biologically implausible. In reality, the theory posits that as fish grow, they gradually allocate less surplus oxygen to growth until, at their maximum size in a given environment, all available oxygen is utilized for non-growth functions. This distinction is crucial; the theory does not suggest that older fish collapse owing to an inability to maintain normal activities, but rather that they reach a point where no surplus oxygen is available to support further growth.At the core of the GOLT lies the modified Pütter's equation (1920), which describes the growth rate (dW/dt) as a function of anabolic processes (HWd) and breakdown processes (kW):(2)While Pütter (1920) assumed that anabolic processes scale universally with exponents of 2/3, the GOLT suggests a range from 0.6 to 0.9 (and always <1) in adults. This implies that as fish grow larger, less energy (i.e. oxygen) is available to build new body mass, which results in decreasing growth rates.Lonthair et al. (2024) ignore the literature that documented a problem with the interpretation of measured oxygen uptake data in respirometry experiments and the resulting definition of standard metabolic rate which is understood as reflecting energy consumption without any overhead costs of growth. This view does not reflect current knowledge on this topic and it neglects the fact that juvenile fish continue to allocate energy to growth even after fasting periods of 24–48 h. This leads to an overestimation of their SMR compared with large (old) fish, which are the only ones that do not allocate resources to growth (see e.g. Parry, 1983; Rosenfeld et al., 2015; Chabot et al., 2016).Like Scheuffele et al. (2021) and Lefevre (2016), Lonthair et al. (2024) assume that fasting fish for 24 h is enough to exclude overhead costs of growth. Rosenfeld et al. (2015), however, who pointed out that fish physiologists use different procedures than colleagues working on endotherms, demonstrated that juvenile fish do not abruptly halt growth after fasting. Instead, the measured values of SMR are heavily influenced by food rations in the days and even weeks before fasting. Animals that were heavily fed before a 35 h fasting period showed overhead costs of growth of up to 65%, suggesting that fasting alone is insufficient to exclude the effects of growth on metabolic rate.The recent critiques of the GOLT (e.g. Scheuffele et al., 2021 and Lefevre, 2016) on whose assumptions Lonthair et al. (2024) base their argument, do not address these issues. Many studies cited in this literature either do not specify fasting periods or employ short fasting durations that do not effectively exclude the effects of growth on metabolic rate. Without proper consideration of these factors, the conclusions drawn by Lonthair et al. (2024) are not supported by evidence.In conclusion, while the critique offered by Lonthair et al. (2024) may be valuable as it adds more data that can be related to this debate, it is essential to ensure that such critiques are grounded in a thorough understanding of the theories that are examined. Failure to consider the fundamental premises and assumptions of the GOLT, as well as overlooking significant methodological issues in oxygen uptake measurements, will unavoidably lead to misinterpretations and flawed conclusions. What is now required are rigorous approaches to evaluate the validity of the GOLT and its implications for understanding the physiological responses of fish to changing environmental conditions.

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