Lonthair et al. (2024) present data from an experiment designed to test the gill oxygen limitation (GOL) hypothesis by coupling measurements of gill surface area (GSA) and metabolic rate (MR) scaling with fish growth. We found that brook trout (Salvelinus fontinalis) reared under warmer temperatures grew slower than those under cold temperatures and concluded that there was no evidence for oxygen limitation at the gills as GSA grew faster (scaled higher) than MR. In contrast, the correspondence article of Pauly and Müller (2024) asserts that our results are not in conflict with GOL. However, after careful review of the prior literature on the topic as well as our data, we maintain the validity of our original data interpretations.

To understand our results, we must first understand the assumptions and predictions of GOL as proposed by Pauly and colleagues. Pauly (1981, 2021) argues that GSA scales with body mass with an allometric slope (b) less than 1.0 because GSA is two-dimensional, while MR should ideally scale with a greater b around 1.0 because it is associated with three-dimensional body volume. Support for the GOL hypothesis has been viewed as either GSA suppressing metabolic scaling (i.e. scenario 1: GSA and MR scale similarly and less than 1.0) or as GSA scaling lower than MR creating a mismatch in oxygen supply and demand with growth (e.g. scenario 2: see Fig. 1, adapted from Lonthair et al., 2024). The physiology community generally agrees that most GSA and MR scaling relationships manifest as scenario 1, but view MR scaling as the driver (Lefevre et al., 2017; Scheuffele et al., 2021) with the gills typically growing to match oxygen demand [rather than the gills constraining metabolism as proposed in Pauly (1981, 2021)]. Thus, the scaling of GSA and MR at similar rates and less than 1.0 are consistent with both classical physiology views and the GOL hypothesis as present in Scenario 1, and this correlation cannot be used to prove either, since correlation does not inform the underlying mechanism. For this reason, examining deviations from the typical pattern can be informative, and as Pauly (2021) asserts, showing that GSA can scale at a rate that does not constrain metabolism (i.e. at or greater than b=1.0) would ‘eviscerate’ the GOL hypothesis. Interestingly, there are several robust datasets in the literature of GSA scaling close to or even above b=1.0, which would seem to negate the GOL hypothesis through Pauly's (2021) own admission (e.g. Holeton, 1976; Prinzing et al., 2023; see Wegner and Farrell, 2024 for review). The strength of Lonthair et al. (2024) is that we provide more than an isolated dataset on gill scaling; we show that brook trout GSA scaling is not significantly different from 1.0, while also showing that brook trout growth slows at warmer temperatures, suggesting that GSA scaling is not the primary factor limiting metabolism and growth.

Fig. 1.

Conceptual diagram depicting two scenarios where hypothesized allometric slopes (b) for gill surface area (GSA) and metabolic rate (MR) could align with expectations of gill oxygen limitation. In scenario 1, as conceptualized by Pauly (2021), geometric constraints on GSA (i.e. surface area to volume relationships) limit the allometric slope of GSA to less than b<1.0, resulting in a similarly constrained allometric slope for MR at b<1.0. Importantly, data that conform to the pattern in scenario 1 could also be driven by the reverse relationship (i.e. MR scales at b<1.0 and GSA scales similarly to meet oxygen demand, see extended discussion in the main text). Under scenario 2, geometric constraints result in GSA scaling less than that of MR, ultimately resulting in a mismatch between oxygen supply and demand. Results from Lonthair et al. (2024) do not support the gill oxygen limitation hypothesis under either scenario. Image reproduced from Lonthair et al. (2024).

Fig. 1.

Conceptual diagram depicting two scenarios where hypothesized allometric slopes (b) for gill surface area (GSA) and metabolic rate (MR) could align with expectations of gill oxygen limitation. In scenario 1, as conceptualized by Pauly (2021), geometric constraints on GSA (i.e. surface area to volume relationships) limit the allometric slope of GSA to less than b<1.0, resulting in a similarly constrained allometric slope for MR at b<1.0. Importantly, data that conform to the pattern in scenario 1 could also be driven by the reverse relationship (i.e. MR scales at b<1.0 and GSA scales similarly to meet oxygen demand, see extended discussion in the main text). Under scenario 2, geometric constraints result in GSA scaling less than that of MR, ultimately resulting in a mismatch between oxygen supply and demand. Results from Lonthair et al. (2024) do not support the gill oxygen limitation hypothesis under either scenario. Image reproduced from Lonthair et al. (2024).

Because the respiratory physiology community generally agrees that GSA can scale at or close to 1.0 if needed to support oxygen demands, others have also searched for a proposed ‘mismatch’ in GSA and metabolic scaling that could indicate a constraint on oxygen supply in relation to oxygen demand as fish grow. This is the basis of scenario 2 in Lonthair et al. (2024) as originally tested in Scheuffele et al. (2021) and subsequently in other studies (e.g. Somo et al., 2023; Prinzing et al., 2023; Skeeles and Clark, 2024). To examine potential evidence for a scaling mismatch between GSA and MR in the literature, Scheuffele et al. (2021) developed the S metric or difference in the allometric scaling of GSA and MR (bS),
in which bS>0 would indicate that more GSA is available per unit of metabolic demand as a fish grows, while bS<0 would support the GOL hypothesis by indicating that less GSA is available per unit of metabolism as a fish grows [Fig. 1, scenario 2 adapted from Lonthair et al. (2024)]. Here again, we see that our results argue against the concept of gill oxygen limitation as bS is positive in all instances for brook trout (whether measuring resting metabolic rate or maximum metabolic rate). Thus, in our experiment, the amount of GSA per unit of metabolism actually increased as the fish grew, even though the fish at warm temperatures grew more slowly. Despite this clear evidence that GSA is not constraining metabolism and growth, Pauly and Müller (2024) argue that the slopes in our data between GSA and MR are ‘similar’ and the differences are ‘random deviations’, and align with GOL expectations. This is simply not accurate: the confidence intervals for GSA and resting metabolic rate (RMR) do not overlap for either temperature.

Finally, in response to Pauly and Müller's (2024) concern on the potential impact of growth on metabolic rate, we must first clarify that Lonthair et al. (2024) measured both RMR and maximum metabolic rate (MMR), not standard metabolic rate (SMR) as stated by Pauly and Müller (2024). We thus report the full range of typical oxygen uptake (aerobic scope) used by brook trout over the size range examined. MMR and aerobic scope were reported in this study to emphasize the ‘excess’ capacity available above baseline (resting) costs, which would include oxygen uptake available for growth. Whether examining RMR or MMR our results do not support gill oxygen limitation as defined above, nor do the vast majority of other paired datasets directly comparing GSA and MR scaling (e.g. Scheuffele et al., 2021; Prinzing et al., 2023; Skeeles and Clark, 2024).

In closing, we contend that understanding the mechanisms driving relationships between fish body size and temperature is critical from both fundamental and applied perspectives. This requires examination of hypotheses proposed in the literature and assessing the weight of evidence in support of each one. To accomplish this, it is imperative that the assumptions and predictions of candidate hypotheses are clear, and that they can be rigorously tested. Hypotheses that rely solely on correlations that can be explained by multiple, contrasting mechanisms not only cast doubt on the likelihood of a unifying theory, but more importantly are essentially untestable, and by extension unfalsifiable. Claiming support for a hypothesis under these circumstances is a false equivalency. Pauly and Müller (2024) contend that the results of Lonthair et al. (2024) do not provide sufficient evidence against GOL due to their design and data interpretations. While we respectfully disagree, if there are alternate or more rigorous experimental designs that would clearly test the validity of the GOL hypothesis, we strongly encourage their elaboration and testing in order to advance our understanding of body size–temperature relationships.

We are thankful for constructive feedback from Timothy Clark, Jill Leonard, and Ken Jeffries on a prior draft of this article. Any use of trade, firm or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.

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