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.
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.
Acknowledgements
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.