We (Seibel et al., 2021) proposed a novel method to quantify the oxygen supply capacity (α), which defines the maximum metabolic rate (MMR) that can be achieved at a given oxygen pressure. In their Correspondence article, Farrell et al. (2021) suggest that our method lacks ‘empirical realism’. The core issue is whether the MMR is linearly related to PO2 and whether that line intercepts the origin as required for the constancy of α, from which its predictive power derives. However, Farrell et al. (2021) overlooked the published derivation and validation of α, which is based on decades of empirical physiology and which demonstrates convincingly that α is constant from rest to maximum exertion (Deutsch et al., 2015; Seibel and Deutsch, 2020).
For a given species, α, calculated as the standard metabolic rate (SMR) divided by its critical PO2 (Pcrit-SMR), accurately predicts MMR measured at any PO2 up to its critical PO2 (Pcrit-max; see Fig. 2D in Seibel and Deutsch, 2020). Thus, α is equal to both SMR/Pcrit-SMR and MMR/Pcrit-max and is effectively the slope of a straight line between those two endpoints that intercepts the origin (Fig. 1). Beyond Pcrit-max, in hyperoxia, MMR plateaus (see Fig. 2B in Seibel and Deutsch, 2020). A non-linear relationship that begins and ends at identical α values would be highly improbable. The interpretation of some of this same data as curvilinear (Farrell et al., 2021) stems, at least in part, from the inclusion of measurements made at oxygen pressures beyond Pcrit-max (i.e. in the hyperoxic plateau). Thus, α does not typically change with oxygen or activity (Fig. 1) and can be used to predict MMR and aerobic scope.
Maximum metabolic rate is linearly related to PO2 between the critical partial pressures (Pcrit-SMR and Pcrit-max, respectively) for standard and maximum rates. Top: standard metabolic rate (SMR) plotted at Pcrit-SMR (red, data from Seibel and Deutsch, 2020; n=52, 1 point per species) and maximum metabolic rate (MMR) plotted at measurement PO2 for individual trials (blue, n≈400 points from 23 of the 52 species in Seibel and Deutsch, 2020; data extracted from published representative plots using webplot digitizer; species and their sources are listed). Data are expressed as percentages of Pcrit-max and MMR at Pcrit-max, resulting in all species falling around the same line despite interspecific differences in the absolute values of both variables. Pcrit-max was estimated as the highest prevailing environmental PO2 (air-saturation for most species; Seibel and Deutsch, 2020). Bottom: oxygen supply capacity (α=MMR/PO2), derived from the data in the top panel. Because all data are expressed as percentages, and because the relationship is linear, α is near 1 for all species regardless of PO2 (i.e. MMR declines by 1% for a 1% decline in PO2).
Maximum metabolic rate is linearly related to PO2 between the critical partial pressures (Pcrit-SMR and Pcrit-max, respectively) for standard and maximum rates. Top: standard metabolic rate (SMR) plotted at Pcrit-SMR (red, data from Seibel and Deutsch, 2020; n=52, 1 point per species) and maximum metabolic rate (MMR) plotted at measurement PO2 for individual trials (blue, n≈400 points from 23 of the 52 species in Seibel and Deutsch, 2020; data extracted from published representative plots using webplot digitizer; species and their sources are listed). Data are expressed as percentages of Pcrit-max and MMR at Pcrit-max, resulting in all species falling around the same line despite interspecific differences in the absolute values of both variables. Pcrit-max was estimated as the highest prevailing environmental PO2 (air-saturation for most species; Seibel and Deutsch, 2020). Bottom: oxygen supply capacity (α=MMR/PO2), derived from the data in the top panel. Because all data are expressed as percentages, and because the relationship is linear, α is near 1 for all species regardless of PO2 (i.e. MMR declines by 1% for a 1% decline in PO2).
The anatomy of the oxygen cascade does change between rest and activity, and some individual steps in the cascade appear non-linearly related to PO2. However, these non-linear steps do not preclude a linear relationship between MMR and inspired PO2 (Seibel and Deutsch, 2020). Regardless of the underlying mechanism, Fig. 1 shows that MMR is linearly related to PO2 for most species analyzed to date. Although there may be species and conditions for which α changes with activity or oxygen, such examples would not diminish the utility of α. Instead, they may reveal how α is acted upon by natural selection. For example, α may vary with swimming in species that ram ventilate, with depth in species that migrate vertically across oxygen and temperature gradients, or with size and life stage as circulatory systems develop.
Methodological issues may also influence the apparent shape of the MMR–PO2 relationship. MMR measurement relies on a fish's willingness to swim during exercise protocols (Slesinger et al., 2019), which may vary with exertion and oxygen. Furthermore, because MMR declines in direct proportion to PO2, supposed ‘normoxic’ MMR measurements may be underestimates. Seibel et al. (2021) recommended that, when feasible, MMR be measured across a range of PO2 values, including hyperoxia, to minimize our shared concern (Farrell et al., 2021) of extrapolating from ‘one experimental data point … that has associated error’. Also, when feasible, MMR should be elicited by more than one protocol (e.g. chase and flume). Our method provides much-needed consistency for determining oxygen supply capacity directly and provides a means of predicting MMR and aerobic scope.
Farrell et al. (2021) are correct that MMR can't continue upward indefinitely with PO2. Instead, it plateaus at Pcrit-max. A realistic estimate of Pcrit-max, rather than aerobic scope as suggested by Farrell et al. (2021), is required to avoid over-estimates of MMR. Pcrit-max has been directly measured for numerous species but, more importantly, it can be approximated as the highest PO2 that persists in a species' natural environment (i.e. air-saturation for most shallow, coastal species; Seibel and Deutsch, 2020).
Farrell et al. (2021) are concerned that α is a ‘black box’ that hides all relevant physiological mechanisms. However, this is true of all integrative physiological metrics, including SMR and aerobic scope, and does not diminish the utility of these metrics or the importance of the underlying mechanistic physiology. Rather, these ‘black boxes’ act to reduce inherent physiological complexity in order to understand relationships at different scales. The α is informative despite the complexity of the oxygen cascade, just as aerobic scope is informative despite incomplete knowledge of the specific oxygen requirements of the underlying processes (Farrell, 2016).
Farrell et al. (2021) state that we dismissed approaches that aim to understand the entire MR versus PO2 response curve and that, having done so, we fail to recognize that our ‘measure of Pcrit-SMR may not actually relate to SMR’. This indicates an important misunderstanding of our method. We are not measuring Pcrit-SMR. We are measuring the oxygen supply capacity (α). We did compare Pcrit-SMR derived from α with that using other methods simply as a demonstration of its relative accuracy and precision. However, our method concerns only α and does not require that Pcrit be measured at SMR because the Pcrit measured for any rate provides the same information (α) from which the Pcrit for any other rate (including SMR) can be calculated. For example, SMR could be independently determined and Pcrit-SMR can then be calculated as SMR/α, even if α was determined at MMR. The physiological changes that occur at PO2 above Pcrit are not relevant to the measurement of α, and statistical descriptions of the entire MR versus PO2 trial apparently seek to answer a different question.
Furthermore, we do not ‘discourage examining data that depart from [our] model’, nor do we simply ‘draw a straight line through two data points’. We determined oxygen supply for every PO2 bin in 50 published trials. The highest value in each trial is the oxygen supply capacity (α) for that individual or species. The metabolic rate divided by α is Pcrit for that rate, whether standard, routine or maximum. Any PO2 (up to Pcrit-max) multiplied by α is the maximum metabolic rate that could be achieved at that PO2. Our theory, rather than ‘trying to enforce itself onto real data’, is derived from real data and provides a powerful tool for understanding how metabolism changes with oxygen and temperature. Our paper ‘breathed new life into Pcrit’ by clarifying its biological significance as a measure of oxygen supply capacity.