The critical oxygen tension (Pcrit) for fishes is the oxygen level below which the rate of oxygen consumption (ṀO2) becomes dependent upon ambient oxygen partial pressure (PO2). We compare multiple curve-fitting approaches to estimate Pcrit of the Gulf killifish, Fundulus grandis, during closed and intermittent-flow respirometry. Fitting two line segments of ṀO2 versus PO2 produced high and variable estimates of Pcrit, as did nonlinear regression using a hyperbolic (Michaelis–Menten) function. Using nonlinear regression fit to an exponential (modified Weibull) function, or linear regression of ṀO2 versus PO2 at low PO2, and determining Pcrit as the PO2 when ṀO2 equals standard metabolic rate (SMR) yielded values that were consistent across fish and among experimental trials. The magnitude of the difference in Pcrit determined by alternative calculation methods exceeded the differences determined in closed and intermittent-flow respirometry, highlighting the need to standardize analytical as well as experimental approaches in determining Pcrit.
There is considerable interest in describing the oxygen dependence of aerobic metabolism of animals, especially for animals from aquatic habitats, where the oxygen concentration is much lower and more variable than in terrestrial habitats. Determination of this oxygen dependence is particularly relevant in the current context of human-induced environmental change, where increased nutrient input, warmer temperatures and changes in hydrology have increased the geographic scope and severity of aquatic hypoxia (Diaz and Rosenberg, 2008; Rabalais et al., 2010).
broken stick regression
mean of the lowest normal distribution
rate of oxygen consumption
linear function of ṀO2 measured at low PO2
linear mixed model
mean of lowest 10 data points
mean of lowest 10% of data after removing the lowest 5 values
critical oxygen tension
oxygen partial pressure
routine metabolic rate
standard metabolic rate
Perhaps the most common metric of the oxygen dependence of aerobic metabolism is the critical oxygen tension, Pcrit. For animals, including most vertebrates, that can regulate aerobic metabolism over a broad range of oxygen levels (i.e. oxy-regulators), Pcrit represents the oxygen partial pressure (PO2) at which the rate of oxygen consumption (ṀO2) switches from being independent to being dependent on PO2 with further decreases in ambient oxygen (Ultsch et al., 1981; Farrell and Richards, 2009; Rogers et al., 2016). Pcrit has also been defined as the PO2 below which an animal's basic metabolic needs, i.e. standard metabolic rate (SMR) in fishes, can no longer be sustained aerobically (Schurmann and Steffensen, 1997; Claireaux and Chabot, 2016; Pan et al., 2016; Snyder et al., 2016). This level of oxygen was originally described by Fry and Hart (1948) as the ‘level of no excess activity’. Although related, these two concepts of Pcrit differ: the former refers to an inflection point as ṀO2 transitions between regulation and conformity, which depends upon the intensity of metabolism (Rogers et al., 2016; Wood, 2018), whereas the latter applies to the level of oxygen that limits a specific metabolic state (Claireaux and Chabot, 2016).
Recently, Wood (2018) questioned the usefulness of the Pcrit concept based on two main concerns: uncertainty of its biological meaning and lack of standardization in its determination. The purpose of the present study is not to argue the biological relevance of Pcrit, as this concern has been addressed (Regan et al., 2019). Rather, we aim to evaluate analytical methods used to determine Pcrit from respirometric data. Traditionally, Pcrit has been estimated as the intersection of two straight lines, one fit to a region where ṀO2 is relatively independent of PO2, and a second describing the decrease in ṀO2 at low PO2 (Yeager and Ultsch, 1989; Rogers et al., 2016). Because respirometric data rarely conform neatly to two straight lines across a broad range of PO2, alternative linear or nonlinear regression solutions to determine Pcrit have been proposed (Marshall et al., 2013; Claireaux and Chabot, 2016; Cobbs and Alexander, 2018).
Here, we measured ṀO2 as a function of PO2 in closed and intermittent-flow respirometry with the Gulf killifish, Fundulus grandis Baird & Girard 1853, and applied multiple curve-fitting methods to estimate Pcrit. Based upon our results, we recommend that Pcrit be determined as the PO2 at which ṀO2 drops below SMR using linear regression of ṀO2 versus PO2 at decreasing PO2 (Claireaux and Chabot, 2016). For this method to be general and reproducible, it is imperative that SMR be accurately determined by standardized methods (Chabot et al., 2016).
MATERIALS AND METHODS
Adult male F. grandis (n=11; mass=5.4–16.2 g) were purchased from local bait shops in the summer of 2018 and housed at The University of New Orleans under a 12 h:12 h (light:dark) photoperiod in aerated, filtered one-third strength seawater (salinity≈10) at ∼27°C. Fish were fed an amount of flake fish food equal to 1–1.5% of their body mass once per day. Fish were identified by unique passive integrated transponder (PIT) tags or housed individually. There were no differences in any metabolic variable between PIT-tagged and individually housed fish (Reemeyer et al., 2019; J.E.R., unpublished observations). Fish were maintained under these conditions for at least 1 month before experiments. Fish were starved for 24 h prior to respirometry. All procedures were approved by The University of New Orleans Institutional Animal Care and Use Committee (protocol no. 18-006).
ṀO2 of each fish was determined in a sequence of three respirometry trials, described in detail below. Trials 1 and 2 employed intermittent-flow respirometry to estimate SMR and routine metabolic rate (RMR) (Svendsen et al., 2016; Reemeyer et al., 2019), followed by closed respirometry to estimate Pcrit. In trial 3, Pcrit was determined by intermittent-flow respirometry. SMR and RMR were not determined in this trial because there were a limited number of ṀO2 measurements at PO2>85% air saturation (see below). Trials were separated by approximately 1 week and they were performed at 27.0±0.5°C in one-third strength seawater.
For trials 1 and 2, fish were weighed (to the nearest 0.01 g) and placed into respirometry chambers between 14:00 and 15:00 h. For the first hour, the following intermittent-flow respirometry protocol was used: 60 s flush, 30 s wait and 120 s ṀO2 measurement. At that point, the protocol was adjusted to 300 s flush, 60 s wait and 240 s ṀO2 measurement, which was continued for approximately 14 h. Throughout the combined ∼15 h period, PO2 was maintained at >85% of the air-saturated value. At 06:00 h the following morning, the flush pumps were turned off. At that point, the chambers, recirculating pumps and oxygen sensors formed closed systems, and the PO2 declined due to ṀO2 by the fish. During the closed period, ṀO2 was measured over consecutive 60 s intervals until the fish were unable to maintain equilibrium for ≥3 s. At that point, the flush pumps were turned on to reoxygenate the chambers. The total time the chambers remained closed ranged from 45 to 108 min. All fish recovered upon reoxygenation, whereupon they were returned to their holding tank.
For trial 3, fish were weighed (to the nearest 0.01 g) and placed in respirometry chambers between 15:00 and 16:00 h. Chambers were flushed continuously with well-aerated water (>95% air saturation) until 21:00 h. At that time, the PO2 was stepped down at 1 h intervals by introducing nitrogen gas via a computer-controlled solenoid valve. Target values of PO2 were 20.75, 13.07, 8.30, 5.19, 3.32 and 2.07 kPa. Over the last 30 min at each PO2, ṀO2 was measured in three cycles of 300 s flush, 60 s wait and 240 s measurement. Runs ended around 03:00 h, after which the water was reoxygenated with air. After 30 min recovery, fish were returned to their holding tanks. Importantly, all Pcrit determinations were done during the dark phase of the photoperiod. The only illumination was that required to operate the computer (e.g. to start a closed respirometry trial or to activate nitrogen gassing in the intermittent-flow trial), from which fish chambers were shielded.
ṀO2 due to microbial respiration was measured for each chamber before and after each respirometry run. It was less than 6% of the average SMR of fish and independent of PO2 across the range used. Thus, the ṀO2 by each fish in each trial was corrected by subtracting a time-weighted value for background respiration (Reemeyer et al., 2019; Rosewarne et al., 2016). After background correction, ṀO2 by fish was determined as µmol min−1 g−1 using standard equations (Svendsen et al., 2016). Oxygen concentrations were corrected for salinity, barometric pressure and temperature.
SMR and RMR determination
We evaluated seven methods of estimating SMR (Chabot et al., 2016) using ṀO2 data collected between 20:00 and 06:00 h in trials 1 and 2, corresponding to 60 ṀO2 measurements per fish per trial: (1) the mean of the lowest 10 data points (low10); (2) the mean of the lowest 10% of the data, after removing the five lowest values (low10pc); (3–6) quantiles that place SMR above the lowest 10–25% of the observations (q0.1, q0.15, q0.2, q0.25); and (7) the mean of the lowest normal distribution (MLND). SMR estimated by low10 was lowest, although not statistically different from low10pc, q0.1, q0.15 or q0.2 (Table S1). In instances when cellular metabolism and gas exchange are not in steady state (e.g. hypoventilation), reliance upon a too few ṀO2 measurements may lead to underestimation of SMR. This concern is greatest when averaging the lowest values (low10) and it is alleviated by methods that exclude outliers (low10pc) or are based upon quantiles. Another criterion in evaluating SMR calculation methods is whether the estimated value of SMR agrees with visual inspection of the raw data (Chabot et al., 2016). SMR values estimated by q0.2 and q0.25 best agreed with the distribution of ṀO2 from more runs than any other estimate. The analytical method should also be reproducible when applied to data generated from multiple experimental runs with the same fish. SMR determined as low10pc, q0.15 and q0.2 were more highly correlated between trials 1 and 2 (Pearson's r>0.80) than SMR determined by other methods (Pearson's r<0.80). As a final test of the robustness of SMR determination, we pooled all the data from 22 runs on 11 fish to generate a frequency distribution of 1320 ṀO2 values and then randomly sampled from this distribution to generate 1000 sets of 60 ṀO2 data points (as in the experimental runs). When SMR was calculated from these randomly generated datasets, q0.2 and q0.25 produced the fewest statistical outliers (Fig. S1). Only the q0.2 approach satisfied all the criteria: it generated a low estimate of SMR without undue influence by potentially spurious low values; it agreed with the distribution of raw ṀO2 data; it was reproducible in repeated runs with the same fish; and it produced consistent values when applied to randomly generated datasets. Therefore, SMR determined by this approach was used for the remainder of these analyses. We also calculated RMR, which includes spontaneous, uncontrolled activity in an otherwise quiet, post-absorptive fish, by taking the average of all 60 ṀO2 values collected between 20:00 and 06:00 h.
Importantly, SMR and RMR were determined during a previous overnight (∼10 h) intermittent-flow respirometry experiment, rather than from ṀO2 determined during the Pcrit measurement, when fish might become agitated and display increased ṀO2. In addition, BSR, MM and W used all the ṀO2 data collected during a given experimental run without subjective data elimination; LLO used only a subset of data determined below the PO2 when ṀO2 fell and remained below SMR. Because SMR and RMR were not determined during trial 3 (see above), the mean SMR or RMR from trials 1 and 2 was used for Pcrit determination by the MM, W and LLO methods in trial 3. For all methods, the PO2 for a given ṀO2 was calculated as the mean PO2 over the measurement period (1 min for closed respirometry; 4 min for intermittent-flow respirometry). Data for a representative fish, along with the methods for determining Pcrit, are shown in Fig. 1.
All statistical analyses were performed in R v3.3.3 (https://www.r-project.org/). The effects of analytical method (i.e. method used to calculate SMR or Pcrit) were determined within a given trial using linear mixed models (LMM) with analytical method as a fixed factor and fish as a random factor. LMMs were fit using the lmer() function of the lme4 package (Bates et al., 2014) with P-values generated by the lmerTest package (Kuznetsova et al., 2017). All possible post hoc pairwise comparisons were made with t-tests on model fit means and employed P-values adjusted for false discovery (Benjamini and Hochberg, 1995) using the emmeans package in R (https://CRAN.R-project.org/package=emmeans). Paired t-tests were used to compare Pcrit values based upon SMR and RMR within the MM, W and LLO methods. The effects of respirometry method (closed versus intermittent flow) on the value of Pcrit determined by a given analytical method were evaluated with LMM with respirometry method as a fixed factor and fish as a random factor. Correlations of values determined by a single analytical method in different respirometry trials were evaluated with Pearson's correlation coefficient (r). Variation in body size was accounted for by including fish as a random factor in our statistical models, or by comparing values for a given fish across trials or analytical technique. Therefore, body mass was not included as a variable in these analyses. Data and R script used in this study are available at figshare.com (https://doi.org/10.6084/m9.figshare.8869253.v1).
RESULTS AND DISCUSSION
Models used to estimate Pcrit
The pattern of ṀO2 versus PO2 among fishes and other aquatic vertebrates has traditionally been modeled by the intersection of two straight lines (Yeager and Ultsch, 1989). In the present study, Pcrit values estimated by BSR were among the highest and most variable estimates, including at least one value >10 kPa (50% air saturation) in each respirometry trial (Fig. 2, Table 1). In addition, Pcrit values estimated by BSR were poorly reproducible between respirometry trials conducted with the same individuals under identical (closed respirometry) conditions, as well as between closed and intermittent-flow respirometry (Table S2). These results are likely due to the variability of ṀO2 at levels of PO2 that do not limit oxygen uptake (i.e. at PO2>Pcrit), as well as the tendency in some individuals for ṀO2 to increase as PO2 decreased from 20 to 5 kPa, resulting in a poor linear fit of ṀO2 data at high PO2 and influencing the intersection of two line segments. This variability occurred even though Pcrit measurements were made after >24 h fasting, after 8–12 h since transferring fish to the respirometer, and during the dark phase of the photoperiod, when this species is less active. Owing to the variability of ṀO2 at high PO2, the use of BSR is frequently coupled with removal of ṀO2 data points that fail to meet certain criteria (see Claireaux and Chabot, 2016 and Wood, 2018 for examples). This practice has raised concern over the rationale and validity of applying data selection criteria (Claireaux and Chabot, 2016; Wood, 2018). In addition, direct comparisons of BSR with various nonlinear regression approaches have shown that BSR is seldom the best model to fit ṀO2 data across a range of PO2 (Marshall et al., 2013; Cobbs and Alexander, 2018). In a recent meta-analysis, BSR was the best model in only one of 68 datasets fit with various statistical models (Cobbs and Alexander, 2018).
With the advent and accessibility of nonlinear regression methods, it is possible to fit a variety of nonlinear functions to ṀO2 data. Here, we focused on two nonlinear models, a hyperbolic function, analogous to the Michaelis–Menten equation for enzyme kinetics, and an exponential function, the Weibull function. Although the relationship between ṀO2 and PO2 in biological material as diverse as mitochondria to fishes can be hyperbolic (Tang, 1933; Gnaiger, 1993; Marshall et al., 2013), ṀO2 by F. grandis was poorly described by a hyperbolic function (Fig. 1). In contrast, the W function generally fit the ṀO2 data well, especially at low PO2 (Fig. 1). This observation agrees with Marshall et al. (2013), who found that the W function fit respirometric data better than other nonlinear functions, including the MM function. Neither the MM nor W functions, however, have a parameter equivalent to Pcrit. For the MM function, the parameter b is the PO2 when ṀO2 is half of the extrapolated maximum ṀO2 in that run. In the earliest attempts to model respirometric data with a hyperbolic function, however, there was no reliable, quantitative relationship between b and Pcrit (Tang, 1933). Also, it is not clear that this parameter has any meaning when applied to whole-animal ṀO2, unlike its meaning in enzyme kinetics (Regan et al., 2019). Marshall et al. (2013) suggested that Pcrit of a nonlinear function be estimated as the PO2 at which the slope of the function approaches zero. In their analysis, the value of 0.065 was chosen as the slope giving a PO2 that ‘best approximates Pcrit’. This is a circular argument and requires prior knowledge of Pcrit, presumably based upon BSR.
Alternatives to inflection points to determine Pcrit
Rather than estimate an inflection point, we used the derived MM and W equations to determine the PO2 at which ṀO2 equaled SMR for each fish. Other studies have similarly determined Pcrit as the value of PO2 when ṀO2 equals SMR based upon linear or nonlinear functions (Schurmann and Steffensen, 1997; Bilberg et al., 2010; Thuy et al., 2010; Snyder et al., 2016; Claireaux and Chabot, 2016). For F. grandis, using the MM function to estimate the PO2 when ṀO2 equals SMR resulted in high and variable estimates of Pcrit (Figs 1, 2, Table 1), owing to the poor fit of the data to the hyperbolic relationship. In contrast, using the W function yielded values of Pcrit that were reproducible within and among trials (Figs 1, 2, Table 1). At low PO2, the decline in ṀO2 by F. grandis was essentially a linear function of ambient oxygen, during both closed and intermittent-flow respirometry (Fig. 1), as it is for numerous fish species (Schurmann and Steffensen, 1997; Thuy et al., 2010; Pan et al., 2016; Snyder et al., 2016; Wong et al., 2018). When Pcrit was determined as the value of PO2 when ṀO2 equals SMR using linear regression of ṀO2 versus PO2 at low PO2 (LLO method), values were similar to those generated by the W method (Fig. 2, Table 1), reproducible for a given respirometry format (closed respirometry, Table S2), and agreed with previously published values for F. grandis (Virani and Rees, 2000). This method is also straightforward and easy to implement, given that SMR is accurately determined.
With respect to the value of ṀO2 to use to solve for Pcrit, we and others advocate the use of SMR (Claireaux and Chabot, 2016). If oxygen drops below this level, the fish cannot sustain its minimal metabolic requirements via aerobic metabolism, thus representing a clear physiological limitation. Among fishes, however, RMR is more commonly used to determine Pcrit (Rogers et al., 2016). This metabolic state includes routine, spontaneous activity, which has been argued to be more ecologically relevant than SMR (Fry and Hart, 1948; Rogers et al., 2016; Wood, 2018). Thus, we also determined Pcrit based upon RMR using the MM, W and LLO functions (Fig. 1). As expected, estimates of Pcrit based upon RMR were significantly higher and more variable than those based upon SMR using all calculation methods (paired t-tests, P<0.05; Table 1). Because RMR includes an uncontrolled and usually undetermined level of activity, behavioral differences among individuals or species may confound comparisons of Pcrit based upon RMR, and potentially obscure fundamental differences in oxygen extraction capacity. Indeed, Wong et al. (2018) found differences in Pcrit among multiple species of triggerfishes when using SMR to calculate Pcrit, but not when using RMR.
Based upon our results with F. grandis and the foregoing discussion, we propose that Pcrit be defined as the PO2 at which ṀO2 equals SMR during declining ambient PO2. This recommendation requires that SMR be determined with high accuracy and using robust analytical techniques that yield a value that is insensitive to occasional low outliers, agrees with the distribution of raw ṀO2 data, and is reproducible across multiple trials (Chabot et al., 2016). In the current experiments, the q0.2 method satisfied these criteria. Once SMR is determined, Pcrit may then be determined in a continuation of the same experiment or in a different experiment if SMR is repeatable over time (Reemeyer et al., 2019). We recommend that Pcrit be estimated as the PO2 at which ṀO2 equals SMR based upon a linear relationship of ṀO2 and PO2 at low PO2 (i.e. the LLO method). Using an exponential function (the W function setting c=1) yielded comparable results and may provide better fits for species where the relationship between ṀO2 and PO2 is not linear at low oxygen (see Bilberg et al., 2010).
There was a trend of lower Pcrit estimates from closed respirometry compared with intermittent-flow respirometry, which was statistically significant when using the LLO method to calculate Pcrit (LMM, P<0.05; Table 1). Also, even though Pcrit values were highly correlated between replicate trials of closed respirometry, they were not correlated between either of the trials of closed respirometry and the single trial of intermittent-flow respirometry (Table S2). The two respirometry formats differ in the accumulation of metabolic wastes and, potentially, the rate at which hypoxia develops, both of which can influence Pcrit (Snyder et al., 2016; Regan and Richards, 2017). Importantly, the magnitude of the difference in Pcrit determined by alternative calculation methods (e.g. BSR and LLO) exceeded the differences determined in closed and intermittent-flow respirometry. Hence, the method used to calculate Pcrit is as important as respirometry format, highlighting the need to standardize analytical as well as experimental approaches in assessing the oxygen dependence of metabolism.
We thank Mohammad Hamed for help with animal care.
Conceptualization: J.E.R., B.B.R.; Methodology: J.E.R., B.B.R.; Software: J.E.R.; Validation: J.E.R.; Formal analysis: J.E.R.; Investigation: J.E.R.; Resources: B.B.R.; Data curation: J.E.R.; Writing - original draft: J.E.R., B.B.R.; Writing - review & editing: J.E.R., B.B.R.; Visualization: J.E.R.; Supervision: B.B.R.; Project administration: B.B.R.; Funding acquisition: B.B.R.
This work was supported by the Greater New Orleans Foundation.
Data and R script used in this study are available from figshare: https://doi.org/10.6084/m9.figshare.8869253.v1.
The authors declare no competing or financial interests.