The utility and determination of P_crit in fishes

Innumerable studies of fishes have measured their metabolic rate – expressed as O₂ uptake rate (Ṁ_O2; on the assumption that there is no significant anaerobic metabolism when O₂ is readily available) – and the effects of different variables upon it. One such variable is water P_O2 (Pw_O2); many studies have analyzed how Ṁ_O2 changes as Pw_O2 decreases. Typically Ṁ_O2 changes only slightly, if at all, until Pw_O2 reaches a level that is too low for the fish to extract sufficient quantities of O₂ to maintain a baseline maintenance Ṁ_O2 (Ṁ_O2,std, which supports standard metabolic rate, SMR; see Glossary); Ṁ_O2 starts to decline as Pw_O2 decreases further. The Pw_O2 at which this decrease starts – i.e. the lowest Pw_O2 at which Ṁ_O2,std can be sustained – has been designated the critical O₂ tension (P_c or P_crit; see Glossary), and has been the subject of many investigations. It is generally assumed that a fish with a lower P_crit is more adapted to hypoxia than one with a higher P_crit, analogous to the assumption that an animal with a low blood P₅₀ (e.g. a llama) is more adapted to hypoxia than one with a higher P₅₀. Recently, the meaningfulness of P_crit has been criticized on both methodological and theoretical grounds, with the suggestion that it should be abandoned (Wood, 2018). We disagree (Regan et al., 2019), and present our reasoning here. It is not our intention to review all the physiological, biochemical and behavioral mechanisms surrounding P_crit (see Richards, 2009, 2011; Pörtner and Grieshaber, 1993; Wells, 2009). Rather, we will concentrate almost entirely on the standards for the determination of Ṁ_O2,std, and its use to calculate P_crit. Standardized methods would enable comparisons among studies and highlight the relevance of P_crit to ecology. The bulk of our discussion will deal with fishes, as a large number of such studies focus on this taxon.

Fig. 1 is a commonly used representation, often applied to fishes, of the various Ṁ_O2 states and how they are affected by ambient P_O2. These states include Ṁ_O2,std (the Ṁ_O2 required to aerobically support SMR), Ṁ_O2,rtn (the Ṁ_O2 required to aerobically support routine metabolic rate; RMR; see Glossary) and Ṁ_O2,dep (the Ṁ_O2 required to support a regulated state of metabolic depression). Several assumptions are made in Fig. 1. One is that the relationship is biphasic with two distinct linear portions. The slope of the curve in the zone of oxyregulation (i.e. at Pw_O2 values between normoxia and P_crit) is assumed to be zero. However, this is not always the case, nor is it required to accurately calculate P_crit; all that is required for this calculation is a sharp change in slope (dṀ_O2/dP_O2) at the break point. Another assumption is that extending the relationship in the zone of oxyconformation will intersect the origin, which is usually not the case.

P_crit is the lowest Pw_O2 at which the animal can maintain some benchmark Ṁ_O2 state. Although the term P_crit has been applied to both Ṁ_O2,rtn (Fig. 1, point A) and Ṁ_O2,std (point B), in most cases this is a misnomer for Ṁ_O2,rtn. This point represents the Pw_O2 at which the fish can no longer aerobically support RMR (i.e. the metabolic rate of a post-absorptive fish that includes the costs of minor activity within the respirometer). Therefore, the situation is not critical for the fish; if the animal lowers its activity level, then ambient Pw_O2 will be sufficient to support its metabolic needs. Nevertheless, many studies have reported point A as the P_crit. More appropriate is Ṁ_O2,std (point B), where the fish is at SMR (i.e. the metabolic rate of a post-absorptive fish that is completely inactive). While it is probably true that organisms in the wild are rarely at SMR, the P_crit calculated at point B is physiologically, ecologically and methodologically relevant for three reasons: (1) at the point B P_crit, the fish's aerobic scope (see Glossary), which has progressively decreased from normoxic Pw_O2, reaches zero, leaving only anaerobic glycolysis to fuel metabolic functions beyond baseline maintenance functions (Claireaux and Chabot, 2016); (2) at Pw_O2 below P_crit, maintaining energy balance requires enhanced reliance on anaerobic glycolysis and/or the induction of a regulated metabolic depression (point C): life at or below the point B P_crit is therefore ultimately unsustainable; (3) Ṁ_O2,std is a more consistent and reliable benchmark Ṁ_O2 state compared with the inherently variable Ṁ_O2,rtn. Consequently, P_crit calculations based on Ṁ_O2,std are more reproducible and comparable than those based on Ṁ_O2,rtn. For these reasons, point B is most relevant to P_crit and will be the focus of our discussion.

Two additional points about Ṁ_O2,std and its relationship to P_crit are worth mentioning. First, while Ṁ_O2,std is preferable to Ṁ_O2,rtn as a P_crit calculation benchmark, there are conditions under which Ṁ_O2,rtn is sufficient or even preferred. For example, within a single study, P_crit based on Ṁ_O2,rtn can be an effective comparator so long as the investigator is consistent in their Ṁ_O2,rtn measurement technique. And for species for which Ṁ_O2,std values are virtually impossible to measure (e.g. those that use ram-jet ventilation; see Glossary), Ṁ_O2,rtn is the only option. Second, as mentioned by Wood (2018), it is impossible to know from Ṁ_O2 data alone what metabolic processes are supported by the O₂ taken up by the fish. Therefore, even if an Ṁ_O2 value measured at a moderately hypoxic (i.e. supra-P_crit) Pw_O2 is the same as the Ṁ_O2,std value measured in normoxia, it is impossible to know whether it is supporting the same maintenance processes that comprise SMR. When Pw_O2 is reduced, there may be (and probably is) a reallocation of resources, including O₂, towards a different suite of processes (e.g. ventilation) that may nevertheless sum to a value of Ṁ_O2 similar to normoxic Ṁ_O2,std. While these Ṁ_O2 values at moderately hypoxic Pw_O2 may not be SMR, they represent baseline Ṁ_O2 values at each Pw_O2. We will therefore refer to them as Ṁ_O2,std even if the unknown suite of processes that comprise them are different from those of baseline Ṁ_O2 in normoxia.

Most fishes studied to date have been found to be oxyregulators (see Glossary) over a wide range of Pw_O2, though some have been reported to be oxyconformers (see Glossary). Debate exists about whether truly oxyconforming species exist (e.g. Steffensen, 2006), and this debate is relevant to P_crit, because P_crit represents the lowest environmental P_O2 at which an animal can regulate Ṁ_O2. Therefore, a truly oxyconforming animal has no P_crit, and this may muddle the underlying theory of P_crit and reduce its comparative value.

The majority of studies of Ṁ_O2 and P_crit have been done on small to moderate-sized teleosts, which pass water over their gills by buccal pumping (see Glossary). These studies have mostly been performed in respiration chambers with zero or moderate flow through the chamber. Under such conditions, the highly efficient gills should have no problem transporting sufficient quantities of O₂ into the blood to sustain Ṁ_O2,std over a reasonable range of Pw_O2. As a result, the vast majority of teleosts have been found to be oxyregulators, but there are occasional reports of oxyconformation. One of the best known was Hall's (1929) study of toadfish – results that appeared in several textbooks for decades. Using a flow-through system, Hall's data clearly showed toadfish to be oxyconformers. But Ultsch et al. (1981) questioned why the toadfish should be an oxyconformer when the vast majority of fishes studied since 1929 were oxyregulators. Using a more sophisticated respirometry system, they demonstrated that toadfish from the same area as Hall's are clearly oxyregulators.

Other oxyconformers have been reported, but this small group is being whittled down by subsequent studies. Common carp (Cyprinus carpio) were suggested to be oxyconformers (Lomholt and Johansen, 1979), but they clearly are not (Dhillon et al., 2013; Ott et al., 1980; Ultsch et al., 1980; Yamanaka et al., 2007; He et al., 2015), which is not surprising considering their low hemoglobin P₅₀ (Weber and Lykkeboe, 1978; Burggren, 1982). The Mayan cichlid (Mayaheros uropthalmus) was reported as an oxyconformer (Martínez-Palacios and Ross, 1986) but has recently been shown to be a strong oxyregulator at three different temperatures (Burggren et al., 2019). Subrahmanyam (1980) reported all four estuarine species he studied to be oxyconformers, one of which was Fundulus grandis. But in a study specifically designed to test this hypothesis, Virani and Rees (2000) found this species to be an oxyregulator. Another of the four species, Leiostomus xanthurus, has also subsequently been found to be an oxyregulator (Cochran and Burnett, 1996). Fundulus heteroclitus was reported as an oxyconformer (Blewett et al., 2013), but a number of other studies found it to be an oxyregulator (Borowiec et al., 2015; Cochran and Burnett, 1996; Richards et al., 2008; McBryan et al., 2016). Both male and female plainfin midshipman (Porichthys notatus) have been reported to be oxyconformers (Craig et al., 2014; Lemoine et al., 2014). However, there have been no additional studies to affirm the finding that this species is oxyconforming.

Sturgeons were reported to be oxyconformers by Burggren and Randall (1978), but subsequent studies found them to be oxyregulators (Ruer et al., 1987; Crocker and Cech, 2002; Randall et al., 1982; Nonette et al., 1993). Interestingly, McKenzie et al. (2007) found that when the sturgeon Acipenser naccarii was exposed to progressive hypoxia under static conditions, it was an oxyconformer; however, when allowed to swim at a low sustained speed, it could regulate Ṁ_O2 down to a P_O2 of 37 mmHg (4.9 kPa). While this fish does not use ram-jet ventilation in the classic sense, the results do raise a point about the importance of swimming in some fishes if one is attempting to determine the Ṁ_O2,std and/or P_crit.

The fishes discussed above use buccal pumps to irrigate their gills. Fishes that swim constantly and/or use ram-jet ventilation can present some special problems in determining their Ṁ_O2,std and P_crit (reviewed by Bushnell and Jones, 1994). Potentially, they could appear to be oxyconformers if constrained within a respiration chamber, when they might be oxyregulators if allowed to swim or provided with a high enough flow within the chamber to ventilate the gills through an open mouth. Several such species have been found to increase swimming speed and/or mouth gape as water becomes hypoxic (bonnethead shark, Sphyrna tiburo: Parsons and Carlson, 1998; several species of tuna: Bushnell and Brill, 1992; Gooding et al., 1981). Therefore, even if P_crit is determined under static conditions, it may have little relevance to their natural state, and the P_crit thus determined might well be reduced with moderate swimming that allows improved gill ventilation. The situation is further complicated with fishes that are not obligate ram-jet ventilators. For example, Steffensen (1985) found a 10.2% reduction in Ṁ_O2 in rainbow trout when they switched from buccal pumping to ram-jet ventilation; however, that study did not attempt to determine a P_crit for each ventilation method. Thus, when comparing the P_crit of different species, one should consider the modes of ventilation and the lifestyles.

We are aware of no studies that deal with P_crit considerations for constantly swimming elasmobranchs. There have been studies on sharks, many of which swim constantly, at least during a significant portion of a 24 h day, but few of these studies were on swimming animals. Scyliorhinus stellaris was reported to be an oxyconformer by Piiper et al. (1970), but Hughes and Umezawa (1968) found that the related Scyliorhinus canicula could regulate down to at least 80 mmHg (10.7 kPa), and Butler and Taylor (1975) also found this species to be an oxyregulator at 12 and 17°C. Even the purportedly hypoxia-tolerant epaulette shark (Hemiscyllium ocellatum; Routley et al., 2002) is an oxyregulator down to 38 mmHg (5.1 kPa), as is the shovelnose ray (Aptychotrema rostrata), with a P_crit of 54 mmHg (7.2 kPa) (Speers-Roesch et al., 2012). An interesting question is whether such fishes, which normally swim constantly, would have a lower P_crit if allowed to swim at slow speeds, or would the extra activity raise their P_crit? And from an ecological viewpoint, would the P_crit determined at normal swimming speeds be the most relevant? Clearly, interspecies comparisons of P_crit among elasmobranchs and other ram-ventilating fishes are more complicated than among the majority of teleosts, especially freshwater species.

One species deserves special mention. The inanga (Galaxias maculatus) has been reported to be an oxyconformer in studies that used both closed systems and intermittent-flow systems (Urbina et al., 2012; Urbina and Glover, 2013). The fish is especially interesting because it is scaleless and obtains about 1/3 of its O₂ in normoxic water cutaneously. When the water becomes severely hypoxic, it emerges (Urbina et al., 2011), and can increase its cutaneous O₂ uptake significantly. Nevertheless, the fish has functional gills that supply 2/3 of its O₂ requirements in normoxic water, and apparently can upregulate its cutaneous O₂ uptake, so it is not evident why it should not be an oxyregulator over at least a moderate range of Pw_O2, with perhaps a comparatively high P_crit.

In summary, we believe that almost all, if not all, fishes are oxyconformers over some appreciable range of Pw_O2, and that findings otherwise are likely to be due to methodology or chance.

Properly determining P_crit involves three processes: (1) measuring Ṁ_O2,std; (2) reducing Pw_O2; and (3) calculating P_crit from the Ṁ_O2 versus Pw_O2 curve. Respirometry is used to accomplish steps 1 and 2, and below we discuss the relevant advantages and disadvantages of three common respirometry techniques (see Table 1) – closed system (CS), intermittent flow (IF) and continuous flow (CF). We then discuss P_crit calculation methods, and end with our recommended best practices for each step.

CS respirometry involves placing the fish in a sealed, gas-impermeable respirometry chamber with a P_O2 sensor and a well-mixed water volume. The fish's Ṁ_O2 is determined from the rate at which its respiration reduces Pw_O2 from some starting Pw_O2 to some lower target Pw_O2. For measuring Ṁ_O2,std, CS respirometry on its own (i.e. without the serial normoxic Ṁ_O2 measurements made during IF; see below) is problematic, because the investigator has no way of knowing whether the Ṁ_O2 measured in normoxia is Ṁ_O2,std or, more likely, some Ṁ_O2 between Ṁ_O2,std and the Ṁ_O2 that supports maximal metabolic rate, Ṁ_O2,max (i.e. Ṁ_O2,rtn). The uncertainty around this benchmark normoxic Ṁ_O2 state consequently reduces the effectiveness of CS respirometry for determining P_crit. CS respirometry relies on the fish's respiration to reduce Pw_O2. The rate of Pw_O2 decline is therefore a function of the fish's metabolic rate and the water volume of the chamber, which leaves the investigator with only indirect control over this rate through control of water volume. Recommended water volume:fish mass ratios of 20:1 to 100:1 (Clark et al., 2013) typically result in Pw_O2 being reduced from normoxia to terminal Pw_O2 in 1–2 h. This rate may be higher than what the species experiences in its natural environment, but it may outpace the onset of P_crit-influencing hypoxic acclimations that are difficult to control for (e.g. Regan and Richards, 2017).

Furthermore, a closed system means that metabolic waste such as CO₂ and ammonia will accumulate in the water. Though often touted as a disadvantage of CS respirometry, CO₂ buildup is unlikely to affect Ṁ_O2,std significantly – even if a fish consumes all the O₂ in the water, the water P_CO2 (Pw_CO2) will not exceed 5 mmHg (0.7 kPa), and studies on a range of species have shown that much higher Pw_CO2 values [up to 90 mmHg (12 kPa) in one case] have no effect on Ṁ_O2 (Beamish, 1964; Cochran and Burnett, 1996; Randall et al., 1976; Sloman et al., 2008; Cruz-Neto and Steffensen, 1997; Crocker and Cech; 2002). However, it is possible that the elevated Pw_CO2 may elevate P_crit through possible red blood cell acidification and subsequent reduction of hemoglobin–O₂ binding affinity. The effects of ammonia are not well studied, but most studies on P_crit use fasting fishes, so ammonia production should be minimal.

When using CS respirometry, it should be noted that the fish's attempts to escape the hypoxic conditions throughout the uncontrolled decline in Pw_O2 often elevate Ṁ_O2 far above Ṁ_O2,std. Some species (e.g. goldfish) tend not to display such escape responses. However, many species do, and the result is a scatter of Ṁ_O2 values as a function of Pw_O2 (Fig. 2). Calculating P_crit from such a data set requires the investigator to apply a set of criteria to isolate the Ṁ_O2 values that best reflect Ṁ_O2,std.

IF respirometry involves intermittently flushing the chamber with fresh water between Ṁ_O2 measurements that are taken using CS respirometry. Flushing replenishes the chamber with O₂, eliminates the buildup of waste products that might affect Ṁ_O2, and allows for serial Ṁ_O2 measurements within a narrow Pw_O2 range. For these reasons, IF respirometry has been widely touted in reviews (Clark et al., 2013; Snyder et al., 2016; Chabot et al., 2016; Eriksen, 2002; Svendsen et al., 2016; Steffensen, 1989). For measuring Ṁ_O2,std, IF respirometry enables serial normoxic Ṁ_O2 measurements over a long habituation period (≥24 h), to which the investigator may then apply some criteria to determine which data points to use for the Ṁ_O2,std estimation (e.g. Steffensen et al., 1994; Murchie et al., 2011; Snyder et al., 2016; Chabot et al., 2016). The result is an accurate estimation of Ṁ_O2,std. For reducing Pw_O2, the investigator reduces the Pw_O2 of sump (or incurrent) water in a stepwise fashion. This prevents the accumulation of end products in the fish chamber (though, as mentioned above, this may not be a problem) and allows hypoxic Pw_O2 environments to be sustained long enough to outlast the fish's acute behavioral responses. Furthermore, as in normoxia, serial Ṁ_O2 measurements can be made at each hypoxic Pw_O2, meaning reasonable estimates of Ṁ_O2,std at each moderately hypoxic (i.e. supra-P_crit) Pw_O2 are possible. This reduces the scatter of Ṁ_O2 values in the oxyregulation portion of the Ṁ_O2 versus P_crit curve, and ultimately makes for a more straightforward P_crit calculation. However, it also requires considerable time, which, when coupled with the time required to equilibrate the Pw_O2 of the sump and chamber water volumes, results in a relatively long P_crit trial of ∼5 h. This is sufficiently long for some species to induce hypoxia acclimation responses (e.g. Regan and Richards, 2017), which may jeopardize the comparative value of the resulting P_crit. Perhaps for this reason or the relative complexity of performing IF respirometry at progressively lower Pw_O2 values, investigators often use IF respirometry to make normoxic Ṁ_O2,std measurements, then abandon flushing when reducing Pw_O2 in favor of straight CS respirometry. This approach presents the same drawbacks described above for CS respirometry. Some investigators mitigate these drawbacks by using a hybrid approach, where IF is used between normoxia and some moderately hypoxic Pw_O2 that is predicted to be above the fish's P_crit (e.g. 8 kPa), and then CS is used from that Pw_O2 down to the terminal Pw_O2 (e.g. Borowiec et al., 2015; Crans et al., 2015).

CF respirometry (sometimes called flow-through respirometry) involves supplying the fish with a continuous flow of fresh water; Ṁ_O2 is measured as the difference between incurrent and excurrent values of Pw_O2 multiplied by the water flow rate. For measuring Ṁ_O2,std, the continuous recording of excurrent Pw_O2 enables a continuous calculation of Ṁ_O2. As with IF respirometry, when a sufficient habituation period (≥24 h) is used and some criteria are applied to these Ṁ_O2 values, the result is an accurate estimate of Ṁ_O2,std (Fig. 3). For reducing Pw_O2, the investigator reduces sump (or incurrent) Pw_O2 in a stepwise fashion. This offers similar benefits to IF respirometry – no waste product accumulation and the ability to maintain any Pw_O2 environment long enough for the fish to reach a stable Ṁ_O2 approaching Ṁ_O2,std. In fact, CF enables the fish's Pw_O2 environment to be held relatively stable. This is not possible with CS or IF because they require Pw_O2 of the respirometer water volume to span the median Pw_O2 for which Ṁ_O2 is measured. This pre-exposes the fish to lower Pw_O2, which, particularly at Pw_O2 around the P_crit, may be problematic. CF respirometry avoids this complication. However, reducing Pw_O2 with CF respirometry results in a lag period during the washout phase as the next Pw_O2 equilibrates across the chamber and both inflow and outflow P_O2 sensors. The typical flow-through equation cannot be used to calculate Ṁ_O2 during this lag period, and this has been cited as a problem with CF respirometry (Clark et al., 2013; Rosewarne et al. 2016; Svendsen et al., 2016). However, there are additional equations that allow Ṁ_O2 to be accurately calculated during these lag periods (Niimi, 1978; Steffensen, 1989; Ultsch and Duke, 1990; Ultsch and Anderson, 1988; Ultsch et al., 1980, 1981), thereby shortening the time over which a P_crit trial using CF respirometry can be run.

There are different methods to calculate P_crit from the Ṁ_O2 versus Pw_O2 curve, some of which use more data than others. According to a recent P_crit meta-analysis (Rogers et al., 2016), the most widely used method of P_crit calculation is a segmented linear regression technique such as that of Yeager and Ultsch (1989). This method uses all (or most) of the Ṁ_O2 data and assumes the Ṁ_O2 response of fishes to declining Pw_O2 is approximately biphasic with two distinct linear portions, an oxyregulation line and an oxyconformation line (Fig. 1). The Pw_O2 at which these lines intersect is the P_crit. The Yeager and Ultsch (1989) method puts no restrictions on the placement of data points. It looks at all sets of data points for two-line fits by starting with Ṁ_O2 at the lowest Pw_O2 in the zone of oxyconformation, plotting a regression line for the first three points, and assigning remaining points to the second line. It then continues the calculations for each line, adding one point at a time to the progressively higher Pw_O2. The process continues until all but the last three points are on the oxyconformation line. The best fit is then defined as the set of two regression lines that give the lowest summed sum of squares of error (SSE). This method is widely applicable because many fishes studied to date display a biphasic response of Ṁ_O2 to declining Pw_O2, the result of their oxyregulatory abilities. However, not all species (or individuals) do, and applying this segmented linear regression technique to them may overestimate P_crit.

There are different ways to calculate P_crit from a non-biphasic Ṁ_O2 versus Pw_O2 curve. Non-linear regression (e.g. Marshall et al., 2013) and Akaike information criterion (Cobbs and Alexander, 2018) do so using all of the available data, but they are complex and perhaps for this reason are not widely used. More common techniques involve omitting certain Ṁ_O2 data points from the P_crit calculation that are thought to be unrepresentative of Ṁ_O2,std, essentially transforming a non-biphasic curve into a biphasic one. The trick here of course is determining which Ṁ_O2 values are kept and which are omitted, as critically assessed by Wood (2018); this is accomplished by applying some criteria to eliminate Ṁ_O2 values that obviously exceed or underestimate Ṁ_O2,std. The remaining data may then be input into a program such as that of Yeager and Ultsch (1989) or Claireaux and Chabot (2016) to calculate P_crit. Perhaps the simplest method involves anchoring the oxyregulation line at the Ṁ_O2,std value determined in normoxia (i.e. >17 kPa Pw_O2), and then extending this value leftward, effectively disregarding the Ṁ_O2 values between normoxia and P_crit (e.g. Snyder et al., 2016). The oxyconformation portion of the curve is then determined by some criteria (e.g. any Ṁ_O2 values >15% below the Ṁ_O2,std line), regressed, and the intersection of this line with the extrapolated Ṁ_O2,std line is the P_crit. This method is relatively easy to execute and eliminates the influence of Ṁ_O2,rtn values at intermediate Pw_O2 values such as activity-related Ṁ_O2 elevations as Pw_O2 approaches P_crit. However, the influence of such activity-related Ṁ_O2,rtn values can be minimized by applying IF or CF respirometry as described above, which also avoids the assumption that the slope of the oxyregulation line is zero. Importantly, although the Ṁ_O2 values at intermediate Pw_O2 are not used in the P_crit calculation, the investigator must nevertheless choose a rate of Pw_O2 decline that is appropriate for the question being addressed and use this rate consistently to control for hypoxia acclimation responses that may affect P_crit (Regan and Richards, 2017).

This normoxia-anchored Ṁ_O2,std method may be used in a different, more complex way to determine P_crit. First, Ṁ_O2,max is measured at various Pw_O2, generating a curve that has a reduced Ṁ_O2,max as Pw_O2 decreases. Next, Ṁ_O2,std is determined at normoxia and extended leftward until it intersects the linear regression line of Ṁ_O2,max and Pw_O2. While this method effectively reveals the Pw_O2 at which aerobic scope reaches zero (a property of P_crit as defined by Fry's concept of aerobic scope; Fry, 1971; Claireaux and Chabot, 2016) and has been used previously (e.g. Claireaux et al., 2000), it is much less practical than methods based on Ṁ_O2,std alone and is virtually impossible to perform on a single individual without the confounding training effects of repeatedly determining Ṁ_O2,max.

When selecting from the array of available respirometry and calculation methods in order to determine P_crit, we feel that the most important issue to consider is how the P_crit data will be used. No single combination of respirometry and calculation is ideal for all situations and scientific questions. For example, if one intends to compare P_crit data with existing literature values, then it is advisable to duplicate the methods of those studies as closely as possible. In many cases, this will be difficult, especially if the previous studies based their calculations on Ṁ_O2,rtn instead of Ṁ_O2,std. Alternatively, if the intended use is to duplicate the O₂ dynamics of a species' natural environment, then it is advisable to use IF or CF respirometry so as to control the rate of Pw_O2 decline as precisely as possible. Or, if the experimental species is a ram ventilator, then it is advisable to conduct P_crit trials in a swim flume even if this precludes the use of Ṁ_O2,std as the benchmark oxyregulatory Ṁ_O2 state.

Aside from scenarios like these, we feel that there are certain best practices that should be followed when performing respirometry and calculating P_crit. Foremost, the respirometry experiments should be conducted as carefully as possible. A calculated P_crit is only as accurate as the Ṁ_O2 data on which it is based, and it is probably true that variation in respirometry experiments explains far more of the inter-study P_crit variation highlighted by Wood (2018) than variation in P_crit calculation method. The reader is guided to reviews by Clark et al. (2013) and Chabot et al. (2016) for details on best respirometry practices, but, briefly, these experiments should involve a habituation period of ≥24 h and a well-circulated water volume, and should control for P_O2 sensor drift and background microbial respiration. Importantly, unless the research question requires Ṁ_O2,rtn, the respirometry method should generate data from which accurate estimates of normoxic Ṁ_O2,std can be obtained. This requires either IF or CF respirometry. Depending on the research question, generating Ṁ_O2,std values not just at normoxia but at Pw_O2 values throughout the Ṁ_O2 versus Pw_O2 curve is ideal.

For Pw_O2 reduction, the technique depends largely on the desired rate of hypoxia induction, as these rates may significantly impact P_crit (Regan and Richards, 2017). High rates are useful for questions involving cross-species comparisons, which would benefit from determining an ‘innate’ P_crit that is minimally influenced by hypoxia acclimation. For this, CS respirometry is ideal, particularly when using a chamber volume:fish mass of ∼30:1 (with the caveat that the fish's activity at moderately hypoxic Pw_O2 may hamper an accurate P_crit calculation). Low, controlled rates of hypoxia induction are useful when addressing questions regarding hypoxia acclimation and/or when duplicating the O₂ dynamics of a species' native hypoxic environment. For these, IF or CF respirometry is ideal, both of which have the added benefits over CS of preventing metabolic end-product accumulation and enabling best estimates of Ṁ_O2,std at each Pw_O2.

For P_crit calculation, we feel that a method based on empirical data is better than one based on extrapolation. Therefore, methods that use all (or most) available Ṁ_O2 versus Pw_O2 data, such as Yeager and Ultsch (1989) and Claireaux and Chabot (2016), are advised over methods that, for example, ignore Ṁ_O2 values at moderately hypoxic Pw_O2 (i.e. supra-P_crit) and instead anchor the oxyregulation line at the normoxic Ṁ_O2,std value. This is most effectively done with Ṁ_O2 data that approximate Ṁ_O2,std at moderately hypoxic Pw_O2. In all cases, accurate measurements of Ṁ_O2,std in normoxia (i.e. ≥17 kPa Pw_O2) are required. These can be made using methods outlined in Chabot et al. (2016), and they serve as a benchmark for Ṁ_O2 values at moderately hypoxic Pw_O2. If values approximating Ṁ_O2,std cannot be measured at moderately hypoxic Pw_O2 for either biological or methodological reasons (i.e. the curve is non-biphasic), then the investigator must decide whether to calculate P_crit using either a non-linear approach or one that anchors the oxyregulation line at the normoxic Ṁ_O2,std value. In any case, all Ṁ_O2 versus Pw_O2 data should be presented.

Finally, there are best practices for reporting P_crit results that maximize their value to the research community. It is imperative that the methods used for respirometry, reducing Pw_O2, and calculating P_crit are clearly described. Furthermore, the raw respirometry data should be presented, either in the manuscript or as supplementary material. So long as the respirometry experiments are properly executed and reported, the Ṁ_O2 versus Pw_O2 data will be useable by readers, thus enhancing the comparative value of the P_crit results. Furthermore, when comparing literature P_crit values, investigators should analyze these values and the methods used to determine them carefully to ensure the comparison is appropriate.

Tolerance can be defined in different ways. Generally, tolerance is the capacity to endure continued subjection to something without adverse reaction. In the fish-hypoxia literature, tolerance is rarely defined, but investigators are often concerned only with the limits of endurance, not continued endurance. These are different definitions with different ecological implications; ‘continued endurance’ implies sustained survival, reproduction and the capacity to do work, whereas ‘limits of endurance’ implies merely surviving. Neither definition is more valid than the other, but investigators should clearly state which they mean (or how they define synonymous phrases such as hypoxic performance, sensitivity and resistance), because certain metrics of ‘tolerance’ may be more appropriate for some definitions than others. Nevertheless, P_crit and most other metrics of tolerance are tied most closely to the ‘limits of endurance’ definition, and so we will proceed using this definition.

As previously mentioned, at P_crit, a fish retains zero aerobic scope for activity. While maintenance functions may be fueled aerobically at this Pw_O2, routine activities relevant to biological fitness need to be fueled anaerobically. This is unsustainable – it is limited by finite fuel stores and accumulation of deleterious waste products – and thus P_crit does not realistically represent the lowest Pw_O2 at which a fish can survive indefinitely. Rather, P_crit defines the lowest Pw_O2 at which maintenance functions are supported aerobically, capturing the suite of aerobic contributions to hypoxia tolerance along a fish's O₂ transport cascade in a single value. Because the sum of these maintenance functions can be accurately measured as Ṁ_O2,std, P_crit serves as an effective comparator of the aerobic contributions to overall hypoxia tolerance. And because aerobic metabolism is a significant contributor to hypoxia tolerance (and P_crit strongly correlates with the nadir Pw_O2 of a species' natural environment; Childress and Seibel, 1998; Mandic et al., 2009; Rogers et al., 2016), P_crit is closely associated with overall hypoxia tolerance. We see no reason to discard this view if appropriate methodology is used to determine P_crit.

Another often-used measurement of hypoxia tolerance is loss of equilibrium (LOE), which can be quantified in two ways: (1) the time at which the fish can no longer right itself (i.e. loses equilibrium) when held at some hypoxic Pw_O2; or (2) the Pw_O2 at which the fish loses equilibrium under conditions of continually decreasing Pw_O2. The longer the time or the lower the Pw_O2, the more hypoxia tolerant the fish. Survival at either LOE point is obviously unsustainable (at least under the experimental conditions), but by accounting for the contributions of anaerobic metabolism and metabolic depression to an animal's hypoxic survival, LOE serves as a comprehensive index of hypoxia tolerance. P_crit, being associated with aerobic metabolism, does not account for these contributions. However, this does not negate the value of P_crit; it simply means that P_crit represents something different (i.e. the capacity for aerobic metabolism in hypoxia, something LOE does not reveal).

Another indicator of hypoxia tolerance is the regulation index (RI; see Glossary) (Mueller and Seymour, 2011), which quantifies an animal's oxyregulatory ability. The RI is a dimensionless number that ranges from zero (perfect oxyconformation) to one (perfect oxyregulation) over a range of P_O2 from high (e.g. normoxic) to zero (anoxic). A fish with a higher RI would be considered more adapted to hypoxia than one with a lower RI. The model is most useful when the relationship between Ṁ_O2 and P_O2 is a gradual curve, but in most cases with fishes it is not – the broken-stick model is the most common result. In this situation, one can still calculate an RI, but the same conclusion will be drawn – the fish with the lower P_crit will have the higher RI. Moreover, P_crit contains some informational value, as it has units, while the RI has none.

In summary, we assert that P_crit is a useful comparator of hypoxia tolerance, so long as it is determined and reported using best practices that maximize its comparative value among studies. We also assert that CF and IF respirometry give the most reliable estimates of Ṁ_O2,std, which under most circumstances is prerequisite to calculating P_crit. Once one has reliable Ṁ_O2,std data over a large range of Pw_O2, the calculation of P_crit, at least for fishes, is straightforward.

We thank Drs Tony Farrell and Milica Mandic for helpful discussions, and the two reviewers for their insight.