ABSTRACT

The critical O2 tension (Pcrit) is the lowest PO2 at which an animal can maintain some benchmark rate of O2 uptake (O2). This PO2 has long served as a comparator of hypoxia tolerance in fishes and aquatic invertebrates, but its usefulness in this role, particularly when applied to fishes, has recently been questioned. We believe that Pcrit remains a useful comparator of hypoxia tolerance provided it is determined using the proper methods and hypoxia tolerance is clearly defined. Here, we review the available methods for each of the three steps of Pcrit determination: (1) measuring the most appropriate benchmark O2 state for Pcrit determination (O2,std, the O2 required to support standard metabolic rate); (2) reducing water PO2; and (3) calculating Pcrit from the O2 versus PO2 curve. We make suggestions on best practices for each step and for how to report Pcrit results to maximize their comparative value. We also discuss the concept of hypoxia tolerance and how Pcrit relates to a fish's overall hypoxia tolerance. When appropriate methods are used, Pcrit provides useful comparative physiological and ecological information about the aerobic contributions to a fish's hypoxic survival. When paired with other hypoxia-related physiological measurements (e.g. lactate accumulation, calorimetry-based measurements of metabolic depression, loss-of-equilibrium experiments), Pcrit contributes to a comprehensive understanding of how a fish combines aerobic metabolism, anaerobic metabolism and metabolic depression in an overall strategy for hypoxia tolerance.

Introduction

Innumerable studies of fishes have measured their metabolic rate – expressed as O2 uptake rate (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 PO2 (PwO2); many studies have analyzed how O2 changes as PwO2 decreases. Typically O2 changes only slightly, if at all, until PwO2 reaches a level that is too low for the fish to extract sufficient quantities of O2 to maintain a baseline maintenance O2 (O2,std, which supports standard metabolic rate, SMR; see Glossary); O2 starts to decline as PwO2 decreases further. The PwO2 at which this decrease starts – i.e. the lowest PwO2 at which O2,std can be sustained – has been designated the critical O2 tension (Pc or Pcrit; see Glossary), and has been the subject of many investigations. It is generally assumed that a fish with a lower Pcrit is more adapted to hypoxia than one with a higher Pcrit, 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 Pcrit 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 Pcrit (see Richards, 2009, 2011; Pörtner and Grieshaber, 1993; Wells, 2009). Rather, we will concentrate almost entirely on the standards for the determination of O2,std, and its use to calculate Pcrit. Standardized methods would enable comparisons among studies and highlight the relevance of Pcrit to ecology. The bulk of our discussion will deal with fishes, as a large number of such studies focus on this taxon.

List of symbols and abbreviations
     
  • CF

    continuous flow

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  • CS

    closed system

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  • IF

    intermittent flow

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  • LOE

    loss of equilibrium, especially the PO2 at which it occurs

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  • O2

    rate of O2 consumption

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  • O2,dep

    O2 that supports a regulated state of metabolic depression

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  • O2,max

    O2 that supports maximal metabolic rate

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  • O2,rtn

    O2 that supports routine metabolic rate

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  • O2,std

    O2 that supports standard metabolic rate

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  • P50

    partial pressure of O2 at which the blood or hemoglobin is 50% saturated with O2

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  • Pcrit

    critical O2 tension

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  • PwO2

    partial pressure of O2 in water

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  • PwCO2

    partial pressure of CO2 in water

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  • RI

    regulation index

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  • RMR

    routine metabolic rate

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  • SMR

    standard metabolic rate

Glossary

Aerobic scope

The difference between O2,std and O2,max in resting, unfed animals.

Buccal pumping

A ventilation method whereby the respiratory medium (e.g. water for fishes) is drawn across the exchange surface (e.g. gills) via pressure changes generated by the mouth.

Oxyconformer

An animal in which O2 declines in direct proportion to declining environmental PO2.

Oxyregulator

An animal that maintains O2 independent of environmental PO2.

Pcrit

The partial pressure of O2 below which the animal can no longer maintain a stable O2; below Pcrit, O2 becomes dependent upon partial pressure (tension) of O2.

Ram-jet ventilation

A ventilation method used by some fishes whereby an open mouth and continuous swimming allow water to continually flow over the gills.

Regulation index (RI)

A dimensionless relative measure of hypoxia tolerance (more specifically, oxyregulatory ability) that ranges from 0 to 1.

Routine metabolic rate (RMR)

Metabolic rate of a fasting, resting animal exhibiting spontaneous activity, typically measured as O2.

Standard metabolic rate (SMR)

Metabolic rate of a fasting, resting animal exhibiting no spontaneous activity, typically measured as O2.

Defining Pcrit

Fig. 1 is a commonly used representation, often applied to fishes, of the various O2 states and how they are affected by ambient PO2. These states include O2,std (the O2 required to aerobically support SMR), O2,rtn (the O2 required to aerobically support routine metabolic rate; RMR; see Glossary) and O2,dep (the 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 PwO2 values between normoxia and Pcrit) is assumed to be zero. However, this is not always the case, nor is it required to accurately calculate Pcrit; all that is required for this calculation is a sharp change in slope (dO2/dPO2) 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.

Fig. 1.

Hypothetical relationships between rate of O2 consumption (O2) and PO2.O2,rtn represents the O2 state for routine metabolic rate, O2,std is the O2 state for standard metabolic rate and O2,dep is the O2 for a regulated and depressed aerobic metabolic rate. Points A–C are the critical O2 tension (Pcrit) for each O2 state level. Zones of oxyregulation and oxyconformation are shown for the O2,stdPcrit curve. PwO2, partial pressure of O2 in water.

Fig. 1.

Hypothetical relationships between rate of O2 consumption (O2) and PO2.O2,rtn represents the O2 state for routine metabolic rate, O2,std is the O2 state for standard metabolic rate and O2,dep is the O2 for a regulated and depressed aerobic metabolic rate. Points A–C are the critical O2 tension (Pcrit) for each O2 state level. Zones of oxyregulation and oxyconformation are shown for the O2,stdPcrit curve. PwO2, partial pressure of O2 in water.

Pcrit is the lowest PwO2 at which the animal can maintain some benchmark O2 state. Although the term Pcrit has been applied to both O2,rtn (Fig. 1, point A) and O2,std (point B), in most cases this is a misnomer for O2,rtn. This point represents the PwO2 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 PwO2 will be sufficient to support its metabolic needs. Nevertheless, many studies have reported point A as the Pcrit. More appropriate is 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 Pcrit calculated at point B is physiologically, ecologically and methodologically relevant for three reasons: (1) at the point B Pcrit, the fish's aerobic scope (see Glossary), which has progressively decreased from normoxic PwO2, reaches zero, leaving only anaerobic glycolysis to fuel metabolic functions beyond baseline maintenance functions (Claireaux and Chabot, 2016); (2) at PwO2 below Pcrit, 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 Pcrit is therefore ultimately unsustainable; (3) O2,std is a more consistent and reliable benchmark O2 state compared with the inherently variable O2,rtn. Consequently, Pcrit calculations based on O2,std are more reproducible and comparable than those based on O2,rtn. For these reasons, point B is most relevant to Pcrit and will be the focus of our discussion.

Two additional points about O2,std and its relationship to Pcrit are worth mentioning. First, while O2,std is preferable to O2,rtn as a Pcrit calculation benchmark, there are conditions under which O2,rtn is sufficient or even preferred. For example, within a single study, Pcrit based on O2,rtn can be an effective comparator so long as the investigator is consistent in their O2,rtn measurement technique. And for species for which O2,std values are virtually impossible to measure (e.g. those that use ram-jet ventilation; see Glossary), O2,rtn is the only option. Second, as mentioned by Wood (2018), it is impossible to know from O2 data alone what metabolic processes are supported by the O2 taken up by the fish. Therefore, even if an O2 value measured at a moderately hypoxic (i.e. supra-Pcrit) PwO2 is the same as the O2,std value measured in normoxia, it is impossible to know whether it is supporting the same maintenance processes that comprise SMR. When PwO2 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 O2 similar to normoxic O2,std. While these O2 values at moderately hypoxic PwO2 may not be SMR, they represent baseline O2 values at each PwO2. We will therefore refer to them as O2,std even if the unknown suite of processes that comprise them are different from those of baseline O2 in normoxia.

Are there fishes with no Pcrit between anoxia and normoxia, i.e. oxyconformers?

Most fishes studied to date have been found to be oxyregulators (see Glossary) over a wide range of PwO2, 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 Pcrit, because Pcrit represents the lowest environmental PO2 at which an animal can regulate O2. Therefore, a truly oxyconforming animal has no Pcrit, and this may muddle the underlying theory of Pcrit and reduce its comparative value.

The majority of studies of O2 and Pcrit 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 O2,std over a reasonable range of PwO2. 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 O2 down to a PO2 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 O2,std and/or Pcrit.

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 O2,std and Pcrit (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 Pcrit is determined under static conditions, it may have little relevance to their natural state, and the Pcrit 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 O2 in rainbow trout when they switched from buccal pumping to ram-jet ventilation; however, that study did not attempt to determine a Pcrit for each ventilation method. Thus, when comparing the Pcrit of different species, one should consider the modes of ventilation and the lifestyles.

We are aware of no studies that deal with Pcrit 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 Scyliorhinuscanicula 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 Pcrit 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 Pcrit if allowed to swim at slow speeds, or would the extra activity raise their Pcrit? And from an ecological viewpoint, would the Pcrit determined at normal swimming speeds be the most relevant? Clearly, interspecies comparisons of Pcrit 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 PwO2, with perhaps a comparatively high Pcrit.

In summary, we believe that almost all, if not all, fishes are oxyconformers over some appreciable range of PwO2, and that findings otherwise are likely to be due to methodology or chance.

Respirometry techniques for measuring O2,std and reducing PwO2

Properly determining Pcrit involves three processes: (1) measuring O2,std; (2) reducing PwO2; and (3) calculating Pcrit from the O2 versus PwO2 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 Pcrit calculation methods, and end with our recommended best practices for each step.

Table 1.

Advantages and disadvantages of different respirometry techniques for determining O2,std and Pcrit

Advantages and disadvantages of different respirometry techniques for determining ṀO2,std and Pcrit
Advantages and disadvantages of different respirometry techniques for determining ṀO2,std and Pcrit

CS respirometry

CS respirometry involves placing the fish in a sealed, gas-impermeable respirometry chamber with a PO2 sensor and a well-mixed water volume. The fish's O2 is determined from the rate at which its respiration reduces PwO2 from some starting PwO2 to some lower target PwO2. For measuring O2,std, CS respirometry on its own (i.e. without the serial normoxic O2 measurements made during IF; see below) is problematic, because the investigator has no way of knowing whether the O2 measured in normoxia is O2,std or, more likely, some O2 between O2,std and the O2 that supports maximal metabolic rate, O2,max (i.e. O2,rtn). The uncertainty around this benchmark normoxic O2 state consequently reduces the effectiveness of CS respirometry for determining Pcrit. CS respirometry relies on the fish's respiration to reduce PwO2. The rate of PwO2 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 PwO2 being reduced from normoxia to terminal PwO2 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 Pcrit-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 O2,std significantly – even if a fish consumes all the O2 in the water, the water PCO2 (PwCO2) will not exceed 5 mmHg (0.7 kPa), and studies on a range of species have shown that much higher PwCO2 values [up to 90 mmHg (12 kPa) in one case] have no effect on 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 PwCO2 may elevate Pcrit 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 Pcrit 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 PwO2 often elevate O2 far above 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 O2 values as a function of PwO2 (Fig. 2). Calculating Pcrit from such a data set requires the investigator to apply a set of criteria to isolate the O2 values that best reflect O2,std.

Fig. 2.

Data scatter resulting from the use of closed-system respirometry, which does not account for activity. Example shown is for Etheostoma squamiceps (Ultsch et al., 1978).

Fig. 2.

Data scatter resulting from the use of closed-system respirometry, which does not account for activity. Example shown is for Etheostoma squamiceps (Ultsch et al., 1978).

IF respirometry

IF respirometry involves intermittently flushing the chamber with fresh water between O2 measurements that are taken using CS respirometry. Flushing replenishes the chamber with O2, eliminates the buildup of waste products that might affect O2, and allows for serial O2 measurements within a narrow PwO2 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 O2,std, IF respirometry enables serial normoxic 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 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 O2,std. For reducing PwO2, the investigator reduces the PwO2 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 PwO2 environments to be sustained long enough to outlast the fish's acute behavioral responses. Furthermore, as in normoxia, serial O2 measurements can be made at each hypoxic PwO2, meaning reasonable estimates of O2,std at each moderately hypoxic (i.e. supra-Pcrit) PwO2 are possible. This reduces the scatter of O2 values in the oxyregulation portion of the O2 versus Pcrit curve, and ultimately makes for a more straightforward Pcrit calculation. However, it also requires considerable time, which, when coupled with the time required to equilibrate the PwO2 of the sump and chamber water volumes, results in a relatively long Pcrit 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 Pcrit. Perhaps for this reason or the relative complexity of performing IF respirometry at progressively lower PwO2 values, investigators often use IF respirometry to make normoxic O2,std measurements, then abandon flushing when reducing PwO2 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 PwO2 that is predicted to be above the fish's Pcrit (e.g. 8 kPa), and then CS is used from that PwO2 down to the terminal PwO2 (e.g. Borowiec et al., 2015; Crans et al., 2015).

CF respirometry

CF respirometry (sometimes called flow-through respirometry) involves supplying the fish with a continuous flow of fresh water; O2 is measured as the difference between incurrent and excurrent values of PwO2 multiplied by the water flow rate. For measuring O2,std, the continuous recording of excurrent PwO2 enables a continuous calculation of O2. As with IF respirometry, when a sufficient habituation period (≥24 h) is used and some criteria are applied to these O2 values, the result is an accurate estimate of O2,std (Fig. 3). For reducing PwO2, the investigator reduces sump (or incurrent) PwO2 in a stepwise fashion. This offers similar benefits to IF respirometry – no waste product accumulation and the ability to maintain any PwO2 environment long enough for the fish to reach a stable O2 approaching O2,std. In fact, CF enables the fish's PwO2 environment to be held relatively stable. This is not possible with CS or IF because they require PwO2 of the respirometer water volume to span the median PwO2 for which O2 is measured. This pre-exposes the fish to lower PwO2, which, particularly at PwO2 around the Pcrit, may be problematic. CF respirometry avoids this complication. However, reducing PwO2 with CF respirometry results in a lag period during the washout phase as the next PwO2 equilibrates across the chamber and both inflow and outflow PO2 sensors. The typical flow-through equation cannot be used to calculate 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 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 Pcrit trial using CF respirometry can be run.

Fig. 3.

O2 of a carp (Cyprinus carpio) measured using a continuous flow system. Data are from Ultsch et al. (1980). O2,std values are visually apparent as the lowest O2 values (i.e. between 15 and 20 h) and may be quantitatively isolated using some applied criteria (e.g. lowest 10% of O2 values).

Fig. 3.

O2 of a carp (Cyprinus carpio) measured using a continuous flow system. Data are from Ultsch et al. (1980). O2,std values are visually apparent as the lowest O2 values (i.e. between 15 and 20 h) and may be quantitatively isolated using some applied criteria (e.g. lowest 10% of O2 values).

Calculating Pcrit

There are different methods to calculate Pcrit from the O2 versus PwO2 curve, some of which use more data than others. According to a recent Pcrit meta-analysis (Rogers et al., 2016), the most widely used method of Pcrit calculation is a segmented linear regression technique such as that of Yeager and Ultsch (1989). This method uses all (or most) of the O2 data and assumes the O2 response of fishes to declining PwO2 is approximately biphasic with two distinct linear portions, an oxyregulation line and an oxyconformation line (Fig. 1). The PwO2 at which these lines intersect is the Pcrit. 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 O2 at the lowest PwO2 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 PwO2. 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 O2 to declining PwO2, the result of their oxyregulatory abilities. However, not all species (or individuals) do, and applying this segmented linear regression technique to them may overestimate Pcrit.

There are different ways to calculate Pcrit from a non-biphasic O2 versus PwO2 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 O2 data points from the Pcrit calculation that are thought to be unrepresentative of O2,std, essentially transforming a non-biphasic curve into a biphasic one. The trick here of course is determining which O2 values are kept and which are omitted, as critically assessed by Wood (2018); this is accomplished by applying some criteria to eliminate O2 values that obviously exceed or underestimate 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 Pcrit. Perhaps the simplest method involves anchoring the oxyregulation line at the O2,std value determined in normoxia (i.e. >17 kPa PwO2), and then extending this value leftward, effectively disregarding the O2 values between normoxia and Pcrit (e.g. Snyder et al., 2016). The oxyconformation portion of the curve is then determined by some criteria (e.g. any O2 values >15% below the O2,std line), regressed, and the intersection of this line with the extrapolated O2,std line is the Pcrit. This method is relatively easy to execute and eliminates the influence of O2,rtn values at intermediate PwO2 values such as activity-related O2 elevations as PwO2 approaches Pcrit. However, the influence of such activity-related 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 O2 values at intermediate PwO2 are not used in the Pcrit calculation, the investigator must nevertheless choose a rate of PwO2 decline that is appropriate for the question being addressed and use this rate consistently to control for hypoxia acclimation responses that may affect Pcrit (Regan and Richards, 2017).

This normoxia-anchored O2,std method may be used in a different, more complex way to determine Pcrit. First, O2,max is measured at various PwO2, generating a curve that has a reduced O2,max as PwO2 decreases. Next, O2,std is determined at normoxia and extended leftward until it intersects the linear regression line of O2,max and PwO2. While this method effectively reveals the PwO2 at which aerobic scope reaches zero (a property of Pcrit 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 O2,std alone and is virtually impossible to perform on a single individual without the confounding training effects of repeatedly determining O2,max.

Recommendations

When selecting from the array of available respirometry and calculation methods in order to determine Pcrit, we feel that the most important issue to consider is how the Pcrit 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 Pcrit 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 O2,rtn instead of 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 PwO2 decline as precisely as possible. Or, if the experimental species is a ram ventilator, then it is advisable to conduct Pcrit trials in a swim flume even if this precludes the use of O2,std as the benchmark oxyregulatory O2 state.

Aside from scenarios like these, we feel that there are certain best practices that should be followed when performing respirometry and calculating Pcrit. Foremost, the respirometry experiments should be conducted as carefully as possible. A calculated Pcrit is only as accurate as the O2 data on which it is based, and it is probably true that variation in respirometry experiments explains far more of the inter-study Pcrit variation highlighted by Wood (2018) than variation in Pcrit 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 PO2 sensor drift and background microbial respiration. Importantly, unless the research question requires O2,rtn, the respirometry method should generate data from which accurate estimates of normoxic O2,std can be obtained. This requires either IF or CF respirometry. Depending on the research question, generating O2,std values not just at normoxia but at PwO2 values throughout the O2 versus PwO2 curve is ideal.

For PwO2 reduction, the technique depends largely on the desired rate of hypoxia induction, as these rates may significantly impact Pcrit (Regan and Richards, 2017). High rates are useful for questions involving cross-species comparisons, which would benefit from determining an ‘innate’ Pcrit 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 PwO2 may hamper an accurate Pcrit 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 O2,std at each PwO2.

For Pcrit 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 O2 versus PwO2 data, such as Yeager and Ultsch (1989) and Claireaux and Chabot (2016), are advised over methods that, for example, ignore O2 values at moderately hypoxic PwO2 (i.e. supra-Pcrit) and instead anchor the oxyregulation line at the normoxic O2,std value. This is most effectively done with O2 data that approximate O2,std at moderately hypoxic PwO2. In all cases, accurate measurements of O2,std in normoxia (i.e. ≥17 kPa PwO2) are required. These can be made using methods outlined in Chabot et al. (2016), and they serve as a benchmark for O2 values at moderately hypoxic PwO2. If values approximating O2,std cannot be measured at moderately hypoxic PwO2 for either biological or methodological reasons (i.e. the curve is non-biphasic), then the investigator must decide whether to calculate Pcrit using either a non-linear approach or one that anchors the oxyregulation line at the normoxic O2,std value. In any case, all O2 versus PwO2 data should be presented.

Finally, there are best practices for reporting Pcrit results that maximize their value to the research community. It is imperative that the methods used for respirometry, reducing PwO2, and calculating Pcrit 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 O2 versus PwO2 data will be useable by readers, thus enhancing the comparative value of the Pcrit results. Furthermore, when comparing literature Pcrit values, investigators should analyze these values and the methods used to determine them carefully to ensure the comparison is appropriate.

Conclusions: does Pcrit give useful comparative information on hypoxia tolerance?

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, Pcrit 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 Pcrit, a fish retains zero aerobic scope for activity. While maintenance functions may be fueled aerobically at this PwO2, 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 Pcrit does not realistically represent the lowest PwO2 at which a fish can survive indefinitely. Rather, Pcrit defines the lowest PwO2 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 O2,std, Pcrit 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 Pcrit strongly correlates with the nadir PwO2 of a species' natural environment; Childress and Seibel, 1998; Mandic et al., 2009; Rogers et al., 2016), Pcrit is closely associated with overall hypoxia tolerance. We see no reason to discard this view if appropriate methodology is used to determine Pcrit.

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 PwO2; or (2) the PwO2 at which the fish loses equilibrium under conditions of continually decreasing PwO2. The longer the time or the lower the PwO2, 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. Pcrit, being associated with aerobic metabolism, does not account for these contributions. However, this does not negate the value of Pcrit; it simply means that Pcrit 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 PO2 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 O2 and PO2 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 Pcrit will have the higher RI. Moreover, Pcrit contains some informational value, as it has units, while the RI has none.

In summary, we assert that Pcrit 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 O2,std, which under most circumstances is prerequisite to calculating Pcrit. Once one has reliable O2,std data over a large range of PwO2, the calculation of Pcrit, at least for fishes, is straightforward.

Acknowledgements

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

Footnotes

Funding

M.D.R. was supported by a Natural Sciences and Engineering Research Council of Canada Postdoctoral Fellowship.

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Competing interests

The authors declare no competing or financial interests.