The fallacy of the P_crit – are there more useful alternatives?

This critical Commentary focuses on the concept of the P_crit specifically in water-breathers, and particularly in fish, where the high density and viscosity of the respiratory medium makes the cost of breathing much higher than in air-breathers (Dejours, 1988). The concept originated with the theoretical work of Tang (1933), who examined the relationship between P_O2 and Ṁ_O2 in a variety of whole animals, plants, tissues and cells. He realized that, in most cases, these were best described by hyperbolic relationships with the dependent variable Ṁ_O2 (the rate of O₂ consumption) on the ordinate, and the independent variable P_O2 (the partial pressure of O₂) on the abscissa. He defined P_crit as ‘the tension at which the curve approaches saturation’. This differs from the usage applied today, where P_crit is generally defined as ‘the P_O2 below which the animal can no longer maintain a stable Ṁ_O2, such that Ṁ_O2 becomes dependent upon P_O2’ (Rogers et al., 2016). This usage can probably be traced back to the pioneering investigations of F. E. J. Fry on fish (e.g. Fry, 1947; Fry and Hart, 1948) and the idealized plots that he showed of two intersecting lines for Ṁ_O2 versus P_O2, one with zero slope in a high P_O2 range (region of oxyregulation; see Glossary), and one with positive slope in a lower P_O2 range (region of oxyconformation; see Glossary) (Fig. 1). Fry actually called the P_O2 at the point of intersection ‘the incipient limiting level’ when determined for active (swimming) metabolism, and the ‘level of no excess activity’ (after Lindroth, 1942) when determined for standard metabolism. In various formats, these plots have been featured in many textbooks of comparative physiology (e.g. Prosser, 1973; Hoar, 1983; Schmidt-Nielsen, 1997; Hill et al., 2004), and have been remarkably effective in promoting the P_crit concept, though perhaps not an understanding of the limitations accompanying it.

As any researcher who has worked with real organisms will know, such relationships rarely occur in individual animals, and real data are not neatly ordered into two intersecting lines, one with zero slope and one with positive slope (see Box 1). Despite this, researchers have persevered using a variety of methodological and statistical techniques to determine this single number (P_crit), largely because it is widely believed to provide a reliable index of hypoxia tolerance – i.e. the lower the P_crit, the greater the hypoxia tolerance (but see below). Indeed, a recent excellent review (Rogers et al., 2016) found 331 P_crit measurements for fish alone, and there are probably a comparable number for aquatic invertebrates. I will argue that while the Ṁ_O2 versus P_O2 relationships in these studies are very valuable, the focus on the P_crit is misguided and counter-productive. I will provide six reasons why the P_crit is flawed, and finish by proposing more useful approaches for quantifying hypoxia tolerance and the relationship between Ṁ_O2 and P_O2.

Any scientific method that routinely involves the choice by the experimenter to use some data points and not others is worrisome. The basis of this choice is invariably that the real data do not fit the rigid paradigm of the P_crit – i.e. the animal did not do what it was ‘expected’ to do. In informal conversation, practitioners of P_crit determination will often comment that the data from certain animals had to be discarded, or individual Ṁ_O2 points had to be ignored, because they just didn't fit the model. Admirably, some researchers report this in the methods section of their papers and provide objective criteria or justification for how they edited the data.

For example, Richards et al. (2008), Henriksson et al. (2008) and McBryan et al. (2016) all noted that ‘any fish that struggled was removed from the data set’, while Dhillon et al. (2013) excluded data from fish which ‘showed signs of distress’. McBryan et al. (2016) were also concerned about an increase that often occurred in Ṁ_O2 at declining P_O2 before P_crit was reached in killifish (see panel B in Box 1), which would cause a negative slope to the upper line. They therefore provided criteria for substituting a constant routine Ṁ_O2 value so the upper line would have a zero slope. Snyder et al. (2016), by contrast, studying shiner perch, kept a zero slope to the upper line based on the standard metabolic rate (SMR), but used some but not all of these elevated Ṁ_O2 points at declining P_O2 to define the slope of the lower line, ‘as the elevated Ṁ_O2 was considered part of the physiological response to hypoxia’. As general guidance for P_crit determination, Claireaux and Chabot (2016) advocated ‘removing outlying (low) Ṁ_O2 values, i.e. values that are so low that they are not expected until the animal is below P_crit’. In their example plots, they also excluded many values that may have been above SMR. Ultsch et al. (1981), studying toadfish, stated somewhat enigmatically that Ṁ_O2 values were accepted as estimates of SMR only ‘if they did not differ by more than ±10% of the mean value of the bordering steady state SMRs’. Yeager and Ultsch (1989) noted that their method for calculating P_crit did not work for about 25% of the datasets in the literature. Barnes et al. (2011) excluded from their P_crit analysis the 44% of Atlantic salmon tested that did not meet their criteria for oxyregulation. Regan et al. (2017), studying goldfish ‘excluded from our routine Ṁ_O2 estimation any Ṁ_O2 value that exceeded 1.5 times the standard deviation of an individual's average Ṁ_O2 between 13 and 21 kPa’ for the line at high P_O2, whereas for the line at low P_O2, Regan and Richards (2017) used only ‘Ṁ_O2 values that were >15% below the mean routine Ṁ_O2 value’. McBryan et al. (2016) did the same, but used a threshold of ‘>12% of calculated routine Ṁ_O2’. This is just a small sample for illustration, but sufficient to demonstrate the heterogeneity of approaches used in data editing to calculate P_crit. I conclude that if a calculation protocol ignores a significant fraction of the real data, the resulting value is suspect, because it does not reflect how the animal performed, but rather how the experimenter wanted it to perform.

Setting aside differences in the calculation method and the criteria for data editing, the value of P_crit obtained appears to depend very much on how the experiment has been done. How else can we explain the great variation in P_crit values for the same species reported by different investigators in Table 1, and illustrated for a single subspecies in Fig. 2? There has been much concern about possible differences associated with closed- versus open-system versus intermittent-flow respirometry (see Glossary), especially due to the potential for the build-up of waste (particularly CO₂) in the former. This concern may have been unwarranted, because there is surprisingly little evidence that this really matters. In their meta-analysis, Rogers et al. (2016) found no consistent differences for most species where parallel data were available, and this has been reinforced by nose-to-nose comparative studies (e.g. Cochran and Burnett, 1996; Regan and Richards, 2017), and studies where P_crit was determined at elevated P_CO2 levels (e.g. Heinrich et al., 2014), though exceptions exist (e.g. Snyder et al., 2016). In my opinion, closed-system respirometry, which has been used in the majority (56%) of fish studies to date (Rogers et al., 2016), is preferred simply because it is more ecologically realistic; natural hypoxia almost always involves concomitant CO₂ build-up, as originally noted by Fry and Hart (1948). An additional benefit is that it is much easier than other methods.

A more serious concern is whether the P_crit is determined under standard (SMR) or routine metabolic rate (RMR) conditions, a factor that is often overlooked when comparing P_crit values amongst species. Clearly, it is easier to do the experiment under RMR conditions, explaining why 84% of the fish studies in the literature used RMR (Rogers et al., 2016). Very probably, this involves less data editing, as it is so difficult to define SMR, and maintain SMR conditions. Like the P_crit, SMR is an artificial experimental construct which almost never occurs in nature. Based on the original paradigm of Fry and Hart (1948) and its conceptualization by Claireaux and Chabot (2016), we would expect P_crit to be higher under RMR than SMR conditions and indeed the higher RMR is above SMR, the higher the expected P_crit until Fry's ‘incipient limiting level’ is reached at maximum sustainable aerobic metabolic rate (MMR) (Fig. 1). While considerable evidence suggests that this general trend is true, I am aware of no rigorous comparison of P_crit values determined under normal resting laboratory criteria (i.e. well-acclimated, fasted, undisturbed animals) for RMR versus SMR on the same species. Regardless, in accord with Rogers et al. (2016), I favour the use of RMR for these types of studies as it is likely to be ‘more ecologically relevant – in the field’.

The rate of P_O2 decline is another important but non-standardized factor highlighted by Rogers et al. (2016) that seems to greatly affect P_crit. Snyder et al. (2016) and Regan and Richards (2017) concluded that a slower rate of P_O2 decline resulted in a much lower P_crit in shiner perch and goldfish, respectively, presumably because a longer period allows more time for functional adjustments such as gill remodelling and improvement of the oxygen affinity of the haemoglobin. These can start to occur very rapidly (e.g. Tetens and Christensen, 1987; Matey et al., 2011), certainly within the time frame (minutes to a few hours) of a typical P_crit experiment. Alternatively, it may also allow more time for other adjustments such as the down-regulation of total metabolic rate or the up-regulation of anaerobic metabolism, which may explain the oxyconforming results of Blewett et al. (2013) on the killifish in Fig. 2.

The killifish is generally recognized as being very hypoxia tolerant (Burnett et al., 2007). Fig. 2 illustrates for a single subspecies, the northern race (Fundulus heteroclitus macrolepidotus), the heterogeneity of reported Ṁ_O2 versus P_O2 relationships. All tests were done at 18–21°C with well-acclimated, fasting, undisturbed fish of similar size under RMR conditions, though there were differences in salinity (4–20 ppt) and methodology (closed system versus intermittent flow) amongst studies. Routine Ṁ_O2 values at normoxic P_O2 varied by no more than 50%, yet the profiles at lower P_O2 differed greatly (Fig. 2). Indeed P_crit values varied from no P_crit (almost perfect oxyconformation; Blewett et al., 2013) to 8.5 kPa (Richards et al., 2008). The speed of hypoxia induction is undoubtedly an important issue. In the dataset where there was no P_crit, the P_O2 was gradually lowered over 7 h (Blewett et al., 2013), which may have allowed the animals to progressively suppress their metabolic rate and/or increase anaerobic metabolism so as to manifest as oxyconformers. In contrast, much more rapid lowering over 1–3 h resulted in P_crit values ranging from 4 to 8.5 kPa, although within this time frame, these values were not correlated to the measurement period. Interestingly, the two almost identical values (∼5.3 kPa) were obtained using different methods (Borowiec et al., 2015: intermittent flow; McBryan et al., 2016: closed system), but as the salinities were different and only one of the studies used data editing, interpretation is confounded. Nevertheless, such wide unexplained variation among different laboratories in P_crit determination within a single subspecies is troublesome, and lessens trust in the index.

Setting aside the methodological criticisms above, the theoretical basis of the P_crit is questionable. The P_crit assumes a single, quantifiable point (P_O2) at which the transition from oxyregulation to oxyconformation occurs. Yet, biological processes almost always reflect a smooth continuum of change, and it is difficult to see how or why such a complex multi-step process as O₂ consumption should exhibit a single sharp transition point. Certainly, the O₂ dissociation curve (see Glossary) of the blood does not have one (Dejours, 1988). Indeed, even the originators of the concept recognized that the real dependence of Ṁ_O2 on environmental P_O2 was closer to hyperbolic (Tang, 1933; Fry, 1947), and this is accepted by some modern workers in the field (e.g. Mueller and Seymour, 2011; Marshall et al., 2013; Claireaux and Chabot, 2016). However, even a hyperbolic relationship may not always be true, and there are a range of non-linear functions (e.g. Mueller and Seymour, 2011; Marshall et al., 2013) that may better fit the data in individual instances (Box 1; see also the next section and ‘Concluding remarks’, below).

Furthermore, Fry (1947) noted that the greatest respiratory dependence (i.e. the clearest transition from oxyregulation to oxyconformation) is seen not in resting animals but in animals respiring at their MMR. Indeed, Fry (1947) advocated measuring SMR separately, and then defining the relationship between MMR and P_O2. The hypothetical intersection of a horizontal SMR line with the MMR versus P_O2 relationship would give his ‘level of no excess activity’ or P_crit (Fig. 1). This is close to the approach advocated by Claireaux and Chabot (2016), but differs greatly from most current approaches, which attempt to actually determine P_crit directly by progressively lowering P_O2 for animals respiring at their SMR or RMR, and then applying one of the many available calculation techniques (e.g. Marshall et al., 2013) to best estimate the transition point as P_crit. Regardless, none of these approaches provide a theoretical justification for a sharp transition point. I conclude that in the absence of such a theoretical framework, it is difficult to see any real benefit in trying to determine P_crit.

The often-stated assumption is that, above the P_crit, the animal is able to meet all its needs for SMR or RMR aerobically (region of oxyregulation), whereas below P_crit, aerobic metabolism is reduced and an increasing amount of anaerobic metabolism is needed (region of oxyconformation). This is not true. Some contribution of anaerobic metabolism occurs even at high environmental P_O2 – otherwise, animals would not normally have lactate in their blood and tissues when respiring under normoxia (e.g. Nonnotte et al., 1993; Maxime et al., 2000; Routley et al., 2002). More importantly, when organisms at RMR or SMR are subjected to progressively declining P_O2, the animal makes adjustments to improve the conditions for O₂ uptake long before the region of oxyconformation is reached. These include changes in the pattern of cardiac output (bradycardia, increased stroke volume), changes in effective gill permeability [lamellar recruitment, thinning of the diffusion barrier, blood shunting (see Glossary) in the gills], changes in arterial–venous O₂ content difference and, most importantly, increases in ventilation (discussed by Perry et al., 2009). This was first noted by van Dam (1938), and there are many reports in the literature of ventilation increasing long before the apparent P_crit is reached during declining P_O2 treatments. Particularly clear examples are summarized in review papers – see, for example, fig. 2 of McMahon (1988) (crabs) and fig. 5.3 of Perry et al. (2009) (teleost fish).

While all of these adjustments carry metabolic cost, the greatest is undoubtedly the expense of increased breathing. Estimates of the cost of breathing such a dense, viscous medium as water range greatly (0.2–70% of metabolic rate; McMahon, 1988), but 10–20% is probably a reasonable value (Schumann and Piiper, 1966; Cameron and Cech, 1970; Edwards, 1971; Jones and Schwarzfeld, 1974; Steffensen, 1985; Farrell and Steffensen, 1987), and this ventilatory cost will increase in absolute terms as ventilatory frequency and ventilatory stroke volume increase. Therefore, as P_O2 declines, an increasing percentage of total Ṁ_O2 is consumed by increased breathing and other physiological adjustments, so less and less is available for the maintenance needs of SMR or RMR, which must now be either fuelled by anaerobic metabolism or reduced by a depression of true metabolic rate. Both are likely to occur, long before apparent P_crit is reached. While absolute Ṁ_O2 may be maintained down to the apparent P_crit, the needs of SMR or RMR are not. Indeed, the apparent P_crit often occurs around the P_O2 at which the animal abandons hyperventilation (Perry et al., 2009), probably because it is so expensive. As McMahon (1988) notes: ‘all of the additional O₂ acquired is used to fuel the pumps, with no net gain to the organism’.

The study of Maxime et al. (2000), who subjected turbot to a progressive decline of P_O2 down to 2.7 kPa over about 300 min, is particularly informative. The apparent P_crit under SMR conditions was about 4 kPa. However, ventilatory frequency and stroke volume, and plasma and muscle lactate concentrations had all increased significantly by the time a P_O2 of 8 kPa was reached, and upon restoration of normoxia, the O₂ debt repaid over the next 360 min was 16-fold greater than the O₂ deficit exhibited in the 100 min period during which P_O2 declined from 4 kPa to 2.7 kPa. Clearly, a massive anaerobic contribution had occurred prior to the point of apparent P_crit.

The earlier quotation from McMahon (1988) captures an important issue that P_crit practitioners wish would not happen: ‘additional O₂’ is often taken up as the animal hyperventilates, so even a hyperbolic relationship may not apply for the Ṁ_O2 versus P_O2 plot. Instead, Ṁ_O2 actually increases as P_O2 falls (see panel B in Box 1), due mainly to the increased costs of this hyperventilation (though excitement may also contribute) and the slope of the upper ‘oxyregulation’ line becomes negative and often bumpy. This was first reported by van Dam (1938). The phenomenon is especially evident when the experimenter is attempting to measure P_crit under SMR conditions. The classic work by Beamish (1964; one of Fry's students) is an excellent example, and indeed this pattern had been anticipated by Fry (1947) himself. Beamish (1964) used a warm-bulb flowmeter to measure spontaneous activity, and estimated the Ṁ_O2 at SMR by extrapolation to zero activity. Using brook trout, carp and goldfish, he found that this Ṁ_O2 increased by 20–80% as P_O2 declined, and only below a much lower P_O2 did Ṁ_O2 finally decline in the region of oxyconformation. He attributed the increase to the cost of hyperventilation. Ott et al. (1980) reported similar phenomena in rainbow trout. In summary, I conclude that a simple P_crit value disguises all of this physiological complexity, and therefore it is misleading.

The reason why P_crit has been so often measured is because it is widely believed to provide a reliable indicator of hypoxia tolerance – the lower the P_crit, the greater the hypoxia tolerance (e.g. Mandic et al., 2009). It probably does not. Some of the most hypoxia-tolerant fish, capable of resisting severe hypoxia for prolonged periods, have unremarkable P_crit values, which often vary considerably among reports (Table 1). Examples of organisms where apparent P_crit values appear to overlap those of hypoxia-sensitive species include killifish, Amazon oscar, tambaqui, oyster toadfish and epaulette shark (Table 1). In many cases, the strategy for survival in hypoxia of these animals is not the ability to maintain Ṁ_O2 but rather the ability to suppress metabolic rate (Nilsson and Renshaw, 2004): in the words of Kjell Johansen: ‘turning down the pilot light’ (Hochachka and Somero, 2002).

The P_crit value would be expected to work best as a measure of hypoxia tolerance within a single species studied by the same investigators, but the evidence is problematical. Sometimes it works (e.g. McBryan et al., 2016), but often it does not. For example, in killifish, significant changes in P_crit caused by acclimation to various hypoxia regimes were generally not accompanied by significant changes in the critical oxygen tension at which the fish lost equilibrium (LOE_crit) (Borowiec et al., 2015). In the sheepshead minnow, acclimation to progressively higher salinities (40–100 ppt) was accompanied by progressive increases in P_crit, but the P_O2 causing lethality did not change (Haney and Nordlie, 1997). Differences in strain and ploidy of trout were accompanied by differences in LOE_crit but not in P_crit (Scott et al., 2014).

The P_crit would also be expected to predict hypoxia tolerance when studied in closely related species within the same lab by the same investigators. However, Dhillon et al. (2013) found no relationship between P_crit and LOE_crit in nine closely related carp species, whether the data were corrected for phylogeny or not. Fu et al. (2014) concluded that LOE_crit was a more reliable indicator than P_crit of hypoxia tolerance in 12 different cyprinids. Mandic et al. (2013) had slightly greater success, showing a significant correlation between P_crit and time to loss of equilibrium (LOE) in constant hypoxia (0.85 kPa) in 11 closely related sculpin species. However, the correlation lost significance when corrected for phylogeny. An additional study by Speers-Roesch et al. (2013) conducted at a fixed percentage (30%) of P_crit for three of these sculpin species also failed to show the correlation. Overall, I conclude that the P_crit value is not a useful indicator of hypoxia tolerance: there are more reliable and easier ways to measure hypoxia tolerance, which are explored below.

There is now an unfortunate tendency to report only P_crit values, and not the whole relationship between Ṁ_O2 and P_O2. P_crit is simply the P_O2 approximating an inflection point, which means very little. Some traditional (e.g. Yeager and Ultsch, 1989) and modern methods (e.g. Claireaux and Chabot, 2016) for P_crit determination simply impose two lines on the data and do not attempt to describe the relationship between Ṁ_O2 and P_O2. As pointed out by Mueller and Seymour (2011), a P_crit value says nothing about the relationship above or below the P_crit. For example, is the slope above the P_crit positive (Box 1, panel D) or negative (Box 1, panel B)? Is the whole relationship hyperbolic (Box 1, panel A), or is it closer to a straight line (Box 1, panel C), or to two straight lines (Fig. 1)? How close or distant from oxyconformation is the whole relationship? Does Ṁ_O2 continue right down to zero P_O2? Indeed, a low apparent P_crit value does not necessarily even indicate a greater ability to regulate Ṁ_O2 in the face of hypoxia, as the Ṁ_O2 above the P_crit may have actually increased before it decreased (Box 1, panel B), or decreased more gradually before it decreased more steeply (Box 1, panel D).

If the goal of the experimenter is to simply measure hypoxia tolerance, a much easier and better way is to measure LOE_crit or time to LOE, because these are straightforward and relatively non-subjective determinations: when the animal can no longer maintain equilibrium, it is ecologically dead, a meaningful endpoint. For both, however, the conditions must be standardized in terms of the criteria for LOE (e.g. first overturn, or failure to right the body position after prodding), rate of P_O2 decline for LOEcrit and absolute P_O2 for time to LOE. To date, however, this has not been done, with each investigator tending to use their own species-specific protocols, so there is a need to develop standardized guidelines for LOE tests.

If the goal is to describe the relationships between Ṁ_O2 and P_O2, then there is nothing the matter with just doing this for different species and treatments, and then comparing specific points and slopes on the Ṁ_O2 versus P_O2 profiles, rather than just focusing in on one number, the apparent P_crit. If the goal is to understand what is really going on, then these profile determinations should be accompanied by other physiological measures that provide mechanistic information. Two very important ones are the quantification of breathing (to assess the role of ventilatory costs) and the measurement of blood or tissue lactate (to assess the onset and extent of increased anaerobic metabolism), both as a function of declining P_O2. A third is to measure the total metabolic rate by direct calorimetry (van Ginneken et al., 1994; Regan et al., 2013), so as to evaluate the extent of metabolic depression, although the technology is not yet widely available. Finally, if the goal is to assess the ability of the animal to regulate Ṁ_O2 from these profiles and express this mathematically, there are two approaches that are much better than P_crit: the regulation index and Michaelis–Menten analysis.

The first was originally conceived by Alexander and McMahon (2004), who called it the ‘regulation value’ (R). It was then further developed on a different mathematical basis and popularized by Mueller and Seymour (2011), who termed it the ‘regulation index’ (RI; Fig. 3), the term which is more widely used today. The approach can be applied to Ṁ_O2 recorded under either standard or routine conditions. Briefly, the RI provides a relative measure of regulatory ability by calculating the area under the Ṁ_O2 versus P_O2 curve that is greater than a linear trend [i.e. the area above the diagonal line of oxyconformation joining the Ṁ_O2 at normoxia (e.g. X Ṁ_O2 at 20.9 kPa) with the origin (0 Ṁ_O2 at 0 kPa)] and then dividing it by the total available area calculated in the same way for perfect oxyregulation (i.e. the area whose upper bound is defined by the horizontal line of perfect regulation). As defined by Mueller and Seymour (2011), this fractional index can vary from 0.0 (perfect oxyconformation) to 1.0 (perfect oxyregulation), but my own interpretation is that there is no reason why the value could not be above 1.0 for organisms in which Ṁ_O2 increases greatly above normoxic values before declining, or less than 0.0 for organisms where Ṁ_O2 falls below the line of perfect oxyconformation; indeed, the original approach of Alexander and McMahon (2004) allowed for this possibility (see their fig. 1, where an R value less than 50% represents an RI value less than 0.0). One valuable feature of the RI is that it captures information embodied in the whole Ṁ_O2 versus P_O2 profile, not just in a single apparent P_crit value. Another benefit is that it is not restricted to any particular model, but can be used with the equation that best fits the data.

While the RI can still be determined from these non-linear regression approaches (e.g. Fig. 3), they provide much more information than the RI, because the derived constants (K_m or P₅₀, Ṁ_O2,max and h) describe the whole relationship mathematically. I would argue that the affinity of the organism for O₂ is much more meaningful than the P_crit, as it integrates the net effect of all the gradually changing processes that occur as the organism encounters declining P_O2. It would, for example, be very instructive to compare this K_m or P₅₀ value with the whole-blood P₅₀ for O₂ among species and experimental treatments. There is additional information content in Ṁ_O2,max, as it predicts what the Ṁ_O2 would be under these conditions if environmental P_O2 availability were not a limiting factor. To illustrate, as activity level increases, and RMR moves upwards towards MMR (Fig. 1), we would expect Ṁ_O2,max to increase. And if at the same time, the O₂ diffusing capacity of the gills were to increase through changes in their effective permeability to O₂ (see the section on the transition from aerobic to anaerobic metabolism, above), we would expect K_m or P₅₀ to decrease. And finally, if there really is ever a need to extract an estimate of the apparent P_crit value, this can be done mathematically using the ‘greatest difference’ method or other approaches if Ṁ_O2,max, K_m or P₅₀, and h are known, as explained by Mueller and Seymour (2011) and Marshall et al. (2013). Use of all of these alternative approaches to the P_crit summarized in this section will help improve our understanding and quantification of hypoxia tolerance in water-breathers.

I thank Anne Cremazy, Marina Giacomin and Tamzin Blewett for very useful discussions, Roger Seymour and an anonymous reviewer for constructive criticism and advice, and Marina Giacomin, Tamzin Blewett, Tara McBryan, Trish Schulte, Brittney Borowiec and Graham Scott for kindly providing data files.