The determination of standard metabolic rate in fishes

Journal of Fish Biology (2016) 88, 81–121

doi:10.1111/jfb.12845, available online at wileyonlinelibrary.com

The determination of standard metabolic rate in fishes

D. Chabot*†, J. F. Steffensen‡ and A. P. Farrell§

*Maurice Lamontagne Institute, Fisheries & Oceans Canada, Mont-Joli, QC, G5H 3Z4,Canada, ‡Department of Biology, Marine Biological Laboratory, University of Copenhagen,

Strandpromenaden 5, DK-3000, Helsingør, Denmark and §Faculty of Land and Food Systems,Department of Zoology, 2357 Main Mall, Vancouver, BC, V6T 1Z4, Canada

This review and data analysis outline how fish biologists should most reliably estimate the minimalamount of oxygen needed by a fish to support its aerobic metabolic rate (termed standard metabolicrate; SMR). By reviewing key literature, it explains the theory, terminology and challenges underlyingSMR measurements in fishes, which are almost always made using respirometry (which measuresoxygen uptake, MO2). Then, the practical difficulties of measuring SMR when activity of the fish is notquantitatively evaluated are comprehensively explored using 85 examples of MO2 data from differentfishes and one crustacean, an analysis that goes well beyond any previous attempt. The main objectivewas to compare eight methods to estimate SMR. The methods were: average of the lowest 10 values(low10) and average of the 10% lowest MO2 values, after removing the five lowest ones as outliers(low10%), mean of the lowest normal distribution (MLND) and quantiles that assign from 10 to 30% ofthe data below SMR (q0⋅1, q0⋅15, q0⋅2, q0⋅25 and q0⋅3). The eight methods yielded significantly differentSMR estimates, as expected. While the differences were small when the variability was low amongstthe MO2 values, they were important (>20%) for several cases. The degree of agreement betweenthe methods was related to the c.v. of the observations that were classified into the lowest normaldistribution, the c.v. MLND (C.V.MLND). When this indicator was low (≤5⋅4), it was advantageous touse the MLND, otherwise, one of the q0⋅2 or q0⋅25 should be used. The second objective was to assess ifthe data recorded during the initial recovery period in the respirometer should be included or excluded,and the recommendation is to exclude them. The final objective was to determine the minimal durationof experiments aiming to estimate SMR. The results show that 12 h is insufficient but 24 h is adequate.A list of basic recommendations for practitioners who use respirometry to measure SMR in fishes isprovided.

© 2016 The Fisheries Society of the British Isles

Key words: minimum metabolic rate; oxygen consumption; quantile; SMR.

INTRODUCTION

Whole-animal metabolic rate (MR) is influenced by a variety of factors such as activitylevel, physiological state, body size, temperature, food intake and anabolism. Indeed,MR can vary upwards of 10 fold in ectothermic animals. Yet, there is a minimum MR(MRmin) for the subsistence of an organism (Hulbert & Else, 2004), which is calledbasal (BMR) or standard MR (SMR). This terminology is discussed below.

†Author to whom correspondence should be addressed. Tel.: +1 418 775 0624; email: [email protected]

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© 2016 The Fisheries Society of the British Isles

82 D . C H A B OT E T A L.

Subsistence living allows for no activity, digestion, growth or production of sexualproducts, but merely supports essential homeostatic activities for cells and wholeorganisms (Brett, 1962; Frappell & Butler, 2004). In mammals, it is estimated that90% of cellular oxygen consumption takes place in the mitochondria (Rolfe & Brown,1997), and this can be further separated into the cost of counteracting mitochondrialproton leak (c. 20%) and ATP production (c. 80%) (Rolfe & Brown, 1997). Theseauthors further estimated that at a whole-animal level, ATP production is used aboutequally for Na+, K+-ATPase activity and protein synthesis (20–25% each), withsignificant contributions for Ca2+-ATPase activity, gluconeogenesis, ureagenesis andactinomyosin-ATPase activity, and c. 6% for all other ATP-consuming processes. Thisis similar in other higher vertebrates (Hulbert & Else, 2004).

If MR is below MRmin, physiological function is in some way impaired and for mostspecies (including fishes), life cannot be sustained for long (Job, 1957; Smit, 1965;Priede, 1985; Claireaux & Chabot, 2016), unless the animal can suppress some ofthese metabolic energy requirements, such as during aestivation or exposure to anoxiaor severe hypoxia (Delaney et al., 1974; Stecyk et al., 2008; Richards, 2010; Seibel,2011). Replacing aerobic metabolism with anaerobic glycolysis is only a temporarysolution because of a less efficient use of fuel and an accumulation of toxic wastes.

The objectives of this study are to review the terminology and methods associatedwith the concept of MRmin. As there is no accepted method in the specific case whenactivity level is unknown during the measurement of MR, the review part of the paper isfollowed by an experimental part that aims at comparing the most often used methodsand make recommendations.

T E R M I N O L O G Y

Because MR has almost always been measured as O2 removal from the water bya fish, MR is actually oxygen uptake (MO2) rather than oxygen consumption by tis-sues. Oxygen uptake is also the most widely used method for mammals, birds andreptiles, and both terrestrial and aquatic invertebrates. The advantages and disadvan-tages of using oxygen uptake instead of direct calorimetry are discussed in Brett &Groves (1979), Cech (1990) and Nelson (2016). Also, MO2 expressed in oxygen unitsrather than energy units is best called respiration rate instead of MR. This review ofthe terminology in the field must, however, by necessity, use the original terms of theliterature cited.

As early as the end of the 18th Century, Séguin & Lavoisier (1789) established thatphysical activity and digestion increased MO2. They also determined that their subjectshad to be exposed to a comfortable temperature, otherwise they would increase theirrate of energy expenditure to cool or warm themselves. They defined the basic condi-tions to measure MR in humans: the subjects must be at rest, fasted and at an ambienttemperature of 26∘ C. MR measured in such conditions became known as BMR.

Krogh (1914, 1916) subsequently reserved the term BMR for the lowest rate of oxy-gen consumption of an organ that is not performing any work. In his view, BMR wasimpossible to measure for a whole organism, because the circulatory and respiratoryfunctions required to maintain an animal alive involved some expenditure of energyabove BMR. Instead, he preferred the term SMR for whole organisms exhibitingminimal functional activity, i.e. in total absence of voluntary muscular movements andwhen no food was being digested or absorbed (Krogh, 1914). SMR was considered

© 2016 The Fisheries Society of the British Isles, Journal of Fish Biology 2016, 88, 81–121

M E A S U R I N G S M R I N F I S H E S 83

to be the ‘nearest attainable approximation’ of basal metabolism, which he arguedwould be attained if all organs were absolutely at rest (Krogh, 1914). Krogh (1914)even attempted to estimate the cost of processes such as circulation and breathing, toevaluate the difference between BMR and SMR. His stringent condition of absolutelyno voluntary activity, however, required immobilizing non-human subjects withcurare or, for fishes, sedation, although in some cases there was no difference in MO2between sedated and quiescent fishes (Ege & Krogh, 1914). This demonstrates thatwhen conditions are right, some species of fish can become essentially motionless in arespirometer, a fact that still influences the design of respirometers and protocols usedto estimate SMR today. It bears repeating that for Krogh (1914), it was theoreticallyimpossible to measure BMR of a live fish. Only SMR measurements were possible, inpart because BMR was more a property of cells rather than animals that rely on organsto perform external work, and SMR required a completely motionless fish.

The possibility of obtaining absolutely quiescent or resting states with undomes-ticated animals, or animals susceptible to excitement from handling or experimentalconfinement, has been questioned frequently. Instead of immobilizing their subjectspharmacologically, other authors adopted the term SMR to mean the lowest MO2commensurate with appropriate experimental techniques but could not ensure thatthere was strictly no contribution from activity (Fry & Hart, 1948; Brett, 1962). In thiscontext, SMR became a practical approximation of BMR, with the possible inclusionof some minimal level of activity, so being different from Krogh’s (1914) SMR thatexcluded all external work.

Whenever subjects show some minor activity in a respirometer (swimming or main-taining station in the case of fishes) many authors prefer the term routine MR (RMR),which includes a minor cost of activity (Winberg, 1960; Brett, 1962; Dall, 1986).This term is necessarily vague because activity is undefined and not quantified, andRMR can be at any level between SMR and the maximum MR (MMR), although goodrespirometer design and protocol should insure that it is closer to SMR than to MMR.When activity is known to be very limited, such as the small fin movements to main-tain position in a respirometer, authors have used terms such as ‘low routine’, ‘resting’or ‘fasting’ MRs as practical approximations of BMR and SMR (MacKinnon, 1973;Howell & Canario, 1987; Blaxter, 1989; Plaut, 2000). Schmidt-Nielsen (1984) alsoobjected to the term BMR but for semantic reasons, because the term implies that MRcannot fall below BMR. In humans, MO2 is lowest during sleep, but BMR is measuredwhen subjects are resting but not asleep. He proposed the term maintenance metabolisminstead of BMR. This is not, however, an improvement as Krogh (1916) had dismissedthis term for semantic reasons of his own: an animal cannot maintain itself on BMR orSMR for any length of time, it will start losing mass to sustain its MR if fasted continu-ously. Jobling (1994) promoted the pragmatic use of ‘minimal’ or ‘fasting’ metabolismbecause of the many different interpretations of SMR.

Tradition is, however, hard to break and BMR and SMR are the recommended termsto represent MRmin, measured in specific conditions, in homeotherms and ectotherms,respectively (McNab, 1997; Frappell & Butler, 2004). A few mammals do not regulatetheir body temperature and their BMR cannot be measured, so their SMR at a giventemperature is measured, just as in ectotherms (McNab, 1997). Both BMR and SMRmeasurements include the cost of the external work of organs such as those involvedin circulation and respiration, but not activity. To reiterate, SMR is the preferredterminology for fishes.



R E L E VA N C E O F S M R I N F I S H E S

The ecological significance of SMR might be thought of as limited, because fishesin the wild are rarely in such states. Exceptions might include periods of food shortageor in environmental extremes such as hypoxia and supra-optimal temperatures, whenthe oxygen delivery system is taxed to the extent that routine activities beyond SMRbecome almost impossible. SMR does, however, have pervasive ecological relevance,with important potential implications for maximum performance, growth rate, lifestyleand social interactions (Clarke, 1991; Metcalfe et al., 1995, 2016; Clarke & Johnston,1999; McCarthy, 2000; Cutts et al., 2002; Millidine et al., 2009; Killen et al., 2010).A valid SMR measurement is needed to determine aerobic scope properly, defined asMMR minus SMR (Fry, 1947, 1971). Aerobic scope and the Fry paradigm, with itsderivative the oxygen and capacity-limited thermal tolerance hypothesis, are usefulframeworks to define limits and optima for temperature tolerance of fishes (Fry, 1971;Claireaux & Lefrançois, 2007; Pörtner & Farrell, 2008; Farrell, 2009; Cucco et al.,2012). Also, an accurate SMR is a prerequisite to measure hypoxia tolerance as O2crit(Claireaux & Chabot, 2016). Furthermore, SMR is an essential input variable for ener-getic models that predict energy portioning and resource allocation (Armstrong et al.,1992; Hansson et al., 1996), even if reliable quantitative information on the energy costof specific activities is sadly lacking, beyond swimming and digestion.

M E A S U R I N G S M R I N F I S H E S

Before addressing the issue of how to measure SMR in fishes, it is useful to con-sider how BMR is measured in homeotherms. The conditions for a BMR measure-ment in human subjects are particularly precise: (1) the individual must be awake andsupine, (2) in a state of complete muscular repose, (3) after a 20–30 min period of rest,(4) fasting for 12–14 h following a last meal at about the maintenance level and thatexcluded caffeine and any subsequent nicotine, (5) isolated from external stimuli in athermoneutral and dark environment, and acclimated to such an environment, (6) freefrom emotional stress and (7) in women, the measurement should not be made imme-diately before or during the menses, or during pregnancy (Harris & Benedict, 1918;Blaxter, 1989; McNab, 1997; Hulbert & Else, 2004; Johnstone et al., 2005).

For other homeotherms, the main conditions are acclimation to the experimentalsetup, fasting, rest (no activity), a thermoneutral environment and regulation of bodyheat (to exclude animals in torpor) (Kleiber, 1975; McNab, 1997). Of course, statesof hibernation, aestivation or torpor add a further but rather specialized layer of com-plexity to defining MRmin, but these states are not considered BMR or SMR. Someauthors restrict the measurement of BMR to adult subjects in a non-reproductive state,to exclude the cost of growth and reproduction (McNab, 1997). The requirement ofusing only non-reproducing adult subjects is mandatory when dealing with interspe-cific comparisons of BMR, in particular the effect of body size on BMR.

The conditions to measure SMR in ectotherms are similar to those for BMR in mam-mals and birds, and are designed to produce low values of MO2. In the case of fishes,SMR at a given temperature is typically measured in post-absorptive (but not starv-ing), inactive individuals, except for minimal fin movements to remain stationary inthe water column for fishes that do not rest on the bottom, after acclimation to theexperimental temperature and setup, and during the inactive part of the fish’s circadiancycle (Fry & Hart, 1948; Brett, 1962). Nonetheless, there are many possible variationsin procedures and analytical techniques.



In this regard, it is important to recognize the advances that have been providedby developments in respirometer design and in technologies to measure dissolvedoxygen (DO). Prior to around 1970, DO was almost always measured by Winklertitration (Winkler, 1888; American Public Health Association American Water WorksAssociation & Water Environment Federation, 1999), an extremely accurate buttime-consuming method that does not yield instantaneous results. Practically, and atbest, only one MO2 measurement was possible every 30–60 min (Keys, 1930; Wells,1932; Fry & Hart, 1948). Consequently, these measurements integrated MO2 over along time period, increasing the risk of activity but decreasing the risk of obtaining avalue of MO2 below SMR. The lowest value of MO2, obtained during the time of daywhen the species was known to be less active, was as close to SMR as could be hopedfor (Fry & Hart, 1948).

Since the 1970s, DO has been measured mostly with electrodes (Clark, 1956; Gattiet al., 2002), and more recently with optodes (Holst & Grunwald, 2001; Glazer et al.,2004; Tengberg et al., 2006). Both offer short time lags in detecting changes in DO andimmediate results. Along with the advent of intermittent-flow and open-flow respirom-eters (Muir & Niimi, 1972; Duthie, 1982; Bushnell et al., 1984; Steffensen, 1989;Svendsen et al., 2016) and data storage on computers, more frequent MO2 measure-ments became the norm, along with real-time analysis and display with commercialsoftware, such as AutoResp (Loligo Systems; www.loligosystems.com) or open-sourcesoftware such as AquaResp (www.aquaresp.com/oxygen). Moreover, a shorter mea-surement period (5–20 min) might allow comparison with prevailing fish behaviour,potentially monitored with video (Crocker & Cech, 1997). The effect of activity anddaily cycles on MO2 are not precluded, therefore, just better managed and accountedfor. The shorter time frame unfortunately introduces a new concern. An individual’soxygen uptake is the sum of many demands made at tissue and organ level (Darveauet al., 2002). The instantaneous oxygen consumption of organs such as the heart andgills would reflect each contraction (Priede, 1985). Brief periods of anaerobic activ-ity can temporarily suspend oxygen consumption by some tissues or organ, followedby greater oxygen consumption during recovery. The lag between oxygen pickup atthe gills and its utilization in tissues buffers some of these short variations of oxy-gen consumption at the individual level, but an integration time of c. 30 min betterreflects steady-state in whole-animal oxygen uptake (Priede, 1985). Therefore, withthe short measurement periods that are now common, consecutive MO2 measurementsare unlikely to be strictly constant even when a fish is in a state corresponding to SMR.Instead, some variation about an average value corresponding to SMR is expected. Itcannot be assumed, therefore, that the single (or several) lowest MO2 values are esti-mates of SMR. Instead, the values associated with SMR should be observed repeatablyand represent a reasonable proportion of the MO2 values, unless the experiment is veryunsuccessful at getting fishes to become inactive in the respirometer. The key questionthen becomes, what is a reasonable proportion? This question is addressed below, byanalysing data from fish respirometry experiments, much of which is new.

Adequate respirometer designAny determination of MO2 requires an appropriate respirometer design, an issue

thoroughly considered elsewhere (Steffensen, 1989; Svendsen et al., 2016). A few keypoints are offered here. Estimating SMR requires numerous determinations of MO2to accommodate acclimation, daily MO2 cycles and variable activity patterns. Thus,



intermittent-flow respirometry or continuous-flow (but suitably corrected for wash-out)respirometry is required. Respirometer volume should be sufficient to avoid stress, butsmall enough to minimize unwanted activity and ensure that variations in oxygen levelsin the system occur and can be accurately quantified within a reasonable time period.It is essential to take precautions to ensure that fishes calm down inside the respirom-eter (Clausen, 1936; Cech, 1990), such as controlling water quality (e.g. DO, pH andammonia), temperature, light, noise and vibration levels.

A species’ natural habitat and behaviours should be considered too because unfamil-iarity can increase MO2. The common sole Solea solea (L. 1758) has a lower MO2when there is substrate in the respirometer; sand was needed to properly estimate SMR(Howell & Canario, 1987). This may be true of other burrowing species such as sandlances (Ammodytidae) (J. F. Steffensen, unpubl. data). Some species require access toa shelter within the respirometer to exhibit their lowest MO2, such as juvenile salmonSalmo salar L. 1758 (Millidine et al., 2006). Similarly, some gregarious species suchas Atlantic menhaden Brevoortia tyrannus (Latrobe 1802) may become hyperactive,stressed and even die when tested alone (Hettler, 1976) such that testing in groups isnecessary. Some researchers recommend the use of ‘conditioned water’, or water thatpreviously contained fishes (Winberg, 1960) or water from the tank where the fish waspreviously held (Fry, 1971), but it has never been shown that these measures lowerMO2 when respirometer design is appropriate and fishes are properly acclimated toexperimental conditions.

Duration of experimentsPerhaps, the greatest initial challenge of measuring SMR is that handling stress and

excitement may elevate MO2 considerably (Smit, 1965; Fry, 1971). Minimally, severalhours are needed to recover from the stress of being moved to the respirometer, andideally several days are needed to then identify any diurnal patterns. The repaymentof an oxygen debt, such as incurred by chasing the fishes or when fishes struggle asthey are placed into a respirometer, elevates MO2 (Keys, 1930). Therefore, MO2 usu-ally remains elevated for several hours once fishes are in a respirometer (Keys, 1930;Steffensen et al., 1994; Herrmann & Enders, 2000; Cheng & Farrell, 2007) and SMRcannot be determined during this period. This period can be shortened by reducinginitial stress, such as by coaxing the fish into a plastic bag with a minimum of chas-ing to transfer it into the respirometer (McKenzie et al., 2007; Dupont-Prinet et al.,2013b), because chasing and air exposure are stressful to fishes (Zahl et al., 2010).Without such precautions, the duration of this period can be 24 h or more (Wells, 1932;Sundnes, 1957a, b). There is no accepted minimum duration for the acclimation period,however, because of species differences. The best solution probably lies in measuringMO2 over a few days and inspecting data to demonstrate that each fish (or minimally asub-sample of fishes, or a pilot experiment; Jobling & Spencer Davies, 1980) regularlyachieve a low and relatively constant MO2 compared with the elevated initial MO2.Minimally, fishes are typically placed in respirometers for 10–48 h before starting tomeasure MO2 to minimize handling stress (Clausen, 1936; Fry & Hart, 1948; Clarket al., 2013). This is often the best solution when experiments are conducted in thefield and there are other constraints on holding the fishes.

Similarly, there is no accepted minimum duration of experiments aiming to deter-mine SMR in fishes. Some species have a circadian cycle of MO2 (Clausen, 1936; Fry,1947; Fry & Hart, 1948; Mehner & Wieser, 1994; Svendsen et al., 2014). While many



species are day-active, some are active during the night, including the Pacific hagfishEptatretus stoutii (Lockington 1878) (Cox et al., 2011) and juvenile Greenland halibutReinhardtius hippoglossoides (Walbaum 1792). Unless a diurnal cycle can be ruled outby prior knowledge or pilot experiments, MO2 should be measured regularly over atleast 24 h (Cech, 1990), preferably 48 h, after the fish is acclimated to the respirom-eter. If shorter experiments are desired, it must be demonstrated that they are timedso that the quiescent part of the cycle occurs after fishes are acclimated (MacKinnon,1973).

The duration of the fasting period, which usually precedes placement in the respirom-eter, has to be sufficient to ensure that fishes are in a post-absorptive state. Strictlyspeaking, this requires knowledge of gut evacuation time. This can be determinedexperimentally or from the literature before the start of respirometry experiments.Ammonia excretion can also be used to verify that a fish is in a post-absorptive state(Brett & Zala, 1975). In general, digestion time decreases with increasing temper-ature (Andersen, 1999) and increases with ration and prey quality (energy density)(Andersen, 1998; Andersen & Beyer, 2005; Fu et al., 2005a, b). Digestion proceedsmore slowly in hypoxia (Jordan & Steffensen, 2007; Zhang et al., 2010). A very largesingle meal (>10% body mass), especially at a cold temperature or low DO level, canincrease MO2 for >5 days (Jordan & Steffensen, 2007; Dupont-Prinet et al., 2013b;Eliason & Farrell, 2014), and even 16 days at −0⋅5∘ C (Secor, 2009). Fishes fed on aregular basis may require even a longer fasting period because repeated meals increaseMO2 more than a single meal (Soofiani & Hawkins, 1982; Fu et al., 2005c), althoughgut evacuation time after the last meal does not always increase (Fu et al., 2005c).For some species, prolonged fasting progressively lowers SMR (Mehner & Wieser,1994; Fu et al., 2005d; Van Leeuwen et al., 2012; McKenzie et al., 2014). Thus, aprogressive decrease in MO2 over days could be related to factors ranging from apostprandial decline, through to habituation and recovery from handling stress, and atransition to a starvation-related suppression of MR if fasting is too long. The durationof the fasting period should be explained and justified when reporting SMR of fishes.When it is impossible to fast the fishes (e.g. fishes captured from the wild for limitedobservations), RMR should be reported.

Test temperature must be controlled and reported because of the strong influence oftemperature on SMR of ectotherms (Fry, 1971; Hulbert & Else, 2004). The necessityto work with thermally acclimated fishes has been emphasized (Fry, 1947; Winberg,1960; Brett, 1962; Beamish, 1964a). While SMR will vary exponentially with an acutetemperature change, often with a quotient of around 2 for every 10∘ C difference, ther-mal acclimation tends to shift MR back towards that of the previous temperature. Thus,in a thermally acclimated fish, the quotient for a 10∘ C difference will be lower, between1 and 2, than the quotient measured following an acute temperature change. Thermalacclimation can require days to weeks, depending on the extent and direction of thetemperature change (Wells, 1935; Barrionuevo, 1998). This consideration is particu-larly important in aerobic scope. For example, the shape of the relationship betweenaerobic scope and temperature differed between killifish Fundulus heteroclitus (L.1766) acclimated to each temperature or acutely exposed to that temperature (Healy &Schulte, 2012). Similarly, the shape of the aerobic scope curve with an acute tempera-ture change varied when goldfish Carassius auratus (L. 1758) were tested at differentacclimation temperatures (Ferreira et al., 2014). When considering adaptability or sus-ceptibility to a slow temperature change, such as global warming, aerobic scope needs



to be measured in thermally acclimated fishes (Clark et al., 2013). This is not to saythat measurements of MO2 in fishes subjected to acute temperature changes (Lee et al.,2003a; Sokolova & Pörtner, 2003; Zakhartsev et al., 2003; Clark et al., 2008, 2011;Steinhausen et al., 2008; Eliason et al., 2011) are not of interest. For example, they helpunderstand how the circulatory and respiratory functions of fishes cope when movingthrough thermally stratified water. A prerequisite to a proper SMR measurement, how-ever, is thermal acclimation and the duration of thermal acclimation should be reportedwith SMR.

Body mass and life stageSMR is influenced by body mass, with large fishes using more oxygen per unit

time, but less oxygen per unit mass per unit time. Within a species (an ontogeniceffect), SMR is linearly related to body mass after logarithmic transformation of bothvariables (Sundnes, 1957a; Winberg, 1960; Beamish, 1964a; Beamish & Mookherjii,1964; MacKinnon, 1973; Duthie, 1982; Ishibashi et al., 2005), but the relationship candiffer for larval and post-larval states (Oikawa et al., 1991; Yagi et al., 2010). There-fore, comparisons of SMR should acknowledge the need to treat mass as a covariateor scale SMR for a standardized mass (Newell et al., 1977; Schurmann & Steffensen,1997). This scaling is only possible for individuals of the same life stage but with dif-ferent masses, as the scaling exponent may change for different life stages (Post & Lee,1996; Killen et al., 2007a, b).

Even though SMR does not include growth-related expenditures, it can be arguedthat it can be measured in fast-growing juvenile fishes, as long as the usual conditionsto measure SMR are met, including an appropriate fasting period. Most fishes haveindeterminate growth and, strictly speaking, it would be difficult to meet a no growthrequirement even in adult fishes. The required post-absorptive state should ensure thatlittle growth occurs during the determination of SMR. A recent study, however, hasshown that the nutritional plane or prevailing nutritional context (long-term food avail-ability) can influence SMR of juvenile fishes, with better-fed fish having a greater SMRthan poorly fed fish (Van Leeuwen et al., 2012), even though SMR was determined afteran appropriate fasting period. Similarly, fishes that were food deprived and then givenad libitum access to food often go through a phase of growth compensation. This hasbeen shown to alter SMR in the common minnow Phoxinus phoxinus (L. 1758) (Killen,2014). Ideally, juvenile fishes should be on a maintenance ration for a few weeks priorto SMR determination (Rosenfeld et al., 2015), but at minimum, feeding conditionsduring the last few weeks leading to the SMR test should be reported. Larval fishes ofmany species are always active and fast growing and cannot be fasted for long periods.It is preferable to report RMR (Bochdansky & Leggett, 2001; Moran & Wells, 2007;Peck & Moyano, 2016).

Adult fishes are characterized by reproductive phases and invest energy into gonadmaturation and gamete production, which by necessity increases MO2 (Wells, 1935;Brett, 1962; Beamish, 1964b). These energy investments can continue during fast-ing because migratory Pacific salmon (Oncorhynchus spp.) cease eating for at least amonth before spawning and yet their gonads continue to grow (Farrell, 2009). Similarly,female Atlantic cod Gadus morhua L. 1758 cease feeding c. 1 month prior to the startof spawning (Fordham & Trippel, 1999). Thus, measuring SMR is impossible in areproductively developing or spawning fish. Instead, RMR must be reported and used



to estimate aerobic scope and, for example, the net cost of transport (Lee et al., 2003a,b; Steinhausen et al., 2008; Eliason et al., 2011, 2013).

Thus, body mass, ontogenic state (if not obvious from body mass), feeding regimeand, for adults, reproductive status of the fishes and season or date should be providedwhen reporting SMR or RMR.

Locomotor activityDealing with spontaneous activity is almost an intractable challenge when measuring

SMR. The problem is two-fold. First, the potential error due to spontaneous activity isvery large because locomotion can increase MO2 up to three to five-fold in most fishspecies, and up to nine-fold in tunas (Thunnini) (Brill & Bushnell, 1991). Second, inac-tivity is not a natural state except for lethargic species and ambush predators, althoughpossibly the latter are spending more energy for muscle tone to be ready to pounce.Some researchers have used sedation (Ege & Krogh, 1914; McFarland, 1960; Piiper& Schuman, 1967; Edwards et al., 1972; Brill, 1987; Houlihan et al., 1995; Hove &Moss, 1997; Leonard et al., 1999; Dowd et al., 2006). Sedation, however, can inter-fere with functions that are now considered part of SMR (e.g. ventilation) and fishescan accumulate an oxygen debt while under sedation (Keys & Wells, 1930; Spoor,1946). Another approach is spinal blockade and artificial ventilation to immobilizea fish (Bushnell et al., 1990; Bushnell & Brill, 1992). Sedation and immobilizationshould be considered a last recourse because of the potential to underestimate SMR.

D E T E R M I N I N G S M R W H E N AC T I V I T Y L E V E L I S M E A S U R E D

It is possible to statistically remove the effect of controlled and spontaneous locomo-tion on MO2. In the first case, different steady-state speeds in a swimming respirom-eter (an aquatic treadmill) create a relationship between MO2 and swimming speedthat can be extrapolated to zero speed, which is assumed to be SMR (Brett, 1964;Brett & Groves, 1979). Indeed, when SMR has been measured in a conventional staticrespirometer and by extrapolation to zero speed, the two measurements can agree(Schurmann & Steffensen, 1997; Roche et al., 2013), although not always (Duthie,1982; Roche et al., 2013). Concerns include the need to prevent spontaneous locomo-tor activity at slow, sustained speeds when it is easily accommodated within the fish’saerobic scope (Brett, 1964; Smit, 1965; Fry, 1971; Bushnell et al., 1994; Reidy et al.,2000). This problem can be reduced by training (acclimation to the experimental setupand to different swimming speeds). Further, anaerobic metabolism increasingly fuelslocomotion at intermediate and high speeds (Puckett & Dill, 1984; Lee et al., 2003b;Svendsen et al., 2010), and this cost should be added before calculating the relation-ship between MO2 and swimming speed. Also, this extrapolation method implicitlyassumes that sustained swimming only translates to an increased MO2, but routine gutblood flow progressively decreases below the normal allocation of 30–40% of the car-diac output with increased swimming speed in some fasted fishes (Thorarensen et al.,1993; Farrell et al., 2001). Thus, MO2 need not necessarily increase appreciably in theearly stages of swimming (Thorarensen & Farrell, 2006) and may underestimate thetrue cost at the highest swimming speeds (Lee et al., 2003b; Farrell, 2007). Other con-siderations include fishes that normally orient into water currents (e.g. salmonids), thatcontinuously swim to assist gill ventilation (e.g. ram ventilation in sharks), or transi-tion to ram ventilation. A gentle water current that does not induce swimming has been



used with great success to minimize spontaneous activity in salmonids using swimmingrespirometers (Farrell et al., 2003). All of these considerations influence the slope andintercept of the relationship between MO2 and swimming velocity, as does the choice ofthe correct mathematical function relating MO2 to swimming speed (Korsmeyer et al.,2002; Roche et al., 2013). Lastly, swimming respirometry systems are more complexand costly than static respirometers, and some species refuse to swim in swimmingrespirometers (Kolok & Farrell, 1994; Roche et al., 2013).

With a static respirometer (no strong, directed water flow) that is large enough toallow spontaneous movement, it is possibly to improve SMR measurement by visu-ally selecting periods when the fish is inactive (Armstrong et al., 1992), perhaps aidedby video observation (Crocker & Cech, 1997). Others have regressed MO2 against anindex of activity level, with SMR corresponding to the extrapolation to zero activity(Spoor, 1946; Beamish, 1964a; Torres & Childress, 1983; Lucas & Priede, 1992; Carl-son et al., 1999; Zimmermann & Kunzmann, 2001; Tudorache et al., 2009). Such asystem is usually less costly than a swimming respirometer. The challenge is the largerange of MO2 values observed with zero spontaneous activity (Zimmermann & Kun-zmann, 2001) as well as high variability around the regression line (Tudorache et al.,2009), probably because of measurement error resulting from the greater water volumerelative to fish mass in respirometers where fishes can move spontaneously (Svend-sen et al., 2016), the imprecision of quantifying activity and the cost of excitement inabsence of activity (Winberg, 1960; Brett, 1962; Smit, 1965; Puckett & Dill, 1984;Millidine et al., 2006). This variability adds to the inherent variability of SMR.

D E T E R M I N I N G S M R W H E N T H E R E I S N O I N F O R M AT I O NO N AC T I V I T Y

Most measurements of MO2 in fishes have not concurrently measured activity. Inthis case, species knowledge may help identify when it is normally quiescent (Fry &Hart, 1948; Dall, 1986; Crear & Forteath, 2000; Ferry-Graham & Gibb, 2001; Fu et al.,2005d). Alternatively and perhaps with less subjectivity, the frequency distribution ofthe MO2 values and their distribution in time are very valuable sources of informationto identify SMR. There is no universally accepted method, however, among these threepreviously used approaches (Nelson & Chabot, 2011), i.e. taking the average of a vari-able number of the lowest values of MO2, taking a variable quantile from the values ofMO2, and assigning MO2 values to a mixture of normal distributions.

By using the lowest values of MO2, the first approach assumes that they correspondto periods of inactivity or a minimal level of spontaneous activity. The concern here isunderestimating SMR with a small number of the lowest MO2 values measured overa short interval because of the temporal variability in SMR and measurement errorassociated with short-term measurements of MO2, and the expectation that MO2 valuesobserved when fishes are at SMR should be approximately normally distributed. Thisis one, but not the only, explanation for SMR estimated by extrapolation to zero spon-taneous activity being larger than the lowest MO2 values (Zimmermann & Kunzmann,2001). Another explanation is that the fishes in these examples may have been nervousor stressed during some of the MO2 measurements made at zero activity, and the twoexplanations are not mutually exclusive. The risk of underestimating SMR decreases,of course, as the number of MO2 values used to estimate SMR increases. This num-ber is highly variable among studies, e.g. one (Wieser & Medgyesy, 1991), three



(Crear & Forteath, 2000; McKenzie, 2001; Roche et al., 2013), five (Lefevre et al.,2012), six (Cruz-Neto & Steffensen, 1997; Schurmann & Steffensen, 1997) or 10(Norin & Malte, 2011; Boldsen et al., 2013; Svendsen et al., 2014). Recognizing thepotential for aberrant low MO2 values, others have used 10% of the values (Herrmann& Enders, 2000; Rosewarne et al., 2014), or all MO2 values obtained during the quietpart of the daily cycle (Castanheira et al., 2011), or after a specific time since thebeginning of the experiment (Cutts et al., 2002). Other variants integrate more databy averaging two quiescent periods (Cheng & Farrell, 2007), or averaging continuousreadings into block means and taking the mean value of a given number of thelowest block means (Eliason et al., 2007, 2008). In some cases, outliers have beensubjectively (Herrmann & Enders, 2000; Boldsen et al., 2013) or statistically (>2 s.d.from the average of the low values, Boldsen et al., 2013) removed. The main problemswith selecting the lowest MO2 values are determining the number of values to be usedand the fact that the lowest values of MO2 are assumed to represent SMR, whereasan assumption of this paper is that values of MO2 should be approximately normallydistributed and the lowest values may be far from the mean.

The second approach to estimate SMR when activity is not measured assumes thatwhen the animal is in the state corresponding to SMR, MO2 values vary around thereal SMR, as explained above, with half of them below and half above SMR. TheseMO2 values are interspersed with other MO2 values that lie variably above SMR dueto spontaneous activity. This assumption fits the concept of a quantile, which splits adata set into the p smallest and the 1− p largest values, where p is a proportion chosenby the experimenter. Van den Thillart et al. (1994) used p values of 0⋅05 and 0⋅1 toestimate SMR in S. solea. There was very little difference between these two valuesand they adopted 0⋅05. Dorcas et al. (2004) used a p of 0⋅25 to estimate SMR of theeastern diamondback rattlesnake Crotalus adamanteus. Others have used intermediatevalues (p= 0⋅1: Daoud et al., 2007; p= 0⋅15: Dupont-Prinet et al., 2013a, b). This thenleads to the quandary of choosing the correct p. Van den Thillart et al. (1994) suggesteda graphical method, i.e. finding a steep gradient of the cumulative frequency distribu-tion, but such a steep gradient is not always present. Instead, the analysis of data thatfollows compares different p values for the same fish as well as across fish species andtemperatures.

The third approach acknowledges that the frequency distribution of a large set ofMO2 values measured over a long period is often bimodal (or multimodal). Steffensenet al. (1994) fitted two normal distributions to MO2 data for Greenland cod Gadusogac Richardson 1836. One distribution accounted for the elevated MO2 values asso-ciated with the acclimation period and spontaneous activity, while the other distributionaccounted for the low values of MO2 obtained after the fish settled down. The mean ofthis lowest normal distribution (MLND) was proposed as a robust estimate of SMR.This method has a strong theoretical appeal because of the assumption that SMR mea-sured for short time periods shows temporal variability around an average whenever thefish is calm, immobile and post-absorptive. Variability around SMR is then the sum ofmeasurement error and biological variability, which are unknown but should be smallwith a well-designed respirometry system. This statistical approach has been adoptedin many recent studies of fish SMR (Behrens & Steffensen, 2007; Jordan & Steffensen,2007; Dupont-Prinet et al., 2010; Skov et al., 2011; Svendsen et al., 2011; Frisk et al.,2012; Roche et al., 2013; Rosewarne et al., 2014).



A possible drawback of the MLND method, especially for excitable species, is thatbouts of low levels of excitement or activity could inflate many of the MO2 values.There may be too much overlap between the distribution of MO2 values correspondingto SMR conditions and those corresponding to low levels of activity or excitement,resulting in a combined distribution that will overestimate SMR. This problem maynot be noticeable by observing fish behaviour, because excitement can increase MO2without observable movements (Winberg, 1960; Puckett & Dill, 1984; Millidine et al.,2006). Examples of this problem are shown below.

O B J E C T I V E S

Without clear support for any single method to estimate SMR when animal activityis not measured, these three approaches are compared for the first time using examplesfrom many species of fishes and one crustacean, with the aim of identifying the morerobust method or methods. Because animals are stressed and often agitated imme-diately after being introduced into the respirometer, these observations are removedbefore calculating SMR (Herrmann & Enders, 2000). A second objective is to assess ifthis step is necessary or if at least some of the methods yield the same SMR estimateswhen data from the acclimation period are retained in the calculation of SMR, as inSteffensen et al. (1994). SMR measurements should minimally last 24 h beyond theacclimation to account for possible circadian activity cycles. To verify this, the datawere truncated after 12 and 24 h post-acclimation and SMR was estimated for each ofthese two scenarios. The effect of experimental duration on SMR estimation was thenassessed.

MATERIALS AND METHODS

DATA BA S E A N D S M R M E T H O D S

The database contained MO2 values from c. 300 individual animals belonging to four speciesof fish [R. hippoglossoides, G. morhua, spotted wolffish Anarhichas minor Olafsen 1772 andbrook trout Salvelinus fontinalis (Mitchill 1814)] and one crustacean (northern shrimp Pandalusborealis). All data were obtained using the same technique, intermittent-flow respirometry in astatic respirometer (Steffensen, 1989; Svendsen et al., 2016) without measuring animal activity.All animals had been without food for usually 4 days but from 2 to 7 days, before being trans-ferred into the respirometer. Raw MO2 data were also obtained from the published literature fora G. ogac (Steffensen et al., 1994), a horse mackerel Trachurus trachurus (L. 1758) (Herrmann& Enders, 2000), a few E. stoutii (Cox et al., 2011) and for three perch Perca fluviatilis L. 1758(E. A. F. Christensen, pers. comm.) to provide greater fish diversity.

MO2 was plotted as a function of time for each animal and a sub-set of 85 cases were selectedfor analysis. The collection of data formed a gradient from a clearly defined, narrow horizontalband of low MO2 values to a very diffused horizontal band on the MO2 plots. Because SMR isnot expected to result in strictly constant MO2 values for measurements lasting 5–30 min, thesebands of low MO2 values were assumed to represent SMR, at least when they were well defined.The sample size for each species is shown in Table I. The average duration of data set for anindividual fish was 53⋅5 h (range: 13⋅7–116⋅4 h). For each animal, SMR was estimated with thefollowing eight methods using a single R script: MLND, quantiles with a range of p values (0⋅1,0⋅15, 0⋅2, 0⋅25 and 0⋅3, also referred to as q0⋅1, q0⋅15, etc.), the average of the 10 lowest valuesof MO2 (low10) and the average of the lowest 10% of the MO2 values, after removal of thefive lowest, considered probable outliers (low10%). All these methods, except q0⋅3, have beenused to estimate the SMR of fishes in published studies. The R script is shown in Appendix SI



Table I. Sample size (n), test temperature (T), experiment duration, acclimation duration andmean fasting period for each species represented in the collection of 85 examples used to com-

pare eight methods of standard metabolic rate (SMR) estimation

Species nT

(∘ C)Experimentduration (h)

Acclimationduration (h)

Mean fastingperiod (h) Source

Anarhichas minor 17 8 60⋅7 12 96 a

Eptatretus stoutii 1 10 45⋅9 5 n/a b

Gadus morhua 26 12 45⋅6 12 92 a

Gadus ogac 1 4⋅5 13⋅7 5 124 c

Pandalus borealis 12 5 46⋅5 12 98 d

Perca fluviatilis 3 10 44⋅8 10 504 e

Reinhardtius hippoglossoides 17 5 72⋅2 10 142 f

Salvelinus fontinalis 7 12 44⋅6 10 56 a

Trachurus trachurus 1 13 37⋅5 5 24 g

aD. Chabot (unpubl. data).bCox et al. (2011).cSteffensen et al. (1994).dDupont-Prinet et al. (2013a).eF. E. A. Christensen (pers. comm.).fDupont-Prinet et al. (2013b).gHerrmann & Enders (2000).

(Supporting Information). Because chasing and handling and of the stress caused by the newsurroundings, MO2 values are elevated after fishes are introduced into a respirometer, the datasets were shortened by removing MO2 values measured during an acclimation period beforecalculating SMR. These are the main data sets. As a compromise between a single durationof acclimation period for all animals and a different duration for each animal, one durationwas chosen for each species so as to remove the descending part of the MO2 values for mostindividuals in the sample (Table I).

The MLND was calculated using the function Mclust of the R package mclust (Fraley &Raftery, 2002; Fraley et al., 2012). Mclust fits a mixture of normal distributions to the data.The optimal number of distributions is automatically chosen between one and nine, but theuser can choose a narrower range of distributions. For each animal, the number, mean (MLND)and c.v. MLND (C.V.MLND) of the MO2 values assigned to the lowest normal distribution werecalculated. To facilitate the comparison of SMR methods across animals with very differentabsolute values of SMR, an overall average of all eight estimates was calculated (SMRMEAN)for each animal and used to obtain scaled deviations of each method from this mean value [e.g.deviationmethod equals (SMRmethod minus SMRMEAN) divided by SMRMEAN].

The MLND method is of particular interest because it is the only one of the eight methodsthat does not assume that a fixed number (low10) or proportion (low10% and all quantile-basedmethods) of the observations are at or below the true SMR. Unlike the other methods, it hasthe potential to adjust to the data without bias. The appropriateness of the MLND method wasassessed semi-qualitatively for each of the 85 animals. Up to a C.V.MLND = 7, the criterion wasin fact quantitative. The MLND was scored as unacceptable if 75% or more of the observationsassigned to the lowest normal distribution by the Mclust procedure were below the MLNDfor a period of at least 6 h [e.g. case 6; Appendix SII (Supporting information)]. Variabilityin short-term MO2 when fishes are calm and resting is assumed to be the sum of changes inthe functions of different organs and to experimental error. Although different fish species arelikely to differ in the proportion of time spent calm and resting in a respirometer, variabilityabout the SMR should be relatively low. This amount of variability is unknown and must beestimated from the data. Some animals had a C.V.MLND as low as about 2% in this study. The



qualitative part of the criterion is that MLND was considered unsuccessful when C.V.MLNDexceeded 7%.

To assess if the acclimation period could be left in when calculating SMR and what dura-tion of MO2 measurements should be sufficient to measure SMR, all eight SMR methods werecalculated three more times for each animal: when using the complete data sets (including theobservations obtained during the acclimation period) and with data sets truncated to just 12 and24 h post-acclimation (truncated 12 h and truncated 24 h). For each method, SMR for the com-plete and the two truncated data sets were compared with SMR calculated for the main data sets.Observations during the acclimation period were always excluded from the analysis except forthe analysis of the complete data sets.

S TAT I S T I C A L A NA LY S E S

Using the main data sets (acclimation period excluded), the eight estimates of SMR were com-pared with a univariate ANOVA for repeated measures. Each animal served as its own control,thereby alleviating the problem of pooling different species with different SMR values. SMRestimates were log10 transformed to obtain homoscedasticity amongst the different methods andanimals. This pooling of species was done deliberately because any estimation method shouldbe independent of the species being considered. The assumption of sphericity (homogeneityof variances of all differences between methods) was tested (Mauchly’s test), and appropriatecorrection to the d.f. effected, with the ez R package (Lawrence, 2013). Lack of sphericity inval-idates post hoc comparisons based on a common error term (pooled variance) (Quinn & Keough,2002). To assess which methods were different, t-tests for paired samples were performed foreach pair of methods, correcting the p level required for significance with the Šidák methodto maintain the family-wise error rate to 0⋅05 (Abdi, 2007). Only significant (P< 0⋅05) differ-ences are reported. To assess the effect of experiment duration, the same procedure was usedto compare four different data sets (main, which excluded observations from the acclimationperiod, complete, which included them, and truncated to 12 and 24 h post-acclimation). In thecase of experiment duration, not all possible pair-wise comparisons were of interest, but only thethree comparisons involving the main data sets. When presenting results of repeated-measuresANOVA, mean values and their s.d. are shown for each treatment (method or duration). Signif-icant differences were often detected despite large s.d. There are two reasons for this. Firstly,the s.d. values were smaller after logarithmic transformation, and secondly, what matters in thistype of analysis are the s.d. of the differences between treatments, and these could not be shownon the tables.

A logistic regression (logit transformation) was fitted to the semi-quantitative assessment ofthe appropriateness of the MLND method and C.V.MLND. The C.V.MLND yielding 50% successwas estimated with the dose.p function from R package MASS (Venables & Ripley, 2002).Regression analysis was used to assess the relationship between the degree of similarity amongstmethods and the variability in the data. All statistical analyses were performed with R (R CoreTeam; www.r-project.org).

RESULTS

U S E F U L N E S S O F T H E N E W M L N D A L G O R I T H M

Unlike the original algorithm for the MLND method, which fitted two normal dis-tribution to the MO2 data (Steffensen et al., 1994), the Mclust function of the mclustR package (Fraley et al., 2012) automatically chooses the optimal number of distribu-tions that best fit the data, from a minimum of one to a maximum of nine. With thisnew method, the optimal number of distributions was greater than two for almost halfof the animals (39 of 85; Table II). When more than four distributions were fitted to thedata, however, the lowest distribution often included only a few data points and failed



Table II. Number of distributions found for three different settings of the Mclust function tocalculate the mean of the lowest normal distribution (MLND) method: the maximum numberof distributions was set to 2, 4 and 9. The total number of animals with a given number of

distributions is reported

Number of distributions found TotalNumber of distributionsallowed 1 2 3 4 7 9

2 2 83 854 2 44 36 3 859 2 42 35 3 2 1 85

Table III. Decrease in the standard metabolic rate (SMR) estimated by the mean of the lowestnormal distribution MLND method when a maximum of four normal distributions is allowed,

instead of two distributions only

Decrease in MLND (%) Number of animals

0 460–2 92–5 125–10 11>10 7Total 85

to represent the SMR. The best results were obtained by limiting the maximum allow-able number of distributions to four. When four distributions were allowed, the SMRestimated by the MLND method was lower, compared with the original method, e.g.two distributions, for the 39 animals with more than two distributions (Table III). Theselower SMR estimates were due to better discrimination of MO2 values correspondingto SMR from higher MO2 values that were likely caused by small amounts of activityor stress (Fig. 1).

C A L C U L AT I N G S M R W H E N T H E AC C L I M AT I O N P E R I O DI S E X C L U D E D

Two measures of variability in the data are used: c.v. of the observations, calledC.V. MO2 (C.V .MO2

), and the c.v. of the observations assigned to the lowest normaldistribution, called C.V.MLND. Examples with low, intermediate and high C.V.MLND areshown in Fig. 2. Another c.v. was calculated for the mean of the eight SMR estimates(C.V.SMR) and served as a measure of agreement between methods. It varied morethan 10 fold (Fig. 3). As expected, agreement was better (lower C.V.SMR) when therewas less variability in the observations (C.V.MO2, range was 2–70%) [Fig. 3(a)]: thedifferent SMR methods used different sub-sets of MO2 when estimating SMR, andthese sub-sets were more similar when the observations were more similar overall(C.V.SMR = 2⋅37+ 0⋅06 C.V.MO2; F1,80 = 28, P< 0⋅001, r2 = 0⋅26). All methods but theMLND target the lowest observations by design when estimating SMR. Therefore,the methods should be more similar whenever the lowest observations are more



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Fig. 1. (a, c) Oxygen uptake (MO2) plot and (b, d) frequency distribution of MO2 of a juvenile Salvelinus fonti-nalis [animal 46, Appendix SII (Supporting Information)], including the normal distributions fitted to thedata ( ). The standard metabolic rate (SMR) is estimated by the mean of the lowest normal distribution(MLND). In (a) and (b), two normal distributions were fitted, as in Steffensen et al. (1994). In (c) and (d),up to four distributions were allowed and the algorithm chose three. This fish had many values of MO2 thatwere intermediate between the high values observed soon after it was placed into the respirometer and themany low values when the fish was assumed to be calm and inactive. In (a) and (c), the is the MLNDand the symbols represent which normal distribution each MO2 was assigned to. Observations from the 10 hhabituation period were included for comparison with Appendix SII (Supporting Information), where theywere excluded.

similar. The C.V.MLND is a measure of the variability amongst the low values of MO2.C.V.MLND varied more than five-fold [Fig. 3(b)] and, as expected, the agreementbetween SMR estimates was strongly related to C.V.MLND (C.V.SMR = 1⋅07+ 0⋅47C.V.MLND; F1,80 = 268, P< 0⋅001, r2 = 0⋅77). In contrast, the relationship betweenC.V.MLND and C.V.MO2 was significant but weak (C.V.MLND = 4⋅06+ 0⋅09 C.V.MO2;F1,80 = 14, P< 0⋅001, r2 = 0⋅14) [Fig. 3(c)]. The ratio of the largest to the smallestSMR estimate, another measure of agreement amongst estimates, was also stronglyrelated to C.V.MLND (C.V.SMR = 1⋅021+ 0⋅018 C.V.MLND; F1,80 = 290, P< 0⋅001,



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Fig. 2. (a, c, e) Oxygen uptake (MO2) plot and (b, d, f) frequency distribution of MO2 of (a–d) Gadus morhuaand (e–f) Anarhichas minor. Horizontal lines on the MO2 plots and vertical lines on the frequency distri-butions represent different estimates of standard metabolic rate (SMR): , the mean of the lowest normaldistribution (MLND); , quantile with p= 0⋅2 (q0⋅2); , the average of the lowest 10% of MO2 valuesafter the removal of the 5 lowest ones; , the average of the 10 lowest MO2 values (low10). The nor-mal distributions that best fit the frequency distributions of MO2 values are also shown ( ). Variabilityamongst the low values of MO2, as measured by the c.v. of the MO2 values assigned to the lowest normaldistribution, was low (2⋅1%) in (b), intermediate (5⋅2%) in (d) and high (8⋅7%) in (f). Not shown to preventthe SMR indices from becoming undistinguishable on the figures, but available in Appendix SIII (Support-ing Information) (IDs 4, 35 and 65), are q0⋅1, q0⋅15, q0⋅25 and q0⋅3. , excluded from the calculation of SMRbecause they occurred too early after each animal was placed into the respirometer to represent SMR.indicate night-time.



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r2 = 0⋅78) [Fig. 3(d)]. Therefore, the various methods of estimating SMR differedthe most when the lowest normal distribution was dispersed. Conversely, SMRestimates were similar when the horizontal band of low MO2 values was not dis-persed. Consequently, if spontaneous activity is minimal (which is the primary sourceof MO2 variability), SMR can be estimated using a variety of methods, such asthose used here. In this study, the largest difference between estimates was <10%in 26 animals, presumably the most quiescent ones. The difference in SMR esti-mates, however, reached 50% for more active individuals and exceeded 20% in 14animals in this study. The analysis that follows examines which of the methodsprovided a good SMR estimate even when the MO2 values are variable due toactivity.



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Fig. 4. Scaled deviations of five of the standard metabolic rate (SMR) estimates calculated for each of 85 fish andshrimp in relation to the variability amongst measurements of oxygen uptake (MO2) assigned to the lowestdistribution of MO2 (C.V.MLND, displayed on a log10 axis). The methods are the mean of the lowest normaldistribution, MLND ( ), quantiles with p set to 0⋅3 ( ), 0⋅2 ( ) and 0⋅1 ( ), the average of thelowest 10% of MO2 values ( ) and the 10 lowest MO2 values ( ). Vertical lines indicate C.V.MLND of

4⋅7 ( ) and 5⋅7% ( ), respectively. The deviations of two indices (q0⋅15 and q0⋅25) are omitted for clarity.

All 85 animals are plotted in increasing order of C.V.MLND in Appendix SII (Support-ing Information), and the eight SMR estimates for each animal are given in AppendixSIII (Supporting information). The scaled deviations as a function of C.V.MLND forthe different methods are presented in Fig. 4 and clearly illustrate the widening differ-ences among SMR methods with increasing C.V.MLND. This figure also reveals rela-tionships amongst different methods. As expected, low10 was the lowest estimate inall 85 animals. Low10% was similar to q0⋅1 and both were below all other methodsexcept low10. The MLND and q0⋅2 estimates were similar when C.V.MLND was low(Fig. 4). Starting at a C.V.MLND of c. 4⋅7, the MLND estimates was equal to or greaterthan the q0⋅2 most of the time, and became greater than q0⋅3 most of the time startingat a C.V.MLND of c. 5⋅7 (Fig. 4). The MLND was almost always judged appropriatewhen the C.V.MLND was low [Fig. 5; see Appendix SIII (Supporting information) forthe semi-quantitative assessment of the appropriateness of the MLND for each animal],and a 50% success rate for the MLND occurred when the C.V.MLND was 5⋅4 (95% c.i.:4⋅7–6⋅2). Therefore, the extensive data sets used to generate Figs 4 and 5 suggest thatthe MLND method becomes unreliable once the C.V.MLND exceeds c. 5⋅4.

The eight methods were first compared on a sub-set of 34 animals with a lowC.V.MLND (≤5⋅4). The MLND was judged successful for 28 of them and for the sixothers, the difference between the MLND method and the centre of the horizontalband of low values never exceeded 2⋅7% [see IDs 5, 9, 20, 28, 31 and 33; AppendixSII (Supporting Information)]. Therefore, the MLND was generally a good estimateof SMR when C.V.MLND was ≤5⋅4. Only the low10 method had an average difference>5% when compared with the MLND estimate. All the same, all but the q0⋅2, q0⋅25 andq0⋅3 estimates differed significantly from the MLND estimate, and from each other,even if the differences in the SMR estimates were not large (Table IV).



205 10 15 25

C.V.MLND

0

0·2

0·4

0·6

0·8

1·0

ML

ND

suc

cess

5.44

Fig. 5. Relationship between the success rate of the Mean of the Lowest Normal Distribution (MLND) methodof Standard Metabolic Rate (SMR) estimation and the variability amongst MO2 values of the lowest distri-bution (C.V.MLND) ( ). Success rate was assessed qualitatively for each case (SIII). ( ): 50% success

rate, which occurs at a C.V.MLND of 5.44. ( ): 95% C.I. 4.73–6.16.

When the MLND method was judged successful and C.V.MLND was between 5⋅4and 7⋅0, three quantiles (q0⋅2, q0⋅25 and q0⋅3) were similar to the MLND method, butthe other methods differed from each other, except that q0⋅1 was similar to low10%and low10, and q0⋅15 was similar to q0⋅2 and to low10%, despite the small samplesizes (Table V; n= 7). Within the same range of C.V.MLND, but when the MLNDwas rejected (n= 13), the MLND method was similar only to the two highest of thequantile methods (q0⋅25 and q0⋅3). Except for the pair q0⋅1 and low10%, all methodsdiffered from each other (Table V).

The MLND was never considered a valid estimate of SMR when C.V.MLND exceeded7%. In other words, the variability in the lowest normal distribution appeared greaterthan the variability in the low horizontal band of MO2 values on MO2 plots. Further,in some cases (e.g. animals 63, 64, 67, 71 and others), there appeared to be anothernormal distribution to the left of the lowest distribution identified by Mclust, butthe algorithm was unable to discriminate it. For animals with such high variability(n= 31), the MLND yielded such a high estimate of SMR that it was significantlyabove all other methods (Table VI). This high variability also caused all other methodsto be significantly different from each other, except for q0⋅1 and low10% (Table VI).

AC C L I M AT I O N P E R I O D A N D E X P E R I M E N T D U R AT I O N

For each method, the four possible durations (main, complete, truncated 12 h andtruncated 24 h) were compared using only the 67 animals with at least 32 h of datapost-acclimation. This was to ensure that the main data sets were longer than thetruncated 24 h data sets. For all eight methods, duration was a significant effect(Table VII). The MLND method was expected to be impervious to the inclusion orexclusion of the acclimation period. For these 67 animals, the average MLND wasindeed similar for the two durations (Table VII). For some individuals, however, the



Tab

leIV

.C

ompa

riso

nof

eigh

tdi

ffer

ent

met

hods

ofst

anda

rdm

etab

olic

rate

(SM

R)

estim

atio

n:m

ean

ofth

elo

wes

tno

rmal

dist

ribu

tion

(ML

ND

),qu

antil

esw

ithp

valu

esra

ngin

gfr

om0.

1to

0.3

(q0.

1to

q 0.3

),m

ean

of10

%of

the

low

est

obse

rvat

ions

,af

ter

rem

ovin

gth

elo

wes

t5

(low

10%

)an

dm

ean

of10

low

esto

bser

vatio

ns(l

ow10

).O

nly

the

34ca

ses

with

low

vari

abili

tyw

ere

incl

uded

(coe

ffici

ento

fva

riat

ion

ofva

lues

inth

elo

wes

tnor

mal

dist

ribu

tion,

C.V

. ML

ND

,≤5.

4).I

nad

ditio

nto

mea

n±

s.d.

for

each

met

hod,

the

devi

atio

nsw

ere

calc

ulat

edbe

twee

nm

etho

ds2

–8

and

met

hod

1(M

LN

D)

and

the

resu

ltsw

ere

expr

esse

das

%of

ML

ND

.The

s.d.

asw

ella

sm

inim

uman

dm

axim

umva

lues

ofth

ese

devi

atio

nsar

esh

own.

SMR

estim

atio

nsw

ere

log 1

0tr

ansf

orm

edbe

fore

stat

istic

alan

alys

is.M

etho

dis

asi

gnifi

cant

effe

ct(F

7,23

1=

69⋅1

,P<

0⋅00

1w

ithG

reen

hous

e–G

eiss

er𝜀=

0⋅22

).M

ean

valu

esof

SMR

with

diff

eren

tsup

ersc

ript

low

er-c

ase

lette

rsar

edi

ffer

ent(

t-te

sts

for

pair

edsa

mpl

esw

ithŠi

dák

corr

ectio

n,P<

0⋅05

)

Met

hod

ML

ND

q 0⋅1

q 0⋅1

5q 0

⋅2q 0

⋅25

q 0⋅3

Low

10%

Low

10

Mea

n±

s.d.

SMR

(μm

olm

in−

1kg

−1)

34⋅6

abc±

19⋅1

33⋅5

e±

18⋅5

33⋅9

d±

18⋅7

34⋅2

c±

18⋅8

34⋅6

b±

18⋅9

35⋅1

a±

19⋅1

33⋅2

f±

18⋅4

32⋅4

g±

18⋅0

Dev

iatio

nfr

omM

LN

D(%

)(m

ean±

s.d.

)−

3⋅3±

1⋅4

−2⋅

0±

1⋅6

−0⋅

8±

2⋅3

0⋅4±

3⋅3

2⋅0±

5⋅4

−4⋅

1±

1⋅6

−6⋅

7±

2⋅8

Min

imum

−6⋅

8−

5⋅4

−4⋅

3−

3⋅5

−2⋅

8−

9⋅7

−17

⋅1M

axim

um−

0⋅4

3⋅1

8⋅6

15⋅5

28⋅ 4

−1⋅

9−

2⋅4



Tab

leV

.C

ompa

riso

nof

eigh

tdi

ffer

ent

met

hods

ofst

anda

rdm

etab

olic

rate

(SM

R)

estim

atio

n:m

ean

ofth

elo

wes

tno

rmal

dist

ribu

tion

(ML

ND

),qu

antil

esw

ithp

valu

esra

ngin

gfr

om0.

1to

0.3

(q0.

1to

q 0.3

),m

ean

of10

%of

the

low

est

obse

rvat

ions

,af

ter

rem

ovin

gth

elo

wes

t5

(low

10%

)an

dm

ean

of10

low

esto

bser

vatio

ns(l

ow10

).O

nly

case

sw

ithin

term

edia

teva

riab

ility

wer

ein

clud

ed(c

oeffi

cien

tof

vari

atio

nof

valu

esin

the

low

estn

orm

aldi

stri

butio

n,C

.V. M

LN

D,5⋅4<

C.V

. ML

ND≤

7⋅0)

.(a)

Ani

mal

sw

itha

succ

essf

ulM

LN

Dan

d(b

)ani

mal

sw

ithun

succ

essf

ulM

LN

D.I

nad

ditio

nto

mea

n±

s.d.

fore

ach

met

hod,

the

devi

atio

nsw

ere

calc

ulat

edbe

twee

nm

etho

ds2

–8

and

met

hod

1(M

LN

D)a

ndth

ere

sults

wer

eex

pres

sed

as%

ofM

LN

D.T

hes.

d.as

wel

las

min

imum

and

max

imum

valu

esof

thes

ede

viat

ions

are

show

n.SM

Res

timat

ions

wer

elo

g 10

tran

sfor

med

befo

rest

atis

tical

com

pari

son.

Met

hod

isa

sign

ifica

ntef

fect

whe

nth

eM

LN

Dm

etho

dis

succ

essf

ul(F

7,42=

37⋅6

,P<

0⋅00

1,w

ithG

reen

hous

e–G

eiss

er𝜀=

0⋅17

)as

wel

las

whe

nit

isno

t(F

7,84=

113,

P<

0⋅00

1,w

ithG

reen

hous

e–G

eiss

er𝜀=

0⋅28

).M

ean

valu

esof

SMR

with

diff

eren

tsup

ersc

ript

low

er-c

ase

lette

rsar

edi

ffer

ent(

t-te

sts

for

pair

edsa

mpl

esw

ithŠi

dák

corr

ectio

n,P<

0⋅05

)

Met

hod

ML

ND

q 0⋅1

q 0⋅1

5q 0

⋅2q 0

⋅25

q 0⋅3

Low

10%

Low

10

(a)

Ani

mal

sw

ithsu

cces

sful

ML

ND

(n=

7)M

ean±

s.d.

SMR

(μm

olm

in−

1kg

−1)

29⋅5

abc±

17⋅1

27⋅9

ef±

16⋅4

28⋅5

cd±

16⋅7

28⋅9

c±

16⋅8

29⋅4

b±

17⋅1

30⋅0

a±

17⋅5

27⋅7

de±

16⋅5

26⋅7

f±

15⋅9

Dev

iatio

nfr

omM

LN

D(%

)(m

ean±

s.d.

)−

5⋅43

±2⋅

04−

3⋅50

±2⋅

23−

1⋅73

±2⋅

650⋅

11±

3⋅29

2⋅19

±4⋅

14−

6⋅64

±1⋅

47−

10⋅3

6±

1⋅74

Min

imum

−7⋅

78−

6⋅28

−5⋅

31−

4⋅54

−3⋅

43−

8⋅35

−12

⋅50

Max

imum

−2⋅

85−

0⋅68

0⋅58

3⋅13

7⋅21

−3⋅

69−

8⋅13

(b)

Ani

mal

sw

ithun

succ

essf

ulM

LN

D(n=

13)

Mea

n±

s.d.

SMR

(μm

olm

in−

1kg

−1)

32⋅8

ab±

19⋅9

30⋅6

e±

18⋅6

31⋅1

d±

18⋅7

31⋅5

c±

19⋅0

31⋅9

b±

19⋅1

32⋅3

a±

19⋅3

30⋅4

e±

18⋅5

29⋅4

f±

18⋅0

Dev

iatio

nfr

omM

LN

D(%

)(m

ean±

s.d.

)−

6⋅6±

1⋅4

−4⋅

8±

1⋅7

−3⋅

7±

2⋅0

−2⋅

5±

2⋅4

−1⋅

1±

3⋅1

−7⋅

3±

1⋅2

−10

⋅6±

1⋅9

Min

imum

−9⋅

1−

6⋅8

−5⋅

8−

5⋅4

−4⋅

2−

9⋅1

−15

⋅2M

axim

um−

4⋅4

−1⋅

01⋅

84⋅

28⋅

0−

5⋅1

−7⋅

8



Tab

leV

I.C

ompa

riso

nof

eigh

tdif

fere

ntm

etho

dsof

stan

dard

met

abol

icra

te(S

MR

):m

ean

ofth

elo

wes

tnor

mal

dist

ribu

tion

(ML

ND

),qu

antil

esw

ithp

valu

esra

ngin

gfr

om0.

1to

0.3

(q0.

1to

q 0.3

),m

ean

of10

%of

the

low

esto

bser

vatio

ns,a

fter

rem

ovin

gth

elo

wes

t5(l

ow10

%)

and

mea

nof

10lo

wes

tob

serv

atio

ns(l

ow10

).O

nly

case

sw

ithhi

ghva

riab

ility

wer

ein

clud

ed(c

oeffi

cien

tof

vari

atio

nof

valu

esin

the

low

est

norm

aldi

stri

butio

n,C

.V. M

LN

D,

(C.V

. ML

ND>

7,N=

31).

Inad

ditio

nto

mea

n(μ

mol

min

−1

kg−

1)

and

s.d.

for

each

met

hod,

the

devi

atio

nsw

ere

calc

ulat

edbe

twee

nm

etho

ds2

–8

and

met

hod

1(M

LN

D)

and

the

resu

ltsw

ere

expr

esse

das

%of

ML

ND

.The

s.d.

asw

ella

sm

inim

uman

dm

axim

umva

lues

ofth

ese

devi

atio

nsar

esh

own.

SMR

estim

atio

nsw

ere

log

tran

sfor

med

befo

rest

atis

tical

com

pari

son.

Met

hod

isa

sign

ifica

ntef

fect

(F7,

210=

142,

P<

0⋅00

1,w

ithG

reen

hous

e–G

eiss

er𝜀=

0⋅24

).M

ean

valu

esof

SMR

with

diff

eren

tlow

er-c

ase

lette

rsar

edi

ffer

ent(

t-te

sts

for

pair

edsa

mpl

esw

ithŠi

dák

corr

ectio

n,p<

0⋅05

).

Met

hod

ML

ND

q 0⋅1

q 0⋅1

5q 0

⋅2q 0

⋅25

q 0⋅3

Low

10%

Low

10

Mea

nSM

R31

⋅5a

28⋅1

f28

⋅7e

29⋅3

d29

⋅8c

30⋅3

b27

⋅7f

26⋅1

g

s.d.

26⋅2

23⋅2

23⋅6

24⋅2

24⋅5

24⋅9

22⋅4

20⋅1

Mea

nde

viat

ion

from

ML

ND

(%)

−10

⋅9−

8⋅9

−6⋅

8−

5⋅0

−3⋅

1−

11⋅6

−16

⋅2s.

d.3⋅

43⋅

12⋅

73⋅

13⋅

63⋅

55⋅

8M

inim

um−

20⋅9

−16

⋅4−

14⋅9

−13

⋅4−

10⋅3

−21

⋅4−

34⋅5

Max

imum

−4⋅

9−

3⋅5

0⋅1

4⋅9

10⋅1

−3⋅

9−

7⋅3



2 5 10 20

12

510

20

2

3

8

25 31

32

40

43

69

75

84(a)

2 5 10 20

–50

510

1520

C.V.MLND, acclimation period excluded

C.V

. ML

ND

, usi

ng a

ll da

ta

Cha

nge

in M

LN

D (

%)

3

6975

80

82

83

84

(b)

Fig. 6. (a) Effect of including or excluding oxygen uptake recorded during the acclimation period on the vari-ability amongst the values of oxygen uptake assigned to the lowest normal distribution (C.V.MLND); , a

change of ≥50% of the C.V.MLND, either positive or negative. The is the line of equality. and showthe limit for an acceptable standard metabolic rate (SMR) estimation by the mean of the lowest normal dis-tribution (MLND) method (C.V.MLND = 5⋅4). (b) Change (%) in SMR estimated by the MLND method ifthe observations from the acclimation period are included, as a function of the C.V.MLND; represents

no effect of including or excluding data from the habituation period and the represents the suggested valueof C.V.MLND (5⋅4) to reject the MLND method. , a change of ≥5% of SMR, either positive or negative.

addition of the data in the acclimation period allowed the algorithm to distinguish twonormal distributions instead of a single one amongst the low MO2 values. The newMLND and C.V.MLND were lower, and seven animals with a C.V.MLND > 5⋅4 when theacclimation period was excluded had an acceptable C.V.MLND (≤5⋅4) when these datawere included (in particular, animals 40, 69 and 75; Fig. 6). Conversely, the addition ofobservations obtained during the acclimation period sometimes caused the algorithmto merge two different distributions into a single one, making the new lowest normaldistribution more variable and MLND estimates higher (animals 3, 25 and 31; Fig. 6).There was no clear advantage or disadvantage in excluding data for the acclimationperiod for the MLND method.

Using observations from the acclimation period entails adding a large number ofobservations, most of them with high values of MO2. The consequence on quantiles isthat a greater number of observations had to be below the chosen quantile and thereforethe SMR estimates were always significantly greater (Table VII). For instance, q0⋅15when the acclimation period was included resembled q0⋅2 when the acclimation periodwas excluded. The low10% method also uses a proportion of the data to estimateSMR, and like quantiles, the addition of a large number of high MO2 values resultedin a significant increase of this SMR estimate (Table VII). Low10 was expected toremain the same when data from the acclimation period were included because novery low MO2 value was expected to occur during the acclimation period. This wasconfirmed (Table VII).



Table VII. Standard metabolic rate (SMR) estimated with eight methods and with four sub-setsof the data sets representing different durations: main (observations from the acclimation periodexcluded), complete (observations from that period included), truncated after 12 and 24 hsince the end of the acclimation period. Only the 67 animals with at least 32 h of recordingpost-acclimation were used. Means± s.d. are reported. Duration was a significant effect for all

methods (F3,198 ≥ 12⋅1, Greenhouse–Geisser adjusted P< 0⋅001)

SMR (μmol min−1 kg−1)

Method Main Complete Truncated 12 h Truncated 24 h

MLND 33⋅1± 23⋅8 33⋅3± 23⋅9 35⋅6*± 26⋅0 33⋅5*± 24⋅0q0⋅1 31⋅0± 21⋅9 31⋅2*± 22⋅1 32⋅4*± 23⋅3 31⋅2± 22⋅1q0⋅15 31⋅5± 22⋅2 31⋅8*± 22⋅4 33⋅2*± 23⋅8 31⋅7± 22⋅4q0⋅2 32⋅0± 22⋅6 32⋅4*± 22⋅8 33⋅8*± 24⋅1 32⋅2± 22⋅7q0⋅25 32⋅4± 22⋅8 33⋅0*± 23⋅2 34⋅4*± 24⋅3 32⋅7± 23⋅0q0⋅3 32⋅9± 23⋅1 33⋅6*± 23⋅5 35⋅1*± 24⋅7 33⋅2± 23⋅5Low10% 30⋅6± 21⋅5 30⋅7*± 21⋅6 33⋅0*± 23⋅3 31⋅1*± 21⋅8Low10 29⋅3± 20⋅2 29⋅3*± 20⋅2 32⋅2*± 22⋅6 30⋅1*± 20⋅7

MLND, mean of the lowest normal distribution.*Different from the estimate obtained with the main data sets (t-tests for paired samples with Šidák correc-tion, P< 0⋅05).

For all methods, estimates of SMR obtained with the shortest data sets, truncated12 h, were significantly higher than those obtained with the main data sets (Table VII).With the truncated 24 h data sets, however, SMR estimates for the quantile methodswere indistinguishable from those obtained with the main data sets (Table VII). TheMLND, low10% and low10 were still higher than when they were calculated with themain data sets.

DISCUSSION

C H O I C E O F M E T H O D T O E S T I M AT E S M R

The main objective of the experimental part of this paper was to compare methods toestimate SMR of fishes when MO2 is measured frequently over short intervals in a staticrespirometer, and fish activity is not monitored, as there is no prescribed method to doso. The selection of MO2 values associated with a calm, motionless animal and requiredto assess SMR must use characteristics of the data. Here, the frequency distributionof the MO2 values, their distribution in time and an estimate of variance were used.The time dimension allows for a rough assessment of important considerations suchas recovery from stress and diurnal rhythms, whereas the frequency dimension allowsthe application of statistical and cut-off techniques. The estimate of variance providedan additional statistical measure to compare the eight methods. Three broad methodshave been used in the literature to calculate SMR, but the relative performance of thesemethods has not been thoroughly assessed until now. These methods are: (1) calculatingthe mean value of the lowest values of MO2 observed for a fish, with many variations inthe number of values that should be used, (2) taking a quantile from the values of MO2,with variants as to which p value to use and (3) assigning MO2 values to a mixture ofnormal distributions and using the MLND or mean of the lowest normal distribution.



This study compared eight variants of these three methods on the same diverse datasets (85 fishes and crustaceans) that probably encompassed most situations encoun-tered when attempting to measure SMR of fishes with intermittent-flow respirometry.The methods tested were two variants of the first approach (low10 and low10%), five ofthe second approach (quantiles with p values ranging from 0⋅1 to 0⋅3) and an improvedversion of the MLND approach, which fits optimally from one to four normal distri-butions, depending on the data, instead of always two normal distributions (Steffensenet al., 1994). The true SMR was unknown for any of these fishes or crustaceans. Akey assumption of this study was that MO2 measured over short intervals (min) is notexpected to be constant even in calm, inactive fish because whole-fish MO2 is the sumof the oxygen usage of different organs, which can vary very quickly (Priede, 1985;Darveau et al., 2002). Also, the possibility of short bouts of anaerobic metabolism dur-ing measurement could underestimate SMR. Steffensen et al. (1994) have shown thatthe MO2 measurements of a calm, inactive fish form an approximately normal distribu-tion and the histograms generated in this study (Appendix SII, Supporting Information)confirm this. On a plot of MO2 v. time, the observations corresponding to this normaldistribution form a horizontal band, more or less pronounced depending on the pro-portion of the time that the fish was at SMR and how variable the measurements werewhen the fish was at SMR. Thus, an estimate of SMR was deemed acceptable when itwas close to the centre of this horizontal band.

The MLND method is an objective statistical approach that works regardless of theproportion of the time the animal was at SMR. Thus, the MLND can reliably calculateSMR when the fully acclimated, quiescent animal is at SMR practically all the time,as in the G. ogac used in Steffensen et al. (1994) and also in this study (animal 1), butit should also work when the animal is at SMR much less often, and many examplesof such situations were evident in the 85 data sets shown in Appendix SII (SupportingInformation) (e.g. animals 7, 8, 15–18 and more). The change to the MLND methodintroduced in this study (e.g. allowing up to four normal distributions instead of two)represented an improvement because the lowest normal distribution was narrower, witha lower mean value, for nearly half of the 85 data sets. Even so, SMR estimated by theMLND method was sometimes amongst the highest or even the highest of all methodstested for an animal. When this happened, the normal distribution assigned to SMRcovered a wide range of MO2 values and had high variance, which does not agree withthe low variation that is expected from temporal variability in organ and tissue oxygendemand when a fish is calm and inactive. As sophisticated as the algorithm used bythe Mclust function is, it is not always successful at isolating MO2 values associatedwith SMR when slightly higher MO2 values are also abundant, i.e., those most likelyassociated with mild activity or perhaps stress. The fact that the MLND method doesnot always reflect SMR is a problem. The results presented in this study suggest that theMLND does represent SMR well when the variability of the data in the lowest normaldistribution (C.V.MLND) is ≤5⋅4. Therefore, C.V.MLND should be used to screen a dataset to determine if the MLND can be reliably used.

The seven other methods use a cut-off approach, which requires the experimenterto decide on a number or proportion of low MO2 values that are acceptable. Thesevalues are then either averaged (low10% and low10) or considered to be below SMR(quantiles). The low10, however, cannot be reconciled with the assumption that MO2values in calm and inactive animal are normally distributed with a mean value thatcorresponds to SMR. On the contrary, it is based on the concept that the lowest values



observed during a trial represent SMR. This method was expected to find the lowestestimates of SMR, and it did. The results shown here do not support the use of thelow10 to estimate SMR for controlled laboratory studies with fishes, even though thismethod or similar variants have been used in a considerable number of previous studies.Earlier, Roche et al. (2013) compared the mean of the lowest three MO2 values and theMLND for 10 individuals of the coral-reef fish Scolopsis bilineata (Bloch 1793) andfound no difference between these two methods. The small sample size in Roche et al.(2013) resulted in lower statistical power than this study. Also, it is possible that MO2variability was very low in their study because, as shown in this study, all methodsprovide similar SMR estimates when the variability is low (Fig. 4).

The number of MO2 values included in the low10% method depends on sample size.When n> 105, the low10% uses more data than the low10 method and produces largerestimates. Even with smaller samples, the low10% yields larger estimates than thelow10 because the five lowest MO2 values are always rejected as outliers. The removalof 5 outliers is also why the low10% is often very similar to the q0⋅1, even though oneis taking the average of the lowest 10% of the data, and the other puts 10% of the databelow SMR. Both methods were almost always below the horizontal band of low MO2values that was assigned to SMR. This agrees with a limited comparison of low10%with MLND in a few (six) individuals of two freshwater crustaceans: low10% alwaysproduced lower estimates than the MLND (Rosewarne et al., 2014). The other quantilesput progressively more data below SMR, from 15 (q0⋅15) to 30% (q0⋅3). One advantageof the quantiles over both the low10% and low10 is robustness against variable numbersof outliers and no requirement for normality. Low10% and low10, on the other hand,calculate the arithmetic mean of what is often the left tail of a normal distribution, eventhough the mean is a measure of central tendency for normal distributions.

The MLND method provided a good estimate of SMR when the C.V.MLND was low(<5⋅4). For the 34 data sets with the lowest C.V.MLND, the lowest normal distributionincluded on average 53⋅4% of the MO2 values obtained after the acclimation period(s.d.= 21⋅2; range= 17–100%). On average, 26% of the observations were belowSMR, but the range was large (8⋅5–50%). It would appear that finding a single numberto use with the cut-off methods is illusory. The quantile approach, however, is robustand the estimates provided by the q0⋅2 and q0⋅25 methods did not differ significantlyfrom the MLND for the 34 data sets with a low C.V.MLND. Estimates from these meth-ods were again similar to those from the MLND method at intermediate variability,except when the MLND was judged to be a poor estimate of SMR. In this situation,as well as in the vast majority of cases when the C.V.MLND was very high (>7), theq0⋅2 and q0⋅25 continued to be close to the centre of the horizontal band of low values,when such a band could be detected.

It is recommended that in cases when the MLND cannot be considered reliable(C.V.MLND > 5⋅4), either the q0⋅2 or q0⋅25 be used instead. There is no statistical reasonto strongly recommend one over the other. Instead, MO2 plots should be examinedand these quantiles should be compared to the position of the horizontal band of lowvalues before deciding which quantile should be considered the best substitute for theMLND method. In practice, D. Chabot (unpubl. data) has found the q0⋅2 to work wellwith the vast majority of fishes and crustaceans. When MO2 variability is very large,and the animal may not have been at SMR often enough to assess SMR reliably, itmay be safest to reject such cases. Some species will remain difficult to study in a



respirometer (e.g. P. borealis and E. stoutii in this study) and the q0⋅2 or q0⋅25 are likelythe best estimates of SMR possible.

With this recommendation, the SMR is well estimated for the vast majority of the85 animals included in this study. In a few cases, this solution is suboptimal. Thus,the MLND was recommended for animals 9, 20 and 28 because of low C.V.MLND(Appendix SII, Supporting Information), but the MLND was ruled unsuccessful withthe semi-quantitative assessment and the q0⋅2 was closer to the centre of the horizon-tal band of low MO2 values. On the contrary, the q0⋅2 was less well positioned thanthe MLND for animals 39 and 57, but the latter was rejected because of the relativelyhigh C.V.MLND (5⋅7 and 7, respectively). The difference between the two methods wassmall and following the recommendation is unlikely to entail problems when studyinga sufficiently large number of fishes. If a single strategy is desired instead of alternatingbetween the MLND and a quantile method within the same study, one of the q0⋅2 orq0⋅25 methods, chosen using the same criterion as above, could be used for all animals,even those with a low C.V.MLND, because of the similarity between these quantiles andthe MLND in conditions of low MO2 variability.

A large number of variable data sets (85 animals) were used here, but the recommen-dations to estimate SMR may not apply to every fish study. If the pivotal C.V.MLND of5⋅4 calculated in this study does not appear to be valid for a given species and exper-imental setup, a quantitative or semi-quantitative method could be used to assess theusefulness of the MLND for each fish, or to calculate a new cut-off value of C.V.MLNDthat is more appropriate. Examination of MO2 plots may suggest that adjustments arerequired for the recommended quantiles as well. Most of the 85 animals used in thisstudy were demersal species that were expected to become inactive in the respirometeroften enough for a band of low values to be apparent. Also, the pelagic S. fontinaliswere virtually motionless in the respirometers most of the time. But, other pelagicspecies may be active more often in a static respirometer (Cech, 1990; Herrmann &Enders, 2000), thus altering the ratio of measurements made when the fish is inac-tive or active. Animal 79, a T. trachurus from Herrmann & Enders (2000; Fig. 3) wasconsidered by these authors to be active often. The MLND method placed most obser-vations into a single normal distribution with a mean that likely represents RMR insteadof SMR and this method is unlikely to estimate SMR well with active pelagic species.Even the q0⋅2 was greater than the SMR calculated by Herrmann & Enders (2000) (114v. 104 μmol min−1 kg−1), suggesting that quantiles with lower p values may be moreappropriate with pelagic species. More work is required to recommend p values for theuse of quantiles to estimate SMR with active pelagic species.

An important final consideration is to avoid ad hoc decisions, such as choosing whichmethod to use (MLND or quantile or different quantiles) case by case, without a rig-orous criterion. As long as a method works well for the majority of animals in a study,cases when the estimated SMR appears to be unacceptable should be rejected insteadof bending the rules for them. Comparisons with other studies will only be possible ifa small number of methods are used, and those recommended here should be valid formost studies of benthic and demersal fishes.

AC C L I M AT I O N P E R I O D

Although fishes are clearly not at SMR soon after being placed into a respirometer,it would be simpler if SMR could be calculated using the entire data sets, without the



need to determine the duration of an acclimation period and the removal of these data.All methods except MLND and low10, however, produced significantly different esti-mates of SMR when observations from the acclimation period were included. Further,even though the average SMR estimated by the MLND method was not influenced bythe acclimation period, the results differed strongly for some animals. Therefore, onlythe low10 was truly unaffected by the inclusion of the acclimation period, which wasexpected because it is unlikely that one or more of the lowest MO2 values should occurduring the acclimation period, unless the duration of this period is made too long. Thisbeing said, all methods used in this study can be adapted to work with complete datasets. The C.V.MLND can still be used to decide if the MLND is reliable. The quantilesare influenced in a predictable manner by the inclusion of the elevated MO2 valuesobserved during the acclimation period. Therefore, the q0⋅2 and q0⋅25, which performedbest when the acclimation period was excluded, could be replaced by the q0⋅15 and q0⋅2,respectively, when the acclimation period is retained. Similarly, a method equivalent tolow10%, but using a smaller percentage of the MO2 values, could be used with com-plete data sets and the results would be comparable to those provided by the low10%after removal of the data recorded during the acclimation period. Nevertheless, thereis an advantage to the removal of data from a period when it is known that the fishcannot to be at SMR: it sets a precedent for the exclusion of other periods, if any, whenthe animal is unlikely to be at SMR, without needing any adjustments to the methods.For example, periods when the experimental protocol provokes disturbances or lastingchanges in MO2 (e.g. feeding the fishes to measure specific dynamic action, SDA), orperiods when environmental variables (temperature, DO and pH) are modified, can beexcluded for the calculation of SMR using the principle that the animal is unlikely tobe at SMR, just as during the acclimation period.

M I N I M U M E X P E R I M E N T D U R AT I O N

For 67 animals used to compare three durations (main, truncated 12 h and truncated24 h data sets), the truncated 12 h data sets yielded significantly higher estimates ofSMR with all eight methods compared in this study. This suggests that experimentslasting only 12 h after fishes have acclimated to the respirometer are too short to eval-uate SMR reliably, and the error (overestimation) is likely to be particularly severe forspecies with a strong circadian activity pattern. Truncation after 12 h may have elimi-nated the period of the day when some of these 67 animals were most quiescent, andin some cases, quiescent MO2 values were still declining after 12 h, perhaps due toon-going SDA in cold water (e.g. animals 2, 8, 9, 13). This may have been avoidedby setting the duration of the acclimation period for each animal, instead of for eachspecies. The high SMR estimates obtained with the truncated 12 h data sets constitute aclear warning that 12 h is usually too short to assess SMR, with the onus on the exper-imenter to demonstrate the feasibility of such short experiments to measure SMR orreport that as RMR.

A period of 24 h ensures that the quiet part of the day is included in the experiment,as long as the acclimation period was well set and the fish was acclimated for this entire24 h period. This duration was expected to be sufficient for accurate determination ofSMR. It was the case for all quantile methods. The MLND, however, was on averagegreater when the records were truncated after 24 h than when the entire record was used.It was shown above that the inclusion or exclusion of the acclimation period sometimes



changed the MLND considerably. The presence of a few additional MO2 values whenthe animal was at SMR can help this method to identify a distribution that correspondsto SMR, and conversely, the addition of a few MO2 values associated with low levelsof stress or agitation can result in two distributions being merged into a single one thatoverestimates SMR. The addition or removal of data measured after 24 h can have thesame effect. Because the MLND estimate of SMR is used only when the C.V.MLNDis low, and when it is not, a quantile is used instead, and because quantile methodsperformed similarly with the main and truncated 24 h data sets, it is safe to recommendexperiments lasting 24 h to estimate SMR. When possible, longer experiments increaserobustness of the SMR determination and confirmation that MO2 values are similar onmultiple days at the time of low activity. It should be noted that the commonly usedlow10 and low10% are particularly sensitive to experiment duration; both methodsproduced significantly greater estimates of SMR when data sets were truncated at 12and 24 h.

Given the effect of experimental period on the SMR estimates, variants of the MLNDand quantile (q0⋅25) methods that made SMR calculation for every possible 24 h win-dow of the experiment in 1 h increments, starting at the beginning, were tested but arenot reported on. The lowest value for each method was retained. These sliding MLNDand q0⋅25 SMR estimates made it unnecessary to remove the data from the acclima-tion period and would, in theory, automatically remove periods when the animal isnot at SMR, such as after a fish has been fed. The added complexity of these meth-ods, however, did not result in a noticeable improvement, except for rare cases whenthe behaviour of an animal changed and the lowest MO2 values observed one day wereconsistently different from those observed the next or previous day [e.g. animals 27 and33; Appendix SII (Supporting Information)] or when an animal was at SMR reliablyat the same time each day, but for a very short period each time [animal 64; AppendixSII (Supporting Information)]. Given the improvements were marginal, it is simpler toreject extremely variable data sets, or to accept the error that comes with the recom-mended methods.

In summary, different variants of three different methods of estimating SMR wereevaluated and compared statistically for the first time using 85 data sets that includeda wide variety of fishes and one crustacean with very different metabolic states duringintermittent respirometry experiments. While the best approach should be as objectiveas possible, the analysis revealed the importance of initial visual inspection of raw MO2data for both trends and variance. Indeed, some data might be rejected on this somewhatsubjective analysis alone. Beyond the initial screening of MO2 data, it was clear that, ifthe fish was largely quiescent after the initial acclimation period (typically up to 10 h),the differences between the various SMR estimations were quantitatively very small,which made the selection of the estimation method less critical, although methods thatoffer no advantage or are biased, such as low10, which always underestimates SMR,should be avoided. When fishes were more active in the respirometer, however, the dif-ferences among the methods became appreciable and some SMR estimation methodsbecame unreliable. In these cases, a choice must be made among the SMR estimationmethods. To make the decision about fish activity less subjective, a novel recommenda-tion is to fit up to four normal distributions to the MO2 values and estimate the varianceof the lowest distribution as a guide to the method. Lastly, a series of general recom-mendations are provided below as a guide to estimate SMR in fishes. In addition, byproviding an R script that automatically calculates SMR with all the methods tested



here, as well as the variability in the lowest normal distribution, individual researcherscan make their own judgments and justifications for the SMR estimation method.

CONCLUSIONS

SMR is defined here as the rate of energy expenditure of a fish that is inpost-absorptive, calm, inactive state after proper thermal acclimation. These con-ditions can be difficult to satisfy. The following recommendations that stem fromthe present review and analyses are offered to increase the reliability of SMR esti-mates in fishes. (1) Use an appropriate respirometry system (intermittent-flow, properrespirometer size, sensitive and reliable oxygen sensors). Swimming respirometersand static respirometers can both be used. In both cases, precautions need to be takento avoid disturbing the fishes. (2) Fishes need to be fasted long enough to ensure thatdigestion and absorption of nutrients does not increase MO2. Postprandial metabolismin fishes can be elevated for close to a week under some conditions, especially at coldtemperature and after a large meal or multiple meals. Justification for the duration ofthe fasting period should be provided. Feeding conditions for the weeks leading toexperiments should be reported, at least in juvenile fishes, because they can influenceSMR. (3) Fishes should be acclimated to the experimental temperature for a propermeasure of SMR. It is necessary to report the duration of the thermal acclimation,and how quickly temperature was changed to reach the acclimation temperature. (4)SMR is influenced by body mass and ontogenic state, both should be reported. (5) Theduration of the measurement period that follows acclimation to a static respirometershould be justified. Ideally, experiments should last a minimum of 24 h after the initialacclimation period to ensure that any period of low activity is incorporated. Longerexperiments add robustness to all SMR estimation with the proviso that fasting fortoo long can lower MO2 below SMR. (6) Original MO2 data should be plotted asa function of time and by inspection the duration of the initial decline in MO2, theduration of the acclimation or recovery period can be determined. Report and justifythe duration of the acclimation period, and then remove these data before SMR isdetermined. SMR can be compared with this plot to ensure that the calculated SMRmakes sense and periods of activity are identified. (7) Adult fishes can exhibit elevatedMR during gonad maturation or spawning, making it impossible to measure SMR. Inthis situation, RMR should be reported, along with season and reproductive status. (8)Locomotor activity is energetically costly. The cost of locomotion can be estimated byforcing fishes to swim at different speeds in a swimming respirometer. Then, SMR canbe estimated by extrapolating the relationship between MO2 and speed back to zerospeed. Possible sources of error with this approach are explained in this review. (9)Locomotor activity can be considered in a large static respirometer by measuring MO2and fish activity simultaneously and statistically removing the effect of activity onMO2. (10) In the absence of information on fish activity, a mixture of up to four normaldistributions should be statistically fitted to the MO2 values, and the mean (MLND)and c.v. (C.V.MLND) of the lowest normal distribution should be calculated. Whenthe C.V.MLND is low(≤5⋅4%) the MLND method is a reliable estimator of SMR butwhen this is not the case, see next recommendation. (11) In the absence of informationon locomotor activity and when the MLND is unreliable, calculate the quantile of theMO2 values, with p= 0⋅2 or 0⋅25, to estimate SMR. Use MO2 plots to assess which



one is best for a given species and experimental setup. (12) If using the same methodfor all fishes of a study is preferable and the data for some fishes have high variability,use a quantile (q0⋅2 or q0⋅25, selected as in the previous recommendation) for all fishes.

Some of these recommendations, especially those dealing with the duration of thefasting period and of experiments, do not apply to fish larvae due to their high metabolicrequirements (Peck & Moyano, 2016). New technologies are making it possible tomeasure MO2 in the field. The stringent requirements for SMR recommended here arelikely to be impractical in the field, and results should be reported as RMR.

The authors are grateful to many persons who helped with the original data shown in this study:C. Audet, L. Beaudin, G. Claireaux, E. F. A. Christensen, T. Hansen, M. Jetté and R. Miller.The authors also thank the authors who provided data (see Table I). S. Killen, D. J. McKen-zie and anonymous reviewers were very helpful to improve the manuscript. This paper was aninvited review based upon decisions made within the EU COST Action FA1004, ConservationPhysiology of Marine Fishes.

Supporting Information

Supporting Information may be found in the online version of this paper:Appendix SI. R script to estimate the standard metabolic rate with multiple methods.Appendix SII. Oxygen uptake plots and frequency distribution of oxygen uptake valuesfor 85 fishes and crustaceans.Appendix SIII. Estimates of the standard metabolic rate with multiple methods for 85fishes and crustaceans.

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The determination of standard metabolic rate in fishes

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