From doubly labelled water to half-life; validating radio-isotopic rubidium turnover to measure metabolism in small vertebrates


Correspondence author. E-mail:


  1. The doubly labelled water method (DLW) is widely used to measure field metabolic rate (FMR), but it has some limitations. Here, we validate an innovative technique for measuring FMR by comparing the turnover of isotopic rubidium (86Rb kb) with DLW depletion and the rate of CO2 production (math formula) measured by flow-through respirometry (FTR) for two dunnart species (Marsupialia: Dasyuridae), Sminthopsis macroura (17 g) and Sminthopsis ooldea (10 g).
  2. The rate of metabolism as assessed by math formula (FTR) and 86Rb kb was significantly correlated for both species (S. macroura, r2 = 0·81, P = 1·19 × 10−5; S. ooldea, r2 = 0·63, P = 3·84 × 10−4), as was math formula from FTR and DLW for S. macroura (r2 = 0·43, P = 0·039), but not for S. ooldea (r2 = 0·29, P = 0·168). There was no relationship between math formula from DLW and 86Rb kb for either species (S. macroura r2 = 0·22, P = 0·169; S. ooldea r2 = 0·21, P = 0·253). We conclude that 86Rb kb provided useful estimates of metabolic rate for dunnarts.
  3. Meta-analysis provided different linear relationships between math formula and 86Rb kb for endotherms and ectotherms, suggesting different proportionalities between metabolic rate and 86Rb kb for different taxa. Understanding the mechanistic basis for this correlation might provide useful insights into the cause of these taxonomic differences in the proportionality. At present, it is essential that the relationship between metabolic rate and 86Rb kb be validated for each taxon of interest.
  4. The advantages of the 86Rb technique over DLW include lower equipment requirements and technical expertise, and the longer time span over which measurements can be made. The 86Rb method might be particularly useful for estimating FMR of groups for which the assumptions of the DLW technique are compromised (e.g. amphibians, diving species and fossorial species), and groups that are practically challenging for DLW studies (e.g. insects).


Energetics underlies many aspects of a species' biology, including reproduction (e.g. McAllan 2003), population dynamics and population density (e.g. Millar & Hickling 1990, 1992), ecological niche and many aspects of behaviour including movement throughout the landscape (e.g. Darling 1938). Field metabolic rate (FMR) measures the rate of energy use that has direct relevance to a species' biology and is particularly relevant ecologically because it is measured in the natural environment. Quantifying FMR has revolutionised the understanding and relevance of ecological energetics in general and ecophysiology in particular. The doubly labelled water (DLW) method is the most commonly used technique for measuring FMR, using the differential fractional turnovers of heavy isotopes of hydrogen (deuterium 2H, or tritium 3H) and oxygen (18O) to measure CO2 production (Lifson & McClintock 1966; Nagy 1983; Speakman 1997). Although DLW has revolutionised the measurement of energy use by free-ranging animals, validations of its accuracy are relatively rare in comparison with the large number of studies that have used the technique (see Williams & Nagy 1984; Williams 1985; Nagy et al. 1990; Tiebout & Nagy 1991; Bevan, Speakman & Butler 1995b; Bevan et al. 1995a; Speakman 1998; Jones et al. 2009). Validation for different taxa is important because there are several requirements for reliability of the technique that are not always easy to meet (Nagy & Costa 1980; Speakman 1997). The easiest of these assumptions to violate is ‘Assumption Three’ (Speakman 1997), that body water pool size (N) is constant throughout the measurement period. Further, because the estimation of CO2 efflux depends on subtracting the efflux of 18O as H2O from overall 18O losses (as CO2 and H2O), the method becomes unreliable for species with a high water efflux relative to metabolic CO2 production, such as amphibians (Hillman et al. 2009) and diving species (Bevan, Speakman & Butler 1995b; Bevan et al. 1995a). ‘Assumption Five’ (Speakman 1997), that all substances entering the animal are labelled at background levels, can also create problems for the DLW technique with species living in atmospheres that can become isotopically enriched by exhaled CO2 and H2O (such as fossorial rodents) because the re-influx of labelled CO2 and H2O can underestimate the fractional turnover rates (Nagy 1980). Furthermore, the most reliable FMR results are measured within one-to-two biological half-lives of the 18O isotope. For large animals, this is a week to 10 days (Speakman 1997), when the isotope concentration falls close to background levels and reliable measurements are no longer possible (Nagy 1983). For small animals this temporal window is much shorter (e.g. as little as 36 h for Tarsipes rostratus; Bradshaw & Bradshaw 2007), meaning that a large proportion of the measurement period is potentially compromised by capture and experimental procedures. Notwithstanding innovations by Anava et al. (2002), blood sampling is the most common and efficacious way of measuring DLW turnover, but Bradshaw & Bradshaw (1999, 2007) note that the stress of repeated blood sampling to measure isotope turnover may influence the subjects' metabolism (especially for small animals). Finally, the 18O-isotope is expensive to procure and analyse (Nagy 1983; Speakman 1997), and these costs can be prohibitive (Speakman 1997). While substantial effort has been expended to overcome or account for these errors using DLW, often very successfully (see Speakman 1997 and references therein), other techniques have been proposed to measure FMR that avoid these limitations.

Other methods that have been used to measure or infer FMR, including heart rate as an index of metabolic rate (see Cooke et al. (2004) and Green (2011) for review), labelled bicarbonate turnover (Hambly, Harper & Speakman 2002), and time/budget analyses (Buttemer et al. 1986). The most common alterative to DLW is heart rate biotelemetry, whereby the heart rate of a free-ranging animal is converted to FMR using a previously derived correlation of heart rate and MR of the animal (in the laboratory). Reservations have been expressed concerning the accuracy of this approach, based on the variability in stroke volume and/or extraction of oxygen by the tissues which will confound the relationship between heart rate and metabolic rate (Gessaman 1980; Green 2011 and references therein). Further, many approaches fail to quantify anaerobic activity, an important component of energy budgets (Cooke et al. 2004). The necessity to measure heart rate precludes its use in invertebrates with multiple cardiac pumps, and intake requires the O2 demand of tissues to be supplied by the heart exclusively (which is not the case in fish, for which the technique has had limited success; Thorarensen, Gallaugher & Farrrel 1996; Green 2011). The method is also very size-limited, because heart rate logger size should not exceed 2–5% of body mass (Caccamise & Hedin 1985; Gursky 1998; Cooke et al. 2004). Even the smallest heart rate monitors have focussed on fish of 200–250 g (Preide & Tytle 1977), and 17 g birds (Cochran & Wikelski 2005). Although telemeters are now small enough to measure the heart rate of small individuals, the battery life of such small units is short (Cooke et al. 2004), leading to similar potential compromising of the data by capture and experimental procedures, as already discussed for the DLW technique. Finally, despite its widespread use, Green (2011) notes that the validation of predictions using the heart rate method are still required to address the substantial variability in the response of heart rate to different environmental and physiological stimuli. The technique does, however, allow scope to identify the costs of specific behaviours (Bevan, Speakman & Butler 1995b; Bevan et al. 1995a, 2002; Green 2011) and to potentially correlate these behaviours to a species' ecology in such paradigms as dynamic energy budgets (Kooijman 2000), thus providing useful management information.

Another approach to the measurement of FMR relates the elimination of a radioactive isotope to metabolic rate (Odum & Golley 1963). Several isotopes, including 32P (Wagner 1970), 137Ce and 59Fe (Baker & Dunaway 1975), 22Na, 51Cr, 54Mn, 60Co, 65Zn and 86Rb (Peters et al. 1995; Peters 1996), have been investigated in this regard. Of these, 86Rb had the strongest correlation with the rate of carbon dioxide production (math formula), with an r of 0·96 for Dipsosaurus dorsalis (Peters et al. 1995), 0·82 for Bufo terrestris (Peters 1996) and 0·93 for T. rostratus (Bradshaw & Bradshaw 2007). Rubidium is an alkali metal that appears to be handled by the body in a similar manner to K+ (Adam & Craik 1989). If the biological turnover of 86Rb (86Rb kb) is proportional to metabolic rate, then measuring 86Rb kb offers the advantages for small animals of not requiring blood collection because the whole animal can be scanned for emissions and measurement can continue over a longer time span and at less expense than for DLW (Bradshaw & Bradshaw 2007). Limitations of the 86Rb technique are a paucity of validation data comparing 86Rb turnovers to math formula for various taxa (Bradshaw & Bradshaw 2007) and a lack of understanding of the mechanism(s) of 86Rb turnover. At present, general inferences about 86Rb kb and FMR cannot be made, and further validation studies are required to show whether FMR can be estimated from 86Rb kb for more than the few species studied so far (Peters et al. 1995; Peters 1996; Bradshaw & Bradshaw 2007).

Here, we report a laboratory study of the relationship between math formula [measured by DLW and by flow-through respirometry (FTR)] and 86Rb kb for two species of small marsupial, Sminthopsis ooldea and S. macroura (Marsupialia; Dasyuridae). If there is a good correlation between math formula and 86Rb kb for these dunnarts, then we can establish a predictive regression that could be used to calculate the FMR of free-ranging individuals. We also examine whether there is a general relationship between math formula and 86Rb kb for small vertebrates (using published data from other taxa).

Materials and methods

Animal capture and maintenance

Eight male S. macroura and eight male S. ooldea were captured from various locations within their natural distribution in Western Australia and transferred to the University of Western Australia (Crawley campus) within a week of capture. They were maintained at a regime of 18 °C for 12 h at night, followed by 28 °C for 12 h during the day, on a diet of c. 1 g of minced red meat (generally kangaroo; Macropus spp.), a similar portion of canned cat food and three mealworms (Tenebrio molitor larvae) per day. The dunnarts were housed separately in containers c. 40 × 50 × 30 cm, on a bed of wood shavings and with a cardboard shelter and other environmental stimuli (such as toilet rolls, mouse toys and shredded paper). Average mass of S. macroura was 17·7 ± 0·42 g, and average mass of S. ooldea was 9·9 ± 0·29 g.

Isotope comparisons

The methodology closely followed a previous validation study for the use of 86Rb to estimate FMR (Bradshaw & Bradshaw 2007) with minor changes consistent with methods that have previously been used to estimate FMR by DLW for Sminthopsis crassicaudata (Nagy et al. 1988). The metabolic rate was assessed by DLW, 86Rb kb and FTR using eight individuals of each species. Each individual dunnart was injected with a mixture of DLW and 86RbCl, and a blood sample was taken to assess equilibration levels of the various isotopes, following a two-sample DLW approach (Speakman 1997). After isotopic enrichment, the dunnarts were held for at least 48 h in a FTR system (see below), during which math formula was measured continuously. Before injection of the isotopes (Speakman & Racey 1987: method D), two blood samples (20 μL) were taken from the infraorbital sinus (Halpern & Pacaud 1951) using preheparinized 100-μL capillary tubes, and the blood was flame-sealed in vacuum-evacuated Pasteur pipettes (Nagy 1983; Speakman 1997) for distillation. The dunnarts were then injected with 0·1 mL of a solution containing 0·5 MBq of 86RbCl (Perkin Elmer, Brisbane Australia) and 0·15 mL of 66% 18O and 50% 2H, enriching them to c. 10 000 ppm 18O and 8000 ppm 2H of the total body water (TBW) volume. Two hours after injection, an equilibration blood sample was taken. After the respirometry trials, a final 20 μL ‘recapture’ blood sample was taken.

Whole-body counts of 86Rb gamma emissions were made before enrichment, two hours post-enrichment and then daily. At each measurement time a minimum of three, 60-s emission counts were made until the coefficient of variation of the average count was <1%, using a Nucleonics PSR8 portable gamma counter (Nucleonics, Edinburgh, UK) with a 5 × 5 × 5 cm sodium iodide (NaI) crystal. For whole-body counting, the dunnarts were confined in an upright, seated position in a 5-cm-diameter plastic vial placed directly over the NaI crystal. The plastic vial was then covered with a lead shield so that the animals remained in the dark, and the NaI crystal was sheltered from background radiation. Movement of the dunnarts was minimal once in darkness, and repeatable counting was achieved once the dunnarts assumed a stable upright sitting position.

The entire protocol (backgrounding, enrichment, equilibration, 2-day respirometry and ‘recapture’ measurements) was performed twice for each dunnart, once at 20 °C and once at 30 °C, in random order. Our rationale was that these temperatures would alter metabolic rate and therefore math formula, allowing comparison of respirometry, DLW and 86Rb kb MRs in situations of altered metabolic rate. It was expected from previous experiments (Geiser & Baudinette 1985; Song, Kortner & Geiser 1995; Tomlinson, Withers & Maloney 2012a,b) that 30 °C would be thermoneutral for the dunnarts, while 20 °C would be below the thermoneutral zone and would result in approximately a doubling of the metabolic rate (Tomlinson, Withers & Maloney 2012a,b). Following the second period of respirometry, the dunnarts were maintained at 30 °C and 86Rb counts were made daily until complete washout had occurred, to determine the ideal time span over which to measure 86Rb kb.

‘FMR’ and turnover calculations

Blood samples were microdistilled (Nagy 1983; Speakman 1997) by gently heating the base of the vacuum-sealed pipettes over several days at c. 40 °C on a Selby hot plate fitted with a custom-made microdistillation unit. The proportion of 2H and 18O in each distillate sample was measured by injecting 2 μL of water manually into an elemental analyser (HT Elementaranalysator HEKAtech GmbH, Wegberg, Germany) accurate to at least 0·01 atom% for deuterium and 0·20 atom% for 18O (one standard deviation) that was connected via a Conflo III Universal Interface (Thermo, Bremen, Germany) to a Delta V Advantage isotope ratio mass spectrometer (Thermo) in the stable isotope laboratory of the Leibniz Institute for Zoo and Wildlife Research in Berlin. Metabolic rate (math formula) was calculated following Speakman (1997) to account for fractionation between the isotopes (Speakman 1997: eqn 7.17), after estimating TBW using the 18O dilution space method (Speakman 1997). Total body water averaged 12·9 ± 0·8 g (c. 73% of body mass) for S. macroura and 6·4 ± 0·5 g (c. 64% of body mass) for S. ooldea.

Gamma emission counts of 86Rb were corrected for isotopic decay because of its short half-life (18·66 day), by dividing all sample counts by the exponential decay constant for 86Rb (e−kp × t; Bradshaw & Bradshaw 2007), where t is the time since enrichment. The biological turnover (kb) of these corrected 86Rb isotope counts between equilibrium and ‘recapture’ was calculated as:

display math

where EC and RC are the corrected equilibrium and ‘recapture’ counts, respectively, and t is the elapsed time in days. The total body burden of the 86Rb isotope at any time (qt) was calculated as:

display math

where q0 is the initial level of enrichment in MBq, kb is the biological turnover, kp is the physical rate of radioactive decay and t is the time elapsed in days.


The average daily metabolic rate (ADMR) was measured using two FTR systems (see Withers 2001). Compressed air flow, regulated at 437 mL min−1 (STPD) by an Aalborg GFC-17 (Aalborg, New York, NY, USA), and a Brooks 5871-A (Brooks Instrument, Hatfield, PA, USA) mass flow controller, passed through a cylindrical PVC chamber (270 × 250 mm; c. 1·4 L) maintained at a constant temperature. Temperature within the system was measured by Vaisala HMP 35B and HMI 33 probes (Vaisala Oyj, Helsinki, Finland). Excurrent air was dried by a Drierite column (anhydrous calcium sulphate; W. A. Hammond Drierite Co. Ltd.) and passed through a David Bishop 280 Combo gas analyser (David Bishop Instruments Ltd., Warwickshire, UK) to measure O2 and CO2. The gas analysers were calibrated to zero per cent O2 and CO2 using N2 (BOC Gases, Welshpool, WA, Australia), to 20·95% O2 using room air and to 0·53% CO2 using a calibration gas mixture (BOC Gases). Data were collected using a PICO ADC11 data acquisition board (Pico Technology, St Neots, Cambridgeshire, UK) and recorded using custom-written Visual Basic (v6) software. Incurrent air was not dried (averaging c. 7% RH), and CO2 was not removed from the excurrent air stream prior to O2 measurement. Baseline readings of background FIO2 and FICO2 were established for two hours before and after metabolic trials. Metabolic data were analysed by a custom-written Visual Basic (v 6.0) program to determine the average math formula for the entire exposure period at each Ta. During the respirometry trials, food and water were available ad libitum, and the dunnarts were not postabsorptive. All results were averaged over the total respirometry trial (in days) and so are representative of ADMR and not BMR.


The number of body pools involved in the isotope turnover was estimated by calculating the ‘reaction progress variable’ for each species from the daily qt over the full washout period (Cerling et al. 2007). Metabolic rates (both DLW and respirometry) and 86Rb kb were compared within species at the two experimental Tas using Student's t-test. Reduced major axis regression, which accounts for errors in both measured variables without specifying either to be dependent upon the other (Clarke 1980), was used to compare the 86Rb kb with math formula obtained from both DLW and from FTR, by incorporating all measurements from both experimental Tas into a single regression data set. RMA regressions were calculated for both DLW and 86Rb kb using pooled data from both species, and the mean absolute percentage error (MA%E) was calculated for each comparison (Mayer & Butler 1993; eqn 2). The effect of time on 86Rb kb was tested using Helmert a priori contrasts to compare the daily mean kb with the mean of all subsequent days. All statistical analyses were conducted using statistiXL v.1.7, except the a priori contrasts that were calculated using custom-written software based on Rencher (2002). Values are given as mean ± SE, and regressions were performed using the metabolic rates of individuals as independent data points.


86Rb biological turnover

The emission counts of 86Rb fitted an exponential decay, reflecting the physical decay of the isotope as well as its biological turnover (Fig. 1). The lower detection limit of the Nucleonics scintillation counter corresponded to a total body burden (qt) of c. 0·008 MBq, which was reached about 20 days postenrichment for both species maintained at 30 °C. At day 14, the average qt was approximately five times the detection limit (0·042 ± 0·003 MBq for S. macroura, 0·040 ± 0·007 MBq for S. ooldea). During the initial 14-day period, 86Rb kb averaged 0·121 ± 0·005 day−1 for S. macroura (n = 7) and 0·130 ± 0·015 day−1 for S. ooldea (n = 7). Helmert a priori contrasts suggested that the turnovers for the first and second day were significantly higher than all subsequent days for both species (TS. macroura(day 1) = 3·87, d.f. = 6, P = 0·008; TS. macroura(day 2) = 4·01, d.f. = 6, P = 0·007; TS. ooldea(day 1) = 2·77, d.f. = 5, P = 0·039; TS. ooldea(day 2) = 3·56, d.f. = 5, P = 0·016). A change in turnover was not supported by curve splining, where a fractional contribution of one indicates an equal contribution to washout at each interval. For S. macroura, the fractional contribution was eb = 0·92 ± 0·023, and for S. ooldea, the fractional contribution was eb = 1·01 ± 0·049 across the entire washout period. Over the 2-day respirometry period, the 86Rb kb for both species was significantly higher at 20 than at 30 °C (S. macroura T8 = 3·28, P = 0·011; S. ooldea T6 = 3·44, P = 0·014; Table 1).

Table 1. The effects of ambient temperature on three measurements of metabolism for two species of dunnart. There was an increase in all three measurements for both species between Ta = 30 and 20 °C, but this was not significant for doubly labelled water (DLW) in either species
Ta (°C) Sminthopsis macroura Sminthopsis ooldea
2030td.f. P2030td.f. P
  1. ADMR, average daily metabolic rate.

  2. Data are mean ± SE (n).

86Rb (−1)0·23 ± 0·02 (7)0·14 ± 0·01 (7)

t8 = 3·2


0·27 ± 0·02 (8)0·17 ± 0·01 (7)

t6 = 3·4


DLW (−1)1·10 ± 0·120 (5)0·86 ± 0·152 (5)

t8 = 1·2


0·84 ± 0·153 (4)0·75 ± 0·084 (4)

t6 = 0·5


Respirometry ADMR (−1)1·34 ± 0·09 (7)0·95 ± 0·04 (7)

t8 = 4·2


0·84 ± 0·04 (8)0·53 ± 0·04 (7)

t6 = 9·4

8·09 × 10−5

Water Turnover Rate (−1)8·32 ± 1·11 (5)8·82 ± 0·39 (5)

t8 = 0·3


4·78 ± 0·57 (4)4·17 ± 0·37 (4)

t13 = 0·9


Figure 1.

Exponential decay of 86Rb for Sminthopsis macroura (●) and Sminthopsis ooldea (○) in thermoneutrality. Solid lines represent the lines of best fit for the exponential decrease in 86Rb. The data are the percentage of initial enrichment remaining, incorporating both physical decay and biological elimination, and show the time for which reliable measurements could be made, which is necessarily limited by the interaction of biological elimination and physical decay. The grey area beyond day 14 represents the time when average qt was within one order of magnitude of the lower detection limit. Data are mean ± SE, n = 8 for each species.

CO2 production

The ADMR measured by FTR was significantly higher at 20 than at 30 °C for both species (Table 1). There was no difference in DLW math formula between 30 and 20 °C for S. macroura or S. ooldea (Table 1). Water turnover rate was not different for either species between 30 and 20 °C (Table 1). The ADMR of dunnarts maintained in their housing boxes during the subsequent 14-day washout period at 30 °C, calculated using the regression relationship of 86Rb kb to math formula (see below), was 1·03 ± 0·02−1 for S. macroura (n = 7) and 0·57 ± 0·04−1 for S. ooldea (n = 7). These values were not significantly different from the ADMR measured by FTR at 30 °C (S. macroura T12 = 2·12, P = 0·055; S. ooldea T11 = 0·668, P = 0·518).

Measurement method comparisons

There was a significant linear relationship between metabolic rate determined by respirometry (FTR math formula) and 86Rb kb for both species: S. macroura (math formula = 3·50[± 0·50] 86Rb + 0·603[± 0·08]; Table 2; Fig. 2a) and S. ooldea (math formula = 3·03[± 0·51] 86Rb + 0·13[±0·10]; Table 2; Fig. 2a). There was a significant linear relationship between FTR math formula (−1) and DLW math formula (−1) for S. macroura (Table 2 Fig. 2b), but not for S. ooldea (Table 2; Fig. 2b). There was no relationship between 86Rb kb and DLW math formula for S. macroura (Table 2; Fig. 2c) or S. ooldea (Table 2; Fig. 2c). There was a general significant relationship (pooled from both species) between DLW math formula and FTR math formula (Table 2) and also between FTR math formula and 86Rb kb.g (Table 2). The mean absolute per cent error (MA%E) for the RMA regression between DLW math formula and FTR math formula was 17·1%, while the MA%E for the RMA regression between 86Rb kb and FTR math formula was 18·2%. In comparing both turnover techniques to FTR math formula, S. macroura had a much lower MA%E (DLW = 12·0%, 86Rb kb.g = 15·3%) than did S. ooldea (DLW = 23·6%, 86Rb kb.g = 21·2%).

Table 2. Linear relationships between flow-through respirometry (FTR math formula), doubly labelled water (DLW math formula) and 86Rb kb for each species individually, and pooled together to test for generalised relationships
  Sminthopsis macroura Sminthopsis ooldea POOLED
FTR math formulaDLW math formulaFTR math formulaDLW math formulaFTR math formula
86Rb kb

F1,13 = 50·2

P = 8·20 × 10−6

r2 = 0·79

F1,8 = 0·42

P = 0·535

r2 = 0·06

F1,13 = 22·5

P = 3·84 × 10−4

r2 = 0·63

F1,6 = 0·02

P = 0·906

r2 = 0·003

F1,16 = 19·0

P = 2·20 × 10−9

r2 = 0·68

DLW math formula

F1,8 = 15·5

P = 0·004

r2 = 0·66


F1,6 = 3·50

P = 0·111

r2 = 0·37


F1,28 = 59·2

P = 4·92 × 10−4

r2 = 0·54

Table 3. A comparison of regression slopes in all the species for which 86Rb kb relationships with math formula have been reported, showing significant differences between endotherms and ectotherms
EctothermsEndotherms P
  1. a

    Four data points excluded (see text).

Dipsosaurus dorsalis 7·52 × 10−3 Tarsipes rostratus a 9·19 × 10−4 
Bufo terrestris 8·86 × 10−3 Sminthopsis macroura 4·38 × 10−3 
Sminthopsis ooldea 2·48 × 10−3 
P 0·6195 P 0·0173 
General9·37 × 10−3General3·44 × 10−32·289 × 10−12
Figure 2.

Linear regression relationships individual metabolism values for Sminthopsis macroura (●) and Sminthopsis ooldea (○); (a) 2-day averaged 86Rb turnover against math formula measured by respirometry [r2 (S. macroura) = 0·81, r2 (S. ooldea) = 0·63]; (b) 2-day averaged 86Rb turnover against math formula measured by the doubly labelled water (DLW) method [r2 (S. macroura) = 0·22, r2 (S. ooldea) = 0·21]; and (c) math formula measured by the DLW method against math formula measured by respirometry [r2 (S. macroura) = 0·43, r2 (S. ooldea) = 0·29]. Solid lines represent significant regression relationships.


The use of DLW for measuring FMR (Lifson, Gordon & McClintock 1955; Lifson & McClintock 1966) has been widely recognised as a revolution in ecophysiology (Speakman 1997; Bradshaw & Bradshaw 2007). The technique permits informative measures of the energetics of free-ranging animals. Subsequent refinements and broad application of the technique to a range of taxa, however, have revealed some limitations to the technique (Bevan, Speakman & Butler 1995b; Bevan et al. 1995a; Speakman 1997; Bradshaw & Bradshaw 2007). The aim of the present study was to test the reliability of an alternative method for estimating FMR by making the first quantitative study of the correlation between 86Rb kb and metabolic rates estimated by DLW and respirometry simultaneously. The work can be considered as an extension of previous validation work that compared 86Rb kb with DLW (Peters et al. 1995; Bradshaw & Bradshaw 2007) or respirometry (Peters 1996).

DLW validations

When we compared our measures of metabolism (math formula) made by DLW and FTR math formula, we found that DLW overestimated FTR math formula by about 12% for S. macroura and 24% for S. ooldea. The larger error for S. ooldea likely reflects the higher variability of metabolic rates reported for this species compared with S. macroura due to more labile thermoregulation (Tomlinson, Withers & Maloney 2012a,b), and the large discrepancies may not reflect uncontrolled methodological errors, but represent genuine variability in the metabolic rates of S. ooldea. Some previous studies have also reported that DLW overestimates math formula, generally by about 8% (Speakman & Racey 1988; Nagy et al. 1990; Tiebout & Nagy 1991; Speakman 1998), but other studies report underestimation of metabolic rate (e.g. Williams & Nagy (1984), Williams (1985), Nagy et al. (1990), and Speakman (1998) and references therein). Most of these studies based on their comparisons on the species mean of math formula measured by DLW compared to the mean of another method, while our correlation of individual responses using several techniques to estimate math formula revealed high levels of inter- and intra-individual variation, congruent with Speakman's (1998) suggestion that there is low repeatability of DLW for reasons yet to be understood.

Generality of 86Rb as a measure of FMR

The rationale for the present study was to investigate whether 86Rb kb was correlated with math formula for two species of dunnart and could therefore be used as a measure of FMR for free-ranging dunnarts, and the significant relationships that we obtained suggest that we can predict FMR of dunnarts by measuring 86Rb kb. However, combining our data with previous comparisons of 86Rb biological turnover to math formula (expressed here as−1; Fig. 3) provide a more general test of 86Rb kb as a measure of FMR. We found that the slope of the relationship was significantly steeper (F2,33 = 31·2, P = 2·0 × 10−8) for ectotherms (9·3 × 10−3) than endotherms (3·4 × 10−3), indicating that ectotherms have a higher turnover of 86Rb per CO2 consumed. Initial examination of the relationship between math formula and 86Rb kb for endotherms suggested a shallower slope (F2,31 = 4·64; P = 0·017) for T. rostratus (Bradshaw & Bradshaw 2007) than the two dunnarts in the present study, with T. rostratus exhibiting smaller increases in 86Rb kb for a given increase in math formula than the dunnarts. Bradshaw & Bradshaw (2007) found that a power curve best fit their data, as a result of four extremely high metabolic rates measured during inclement conditions at their study site that were inconsistent with relationship at the lower DLW math formula and 86Rb kb. Following exclusion of these four unreasonably high points, their data were similar to ours, which are the only other validations conducted for endotherms. In our data, there was a significant regression between 86Rb kb and math formula with a slope of 4·0 × 10−3. As a result, although we do not suggest the use of 86Rb kb as the only or even the best alternative technique to DLW, given the large volume of work exploring heart rate telemetry (see Cooke et al. (2004) and Green (2011) for review) and other techniques (Hambly, Harper & Speakman 2002), our meta-analysis suggests that 86Rb kb has a general relationship with math formula for all of the taxa studied so far.

Figure 3.

Comparisons of previous regressions of 86Rb turnover with metabolism (converted here to math formula in−1 from the original published data sets) for the toad Bufo terrestris (∆, r2 = 0·67; Peters 1996), lizard Dipsosaurus dorsalis (□, r2 = 0·93; Peters et al. 1995), Tarsipes rostratus (◊, r2 = 0·74; Bradshaw & Bradshaw 2007), Sminthopsis macroura (•, r2 = 0·73) and Sminthopsis ooldea (■, r2 = 0·46). The overall endothermic relationship is 86Rb = (3·4 × 10−3) × math formula − (4·6 × 10−4) (r2 = 0·76, P = 2·9 × 10−12), and the ectothermic relationship is 86Rb = (9·3 × 10−3) × math formula − (2·1 × 10−4) (r2 = 0·96, P = 4·7 × 10–22). All published regressions used to compile this figure were significant.

Our understanding of the physiology and biochemistry of 86Rb kb is currently poor. Being an alkali metal of higher molecular weight than potassium, it is thought that Rb+ is substituted for K+ in metabolic processes (Adam & Craik 1989; Bradshaw & Bradshaw 2007). The precise nature of that substitution is not known, and so a sound theoretical basis for why 86Rb kb reflects metabolic rate is lacking. Hence, there is currently an apparent requirement to validate the FMR–86Rb kb relationship for each species in which it might be used. To validate that relationship requires some measure of FMR as a comparator. Flow-through respirometry is recognised as the best method of measuring standardised energy use by animals other than direct heat production (Frappell 2006). Techniques that measure ADMR (such as isotope turnovers) require long washout times, as shown in Fig. 1. Therefore, when respirometry is used to validate isotope methods, there is a requirement to make comparisons over a long period. With this in mind, FTR should provide a reliable avenue to validate 86Rb kb.

The significantly different slopes of the relationship between math formula and 86Rb kb that we have identified for ectothermic and endothermic species raise questions concerning the generality of the 86Rb technique. Endotherms apparently have a lower 86Rb kb for a given math formula than ectotherms, but a more intuitive way of interpreting these data may be that endotherms have higher math formula for any given 86Rb kb, perhaps consistent with the higher metabolic scope of endotherms compared with ectotherms (Hemmingsen 1950; Schmidt-Nielsen 1983; Withers 1992). It will be interesting to see whether future studies indicate that eutherian mammals conform to endothermic expectations and whether the relationship is different for birds, as may be expected by their phylogenetically related higher metabolic rates (Schmidt-Nielsen 1983; Withers 1992). Although there are clearly two different relationships, potentially due to basal energy requirements, these relationships are both robust and significant, and we conclude that 86Rb kb is a reliable method to infer FMR of ectotherms and endotherms.

The rate of 86Rb washout measured here supports the proposition made by Bradshaw & Bradshaw (2007) that the washout of 86Rb is slower than H and O isotopes, and so it allows a longer period between enrichment and recapture than the DLW technique. In a previous study of FMR of Sminthopsis made using DLW, the data collection period was limited to 3 days because of the rapid washout of DLW isotopes (Nagy et al. 1988). The 86Rb washout rates measured here suggest that FMR could be estimated using 86Rb for as long as 14 days after enrichment for Sminthopsis. Despite the fact that curve splining (Cerling et al. 2007) suggested only a single pool turnover system for the elimination of 86Rb, the significantly higher 86Rb kb in the first 2 days following enrichment may result in noise in those initial days that require a longer washout period to attenuate, suggesting that the longer the animals can be left free ranging, the more reliable will be the estimate of FMR. A longer period between initial enrichment and final recapture reduces the proportion of the washout period that an animal spends in captivity relative to the free ranging.

Advantages of the 86Rb technique to infer FMR, at least for small animals, include lower cost, lower equipment requirements and technical expertise, reduced animal stress during measurement and the longer time span during which effective measurements can be made (Bradshaw & Bradshaw 2007). Our results provide much to support some of these advantages for the 86Rb method. Our 86Rb turnover measurement cost was c. 12% of our DLW measurement. Given that isotope and analysis costs are cited as prohibitive restrictions to measures of FMR in large species (Westerterp & Speakman 2008; Zub et al. 2009), 86Rb potentially provides a very useful tool for investigations in large species. The further complications of correct and complete sample distillation and sometimes complex calculations required to correct for changes in body mass, body water content and dilution spaces, make DLW the more complicated of the two methods, even in a controlled laboratory validation. Where the 86Rb technique is to be used in the field, costs and ethical limitations of any study can be much reduced, and NaI crystal gamma counters are portable, allowing measurements to be made in the field. A practical limitation at present is the necessity to validate the 86Rb kb to math formula relationship, which can be achieved using FTR in the laboratory, but this is not straightforward for large species.

There are several limitations currently associated with 86Rb kb, not least of which are the indirect method of estimation, the paucity of comparative validation for the technique and a poor understanding of the mechanism(s) of turnover. Even the generalised regression lines for ectotherms and endotherms may not provide a sufficiently specific correlation between math formula and 86Rb kb for a particular species, because very little is known about the comparative physiology of normal potassium metabolism other than for pathological disorders (Greenberg et al. 1938; English 1966). Without a general understanding of the role of K+ in metabolism, and whether it correlates with metabolism under all conditions, any taxonomic generalities about 86Rb kb remain difficult to interpret. Furthermore, if 86Rb is a proxy for K+, then it will be distributed mainly in the intracellular space, and using blood to estimate total body burden of 86Rb will vary with haematocrit. A second difficulty that remains to be overcome for the 86Rb technique is a limitation of size. Whole-body counting of animals much larger than the dunnarts studied here becomes impossible, or at the very least expensive, and the equipment involved becomes nonportable. Subsampling of a body pool, such as blood from larger animals, may provide an avenue to measure gamma emissions and infer the total body burden of 86Rb, but this has not been validated. The 86Rb isotope required also has substantial safety and environmental concerns associated with the control of radioactive substances. It must be explicitly noted; however, that the levels of enrichment required for small animals constitute a fraction of the internationally recognised safe limits of exposure of 1 mGyd−1 (International Atomic Energy Agency 1992; Peters et al. 1995). Radiation exposure levels were monitored during this study by the Australian Radiation Council for all participants, and dangerous exposure was never recorded, even during high-intensity laboratory validation programmes. The risks of working with smaller animals are negligible providing that proper equipment and training are available. This risk is likely to increase with the levels of enrichments required for larger animals and may become a radiation hazard to the experimenters and to the animals themselves. To avoid this, the dosage requirements to optimise the signal to noise ratio need to be further investigated. Finally, DLW gives the advantage of measuring both math formula and water flux (Nagy 1983; Speakman 1997), but 86Rb kb cannot presumably provide any information on water use. There are also some practical requirements for the use of radioisotopes to measure metabolism (compared to the stable isotopes used for DLW), including the need to have current radiation licences and appropriate training for the use of unsealed radioisotopes, and the need for appropriate decontamination and waste disposal.

Future research

We have established that there is a good correlation between the directly measured math formula and 86Rb kb for dunnarts, and general correlations for ectotherms and endotherms. Validation studies on more taxa are still required to establish whether correlations between 86Rb kb and metabolic rate can be generalised or whether validation is required on a species-by-species basis. It remains to be established whether the same relationship holds for all endotherms (e.g. eutherian mammals, passerine and nonpasserine birds). While there remain questions regarding the generality of the 86Rb kb technique as a measure of FMR, validation of the method will permit measurements for problematic species with a high water turnover relative to math formula, such as in nectarivores (Williams 1985; Weathers & Stiles 1989; Powers & Conley 1994; Geiser & Coburn 1999; Voigt, Kelm & Visser 2006; Bradshaw & Bradshaw 2007), diving species (Bevan, Speakman & Butler 1995b; Bevan et al. 1995a; Sparling et al. 2008; Jones et al. 2009) and amphibians (Hillman et al. 2009). Similarly, FMR could be measured for fossorial animals, where the atmosphere within a burrow may become DLW enriched and the isotopes re-enter the animal (Nagy 1980). This is because the 86Rb isotope is not volatile (i.e. it cannot enrich the atmosphere of the burrow) and is unlikely to re-enter the animal passively by respiration in the same way that DLW may do. Problematic taxa such as these should be studied to determine if 86Rb kb does provide a meaningful measure of FMR. The assumption that 86Rb is a K+ analogue should be tested, and appropriate dosimetry of 86Rb enrichment to body mass should be optimised to make the method safer and more efficient. This would go some way to informing how the assimilation of 86Rb into the metabolic pathways reflects metabolic processes.


This research was funded by the School of Animal Biology, UWA and the Holsworth Wildlife Research Endowment (ANZ Philanthropy Partners) and Fundação de Amparo a Pesquisa do Estado de São Paulo, Brazil (FAPESP – proc. 2008/57687-0). S.T. was supported by an Australian Postgraduate Award. A.P.C.N. would like to thank Fundação de Amparo a Pesquisa do Estado de São Paulo (FAPESP) for a scholarship while at the University of Western Australia and Curtin University. All animal procedures conformed to guidelines of the National Health and Medical Research Council and were approved by the Animal Ethics Committee of The University of Western Australia under permits RA/3/100/654, RA/3/100/704 and RA/3/100/868, and by the Radiation Safety Office of The University of Western Australia under permits 08/01/01. We acknowledge S.D. Bradshaw's advice and loan of equipment.