Loss of deuterium in faecal solids and by sequestration in reindeer : effect on doubly labelled water studies

An underlying assumption when estimating total energy expenditure (TEE) using doubly labelled water (DLW) is that the injected isotopes ( l sO and 2H) leave the body only in the form of CO, and H 2 0 . However, both isotopes have additional routes of loss. We quantified the loss of 2 H (i) attached to faecal solids and (ii) by sequestration into newly synthesised fat in reindeer {Rangifer tarandus tarandus). Estimates of the errors caused by these processes were applied to data from DLW studies with reindeer in summer and in winter. Given the net rate of faecal dry matter output and lipid synthesis in the present study, ignoring both sources of error caused the TEE of reindeer to be underestimated by approximately 5% in winter and approximately 9% in summer. The separate effect of each source of error was evaluated in summer. If ignored, loss of 2 H through sequestration alone caused TEE to be underestimated by approximately 3.7%. Similarly, if ignored, loss of 2 H attached to faecal solids alone caused TEE to be underestimated by approximately 5.9%.


Introduction
The doubly labelled water (DLW) technique (Lifson et al., 1955) for the measurement of carbon dioxide production rate (rCC)2) and the estimation of total energy expenditure (TEE) has been applied in a wide variety of species of birds and mammals (e.g.Nagy, 1987;1994).The method is based on injection and subsequent measurement of the rate of disappearance of the oxygen isotope ls O and a hydrogen isotope (most commonly 2 H, although 3 H is also used) from the body water pool.The basic assumption underlying this method is that 2 H is washed out as water whilst ls O is lost as both water Rangifer, 20 (1), 2000 Rangifer,20(1): 31-41 and COz.The amount of C02 produced by the animal during the experiment can then be calculated from the difference in the rates of disappearance of the two isotopes.TEE in the same period can be calculated from the volume of CO, produced provided the respiratory quotient (RQ) is known.The successful application of the DLW method rests on the assumption that the isotopes leave the body only as H20 and C02.However, 2 H atoms in particular can also be lost from the body water pool by exchanging with 'H in labile positions on other molecules which are subsequently exported from the body (e.g.milk solids, faecal solids) and by sequestration into de novo synthesised molecules.
Notwithstanding its widespread application in physiological research, particularly in humans, the DLW method has been applied in only six species of ruminants (Fancy et al, 1986;Nagy et al, 1990;Parker et al, 1990;Midwood et al, 1994;Nagy & Knight, 1994;Gotaas et al, 1997;Haggarty et al, 1998).The paucity of DLW studies in ruminants can be attributed to uncertainty of (i) the effect of the large quantity of water in the gastrointestinal tract relative to the total body mass on the rate of equilibration of isotopically labelled water, (ii) the loss of 2 H in methane produced by microbial fermentation in the rumen, (iii) the loss of 2 H in faecal solids which might be of greater importance in ruminants than in monogastric animals because ruminants produce more faeces, and (iv) the sequestration of 2 H in de novo synthesised tissue, especially fat (e.g.Fancy et al, 1986;Midwood et al, 1993).
In reindeer, ?H20 injected either intravenously or intraruminally is fully equilibrated within 8 h (Gotaas & Tyler, 1995).The loss of 2 H in the methane produced by these animals results in an underestimation of the rate of production of C02 (rC02) measured by the DLW method of less than 3% (Gotaas & Tyler, unpubl.)compared to 6.5% in sheep (Midwood et al, 1989).The present study examined the remaining issues of non-water losses of 2 H in reindeer (Rangifer tarandus tarandus) (i) in labile positions on faecal solids ('exchangeable loss') and (ii) by sequestration into de novo synthesised fat.The effect of these processes on the DLW method were assessed by relating the results to data from two DLW studies in reindeer, one with four adult captive female animals in summer and in winter (Gotaas et al, 1997) and one with three young (22 months) free-living male animals in winter (Gotaas et al, in press).

Loss of 2 H in faecal solids
Experimental trials Trials were carried out in three adult (>4 years old) non-pregnant, non-lactating female Norwegian reindeer [A, B and C, mean body mass (BM) 86.2 (range 79-0 -91-0) kg in summer and 82.0 (range 78.0 -85.0) kg in winter} which had been accustomed to handling over several years.The study consisted of one summer experiment (conducted between 29th June and 13th July 1993) and one winter experiment (conducted between 11th January and 8th February 1994).Prior to and be-tween experiments the animals were kept together in an outdoor enclosure (approximately 2700 m 2 ) at the Department of Arctic Biology, University of Tromsø (69°40'N), where they had access to natural vegetation including birch {Betula pubescens), willows (Salix spp.) and sedges (Carex spp.) and were also provided with a commercially available pelleted ration, RF-80 (Bøe & Jacobsen, 1981) and water or snow ad lib.One week before and throughout each trial they were kept in individual semi-outdoors gravelled paddocks (area approximately 120 m 2 ) with ad lib.access to the pelleted ration and water or snow.
At each trial the animals were weighed to 0.1 kg on an electronic balance (Alpha-100, Farmer Tronic, Denmark) and then injected with sufficient DLW (approximately 90 g; enrichment of 2 H,0 and H2 ,8 0 of approximately 10%) to enrich body water to approximately 160 ppm excess.A 50 cm silicone tube leading from a 50 ml syringe containing physiological saline was connected to a catheter inserted into the left jugular vein.Pyrogen-free DLW made isotonic by adding 0.9% w/v NaCl was injected from a syringe into the lumen of the tube which was flushed with saline before the needle was withdrawn, thus ensuring complete administration of the isotopes.The exact amount of DLW injected was determined gravimetrically by weighing the dose syringe with its needle to 0.001 g before and after injection.
Between three and six days after dosing with DLW, samples of faeces (approximately 25 g wet weight per sample) were taken from the rectum of each reindeer, put immediately into screw-cap plastic vials and stored at -20 °C.
Exchangeable 2 H Four aliquots from each sample of faeces (each aliquot approximately 1.5 g wet weight, weight recorded to 0.0001 g) were placed in separate tubes and freeze-dried by vacuum sublimation using the method of Midwood (1990).The extracted water was combined by aliquot and stored at -20 °C prior to determination of 2 H.The remaining dry matter from each aliquot was then placed in a screw-cap vial to which was added 3 g of unenriched tap water, the exact amount and initial enrichment of 2 H of which was known.The vials were placed in a sonic water bath (Branson B2200 E4, U.S.A.) for three hours followed by a shaking water bath at 37 °C for 21 h to ensure thorough mixing of the dry matter and the wash-water.The wash-water was then removed by vacuum sublimation, combined by aliquot and stored at -20 °C for determination of 2 H. Calculation of apparent water flux due to loss of 2 H in faecal solids For each animal, we determined the apparent water flux due to loss of 2 H in faecal solids (expressed as g H20-g"' faeces dry matter (DM)) according to Midwood etal. (1993): mol 2 H-g 1 faeces DM g faeces DM moFH-g" 1 body water (equation 1) In equation 1, mol 2 H per gram faeces DM is determined by: mol 2 H'g 1 faeces DM = g wash-water wash-water final enrichment-10 ' 18.0152 g faeces DM (equation 2) where 'g wash-water' is the amount of wash-water added to the dry faeces, 18.0152 is the molecular weight of H20, 'wash-water final enrichment' is the 2 H20-enrichment (ppm excess) of the wash-water after resuspension and 'g faeces DM' is the amount of faecal dry matter to which the wash-water was added.
Mol 2 H per gram body water in equation 1 is given by: body water enrichment -10 '' moPH-g 1 body water = • 18.0152 (equation 3) where 'body warer enrichment' is the 2 H20-enrichment (ppm excess) of body water relative to the predose level.

Sequestration of 2 H in newly formed fat
Experimental trials Trials were carried out on five male reindeer (E, F, G, H and I) born in May 1994.The animals were taken to the Department of Arctic Biology from natural mountain pasture in northern Norway in March 1995.At the time of arrival the animals had a mean BM of 31.7 (s = 3.9; range 25.0 -35.0) kg.The animals were kept together in an outdoor enclosure (approximately 2700 m 2 ) where they had access to food and snow or water ad lib.as described above.After four months (i.e. in July 1995) the animals were moved to individual metabolism crares placed side by side in a temperature controlled room (temperature 5 to 10 °C) where they were exposed to simulated natural photoperiod and provided with the pelleted ration (RF-80) at approximately 90% of their ad lib.level.The animals were weighed to 0.1 kg on an electronic balance approximately once every ten days in the enclosure and once every three days while in the crates.After three weeks in the crates, the animals were weighed (mean BM 71.0 (J-= 5.9; range 61.5 -77.0) kg and a blood sample (10 ml), from which to assess background levels of 2 H, was collected from each animal via an indwelling catheter in the right jugular vein.Four of the reindeer were then injected with sufficient sterile, pyrogen-free 2 H20 (approximately 15 ml 99-8% enrichment) to enrich body water to approximately 300 ppm excess 2 H.The 2 H20 was injected intravenously in the left jugular vein in the manner described above.The control animal was injected intravenously with 15 ml sterile, pyrogen-free physiological saline.
A high level of 2 H was maintained in the body water pool of the four experimental animals to maximise the incorporation of 2 H into de novo synthesised fat by providing them with ad lib.drinking water with a known enrichment of 2 H (approximately 300 ppm excess) for three weeks following injection of the dose.The control animal was provided with local tap watet.Blood samples (20 ml) were collected from all animals once a week by jugular venipuncture using heparinized Vacutainer® tubes (Becton Dickinson Vacutainer Systems Europe, France) and centrifuged (15 min at l600g) immediately after collection.The plasma was then transferred to Ultrafree-CL S tubes (30 000 NMWL) (Nihon Millipore Ltd., Japan) and centrifuged for 2 h at 4300g in a Sorvall RC5C centrifuge equipped with a Sorvall SS-34 rotor (DuPont Company, Newtown, CT, U.S.A.).The ultrafiltrate was stored in cryo-tubes (Greiner labortechnik, Germany) at -20 °C prior to determination of 2 H.
All five animals were slaughtered three weeks post-injection.The gastrointestinal tract (oesophagus to anus) was emptied, washed with water and homogenised in a mincer (TK 20, Kilia Fleischer¬ eimaschinenfabrik, Fritz Reimers Gmbh.u.Co., KG, Kiel, Germany) together with all visceral organs.One half by weight of the homogenate was then ground with one sagittal half of the corresponding empty carcass (consisting of the animal including head and feet, but excluding skin and fur) in a grinder (Palmia No. 4726,Palmia,Sweden) equipped with a 18 mm mesh sieve.The resulting material was then homogenised in a mincer (TK 20).One kg of homogenate from each animal was freeze dried (Alpha 1-4, Martin Christ Gefrierertrockningsanlagen GmbH, Germany) and ground to powder in a commercial blender (Waring, New Hartford, CT, U.S.A.).Fatty acids (FA) were saponified with 30 ml of 2 M KOH and extracted with diethyl-ether from a 1 g aliquot of the dry powder from each animal following a procedure similar to that described by Haggarty et al. (1987) and Midwood et al. (1993).After sealed bomb combustion (McGaw et al., 1988) of the extracted FAs, the Calculation of apparent water flux due to loss of2 H from sequestration The apparent water flux due to loss of 2 H by incorporation into newly synthesised lipid was determined by combining a water equivalence factor based on the stoichiometry of 2 H incorporation into FAs, with the estimated rate of FA synthesis for each animal.The water equivalence factor (g H2O g 1 FA synthesised) was calculated according to Haggarty (1990) from the chemical composition of reindeer adipose tissue (Garton & Duncan, 1971) where the average fatty acid (FA) formula is Cn 298H,3 ;07O2 (mol wt 273.737 amu, triacylglycerol (TGA) mol wt 859.259 amu).Jungas (1968) showed that 53% of the hydrogen of synthesised FAs was derived from water.Accordingly, if all FAs in a sample are de novo synthesised, the 2 H enrichment in the FAs will be 53% of that in the precursor body water labelled with 2 H. Hence, the synthesis of one mole of FA in a reindeer will result in the incorporation of 17.865 moles of 2 H (33.707 • 0.53) and the deposition of one mole of TGA will result in the sequestration of 53.594 moles of 2 H, equivalent to 62.372 millimoles 2 H per gram fat (53.594/859.259• 1000).In terms of apparent water flux this corresponds to 0.5618 g H20 • g 1 fat synthesised.
The net rate of FA synthesis during the entire experimental period was estimated according to Haggarty et al. (1991): FA synthesis (mol) combustion water enrichment body water enrichment-0.53 •Total FA (equation 4) where the enrichment of both the water produced by combustion of FA and the body (precursor) water is given in ppm excess.The total FA content of the carcass is given by: weight of lipid (g) Total FA (mol) = 3 mol wight of lipid (amu) (equation 5) where the weight of lipid in the carcass is given in grams and the mol weight of reindeer lipid expressed in gram • mol 1 is calculated from data published by Garton et al. (1971).
Finally, the number of mol of 2 H in FA is given by: mol 2 H in FA=mol H in FA-2 H ppm excess in FA-10 6 (equation 6) where mol H in FA is the total number of moles of hydrogen in FA and the 2 H20 enrichment in FA is given in ppm excess.

Application of adjustment factors on data from DLW studies
The derived adjustment factors were applied to data from two previous DLW studies with reindeer in different physiological states to examine the effect of losses of 2 H through sequestration and in faecal solids on the estimates of rC02 and TEE.The first study was conducted on four captive, adult female reindeer (Fl, F2, F3 and F4) in summer and in winter (Gotaas et al., 1997) while the second was conducted on three free-living, sub-adult male reindeer (Ml, M2 and M3) in winter (Gotaas et al, accepted).The TEE values presented here for reindeer Fl, F2, F3 and F4 differ slightly from the previously published values owing to their being re-calculated using slightly altered equations.Moreover, unlike in the original DLW studies (Gotaas et al, 1997;accepted), no adjustment has been made for loss of 2 H through microbially produced methane.
The water equivalence factor derived from the measured loss of 2 H in faecal solids (g H20 • g _1 faeces DM) was combined with an estimate of total faecal DM output to yield an estimate of the apparent water flux due to loss of 2 H in faecal solids.Faecal DM output was estimated by combining an assumed food intake of the pelleted ration (RF-80) in captive female reindeer of 15 g DM • kg A BM in winter and 30 g DM • kg" 1 BM in summer (Gotaas & Tyler, unpubl.)and an assumed intake of lichen in free-living male animals of 15 g DM • kg 1 BM per day with known digestibilities of RF-80 and lichen Body water enrichment is given as ppm excess relative to the background level prior to injection of isotopes.Wash-water final enrichment is given as ppm excess relative to 'pure' wash-water (143.69 ppm).
The water equivalence factor of 0.5618 g H2O g 1 FA synthesised was applied to the data from the study in summer assuming that the specific net rate of FA synthesis (g FA synthesised • kg" 1 BM) in the adult females was the same as that recorded in the sequestration study presented here.The net rate of FA synthesis in free-living female reindeer in winter in this part of Norway is < 10 g-d 1 (Christiansen et al., 1997) and we therefore assumed that the loss of 2 H through FA synthesis was negligible in DLW studies in both captiye and free-living reindeer in winter.Hence, no adjustment for sequestration was made on data from the winter studies.

Isotope analyses
2 H20 in all samples was converted to hydrogen gas by zinc reduction (Wong et al., 1987) with the modification that 500 mg zinc was used for the reduction.The 2 H content was determined using a SIRA 10 isotope ratio mass spectrometer (VG Isogas, Middlewhich, UK).All analyses were performed in at least three replicates and the mean values were used in subsequent calculations.The coefficient of variation on repeated analysis was less than 0.4%.

Statistical analyses
Water equivalence factors calculated from loss of 2 H attached to faecal solids were compared between groups using the Mann-Whitney [/-test.H0 was rejected at P (two-tailed) > 0.05 in all tests.
The experiments described in this article have Rangifer, 20 (1), 2000 been conducted in accordance with current regulations for experimental research involving live animals in Norway.

Exchangeable loss of deuterium in faecal solids
The exchangeable loss of 2 H attached to faecal solids was equivalent to an apparent water flux of 0.09 to 0.17 g H20 • g 1 faeces DM in summer and 0.14 to 0.19 g H20 • g 1 faeces DM in winter (Table 1).However, the difference in the apparent water flux between seasons was not significant (P > 0.80) and a mean water equivalence factor of 0.15 g H20 • g 1 faeces DM (s = 0.04, n = 6; Table 1) was therefore used in the subsequent calculations.

Sequestration of deuterium into newly synthesised fat
The mean enrichment of 2 H in the body water of the animals over the 21 day experimental period was 266.9 ppm excess (s = 2.8, n = 4) relative to the control animal.The steady state concentration of 2 H20 was maintained throughout the experiment by the intake of labelled drinking water as the mean decline in enrichment of 2 H during the experiment was only 0.23 ppm • d 1 (s = 0.10, n = 4; Table 2).At the end of the experiment the mean enrichment of 2 H in water produced by sealed bomb combustion of extracted FAs was 41.2 ppm excess (s = 4.1, n = 4) relative to an identically processed sample from the control animal ( hl All enrichments of combustion water are given as ppm excess relative to the enrichment of combustion water from FAs from the control animal (reindeer I; 117.60 ppm).
factor of 0.5618 g H20 • g 1 fat synthesised, the sequestration of 2 H corresponded to a mean apparent water flux of 42.36 g • d 1 (s = 7.42, n = 4; Table 2).
A similar effect was found in captive female reindeer in winter ( Gotaas et al., 1997).Failure to adjust for loss of 2 H in faecal solids resulted in an average overestimation of JH2Q of 1.30% (s = 0.33, » = 4, Table 3), an underestimation of rC02 of 5.25% (s -0.46, n = 4, Table 3) and an underestimation of TEE of 4.73% (s -0.46, n -4, Table 3).The higher error on TEE in captive reindeer reflects the higher faecal DM output in these animals (Table 3).
Failure to adjust for loss of 2 H by sequestration and attached to faecal solids in captive reindeer in summer resulted in an overestimation of JH2D of 1.42% (s ' 0.21, » « 4, Table 3), an underestimation of rro2 of 9.00% (j = 2.34, * = 4, Table 3) and an underestimation of TEE of 9.10% {s = 2.06, n 4, Table 3).When examining each component separately, we found that adjusting for loss of 2 H

Discussion
The potential significance of losses of 2 H in faecal solids and through sequestration has been largely ignored in previous DLW studies in ruminants.For instance, Parker et al. (1990) made no mention of adjusting for these non-water losses of 2 H in a study of caribou (R. t. granti) and muskoxen {Ovibos moschatus) neonates despite the fact that the body mass of the experimental animals increased considerably during the period.Likewise, neither Nagy et al. (1990) in a study of two species of marsupials and of black-tailed deer (Odocoileus hemionus) nor Nagy & Knight (1994) in a study of springbok antelope {Antidorcas marsupialis) nor Fancy et al. (1986) in a study of caribou (R. t. granti) and reindeer (R. t. tarandus) reported making any adjustments to compensate for non-water losses of 2 H.We have shown, however, that unless adjustment is made for losses of 2 H attached to faecal solids and through sequestration in DLW studies with reindeer, TEE can be underestimated by approximately 5% in winter and by approximately 9% in summer.

Exchangeable loss of deuterium in faecal solids
The water equivalence factor due to exchangeable loss of 2 H of 0.15 g H20 • g 1 faeces DM in our rein-Rangifer, 20 (1), 2000 deer is 28% higher than the value of 0.117 g H20 • g 1 faeces DM in sheep (Midwood *<*/., 1993) and 56% higher than the assumed value of 0.096 g H20 • g 1 faeces DM in pigs (Haggarty a al., 1994).Haggarty et al. (1994) suggested that the difference in the water equivalence factor between sheep and pigs might be a consequence of the sheep being given a diet rich in cellulose and, hence, producing faeces with a higher proportion of sites available for exchange of 2 H.Our data suggest that the faeces produced by reindeer given a pelleted ration has an even higher proportion of hydrogen exchange sites.Despite the high water equivalence factor in reindeer compared to both sheep and pigs, the effect of exchangeable loss of 2 H on JH20 was low in free-living reindeer in winter (0.38%) compared to that in sheep (0.75%; Midwood et al., 1993) and in pigs (0.53% in pigs on a restricted diet and 0.98% in pigs fed ad lib.;Haggarty et al., 1994).This reflected the very low low estimated faeces DM output in the free-living reindeer in winter (126.3 g • d" 1 ).Faecal DM output in reindeer, however, varies both with season and diet.For instance, the estimated output in captive reindeer in winter was almost identical to that measured in sheep by Midwood et al. (1993)   but increased to 551.9 g • d" 1 in summer.By comparison, the faecal DM output in pigs has been found to be 320 g • d _1 in animals fed ad lib.(Haggarty et al., 1994).The resulting overestimate of JH2Q was therefore higher in captive reindeer than in both sheep and pigs (1.30% and 1.42% in captive reindeer in winter and in summer, respectively, but only 0.75% in sheep (Midwood et al, 1993), 0.53% in pigs on a restricted diet and 0.98% in pigs fed ad lib.(Haggarty et al, 1994)).Faecal DM output is clearly an important variable determining exchangeable losses of 2 H in highly seasonal animals like reindeer.Midwood et al (1993) took the further precaution of measuring the non-exchangeable loss of 2 H in faecal solids in sheep.They found the water equivalence factor due to this loss to be 0.013 g HjO-g 1 faeces DM (s = 0.002, n = 4), i.e. approximately 10% of the value derived for the exchangeable loss.Non-exchangeable losses of 2 H were not quantified in the present study.However, assuming that the ratio between exchangeable and nonexchangeable loss of 2 H is similar in sheep and in reindeer, this omission would introduce an error of only approximately 0.5% on the estimated TEE values when applying the adjustment factors on data from DLW studies with both captive and free-living reindeer.
A loss of ,s O would reduce the estimated error on rH20, rC02 and TEE.However, this effect is likely to 38 be small compared to the loss of 2 H due to the dominance of hydrogen over oxygen in most biological materials including faeces (Midwood et al, 1993).Therefore we did not measure the content of ls O in the wash-water from the faecal solids (i.e.exchangeable loss of ia O).

Sequestration of deuterium into newly synthesised fat
The water equivalence factor due to sequestration was 0.5618 g H20 • g 1 FA synthesised in reindeer.The corresponding value in sheep was 0.5536 g H20 • g 1 FA synthesised (calculated from data published by Midwood et al (1993)), in pigs 0.5599 g H,0 • g 1 FA synthesised (calculated from data published by Haggarty et al. (1991)) and in humans 0.5333 g H20 • g _1 FA synthesised (Haggarty, 1990).The differences between species are small owing to the similarity of the chemical composition of their adipose tissue and, consequently, any species differences in the error introduced to estimates of rm2, JH20 and TEE by sequestration cannot be due to differences in rhe stoichiometry of 2 H incorporation but will depend mainly on the rate of FA synthesis.Unlike the water equivalence factor, the rate of FA synthesis differed substantially between species.For instance, the estimated rate of FA synthesis was 75.39 g • d _1 in our reindeer compared to 0.42 to 6.37 g • d _1 in sheep (Midwood et al, 1993) and 10.2 g • d _1 in pigs fed a restricted diet (Haggarty et al, 1994).By comparison, pigs fed ad lib.a high Rangifer, 20 (1), 2000 carbohydrate diet had a much higher rate of FA synthesis (119-5 g • d 1 ; Haggarty etal, 1994).
Sequestration in our reindeer was quantified in the period from late July to mid August, coinciding with the annual peak in the rate of body mass increase and fat deposition recorded in caribou and reindeer (e.g.McEwan, 1968;Ryg & Jacobsen, 1982;Larsen & Blix, 1985;Tyler, 1987).Furthermore, the animals investigated (young males) are known to have proportionally the largest body mass increase during this period (McEwan, 1968;Ryg & Jacobsen, 1982).Given the age and sex of the animals, the timing of the study and the fact that they were given a high-quality ration, we assume that the estimated net rate of FA synthesis (75.39 g-d 0 and hence, the rate of incorporation of 2 H, was close to maximal.Our value, in fact, compares closely with the net rate of FA synthesis (approximately 70 g • d' 1 ) recorded in free-living adult female caribou (JR.t. groenlandicus) on a natural pasture in summer (Adamczewski et ah, 1987).

Error on measurements of rc02 and estimates of TEE in DLW studies
The ratio of [errors on rc02]: [errors on estimates of TEE] varied substantially between experiments.The non-water losses of 2 H generated an underestimate of rCD2 of 1.71% in free-living males in winter, 5.25% in captive females in winter and 9.00% in captive females in summer, respectively.These errors, in turn, translated into underestimates of TEE of 4.58%, 4.73% and 9-10%, respectively, in these three experiments.The ratios of [errors on tcccMerrors on estimates of TEE] in the different experiments were, thus, 0.37, 1.11 and 0.99, respectively.These ratios deviate both from unity and from each other because the estimate of rC02 depends on the proportion of the water loss exposed to fractionation (X), while the estimate of TEE depends both on X and the respiratory quotient (RQ) and the values of both X and RQ vary from experiment to experiment (Gotaas et al., 1997;in press).

Conclusions and perspectives
Loss of 2 H attached to faecal solids and through sequestration, so-called non-water losses, can be responsible for significant underestimation of TEE in reindeer determined using the DLW method.Given the net rate of lipid synthesis and the rate of faecal DM output described in the present study, Rangtfer, 20 (1), 2000 the non-water losses of 2 H caused TEE to be underestimated by approximately 5% in winter and approximately 9% in summer.The estimates of TEE can be significantly improved by the application of the adjustment factors described in this paper.Knowledge of the net rates of lipid synthesis and of faecal DM output is a prerequisite for making the necessary adjustments.
Energy is the universal currency used to measure and assess production and the efficiency of production in animals.At present, the DLW method is the only practical way of estimating TEE in free-living individuals over significant periods (days or weeks in large animals).Successful application of the DLW method, however, requires knowledge of the potential sources of error inherent in it and the generation of reliable adjustment factors to correct for these.The water equivalence factor used in the correction for non-water losses of 2 H in FA in the present study (i.e.g H20 • g 1 FA) can be assumed to be constant in reindeer because the composition of FA is unlikely to vary greatly throughout the year.This assumption may not be valid for faeces, however, and the water equivalence factor (g H20 • g~l faeces DM) might have to be revised depending on season.
Net rates of FA synthesis and voluntary food intake, and presumably also faecal DM output, are seasonally highly variable in reindeer and the latter, in particular, is poorly documented.Better data on faecal DM output combined with the water equivalence factors described in this study and known net rates of FA synthesis would enable complete correction for two important non-water losses of 2 H in any ecological or production context in which the energetics of free-living reindeer are studied.

Table 1 .
Calculation of the loss of exchangeable marker in faeces dry matter in three captive non-pregnant, non-lactating adult female reindeer in summer and in winter.

Table 2
Body water entichments are given as ppm excess relative to the mean enrichment of the body water of the control animal (reindeer I; 148.94 ppm).By comparison, the mean body water enrichment of all five animals prior to injection of isotope was 147.93 ppm (s = 0.30).
).The measured increase in the enrichment of FAs was equivalent to a mean rate of FA synthesis of 75.4 g • d 1 (s = 13.2, n = 4; Table2).Combined with a water equivalence Tabk 2. Sequestration of 2 H in fatty acids, rate of fatty acid synthesis and loss of 2 H converted into water equivalents (g-day') in four young (13 mo.) male reindeer in captivity in summer.

Table 4 .
Partitioning of non-water losses of 2 H to evaluate the separate effects of loss in faecal solids and through sequestration in studies in four captive, adult (>4 yrs), non-pregnanr, non-lactating female reindeer (Fl, F2, F3 and F4) in summer.