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J. Anim. Sci. 2005. 83:842-851
© 2005 American Society of Animal Science


ANIMAL NUTRITION

Comparing efficiency of metabolizable energy utilization by rainbow trout (Oncorhynchus mykiss) and Atlantic salmon (Salmo salar) using factorial and multivariate approaches

P. A. Azevedo*, J. van Milgen{dagger}, S. Leeson* and D. P. Bureau*,1

* Department of Animal and Poultry Science, University of Guelph, Guelph, Ontario N1G 2W1, Canada; and and {dagger} Unité Mixte de Recherches sur le Veau et le Porc, Institut National de la Recherche Agronomique, 35590 St. Gilles, France


    Abstract
 Top
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 Implications
 Literature Cited
 
A study was conducted to compare utilization of ME for growth vs. maintenance in rainbow trout and Atlantic salmon. Fish were hand-fed to satiation one of four isoenergetic diets (DE = 20 MJ/kg, as-fed basis) with different digestible protein (DP) to DE ratios (24, 22, 20, and 18 g/MJ). Intake of ME (kJ/d), energy deposited as protein (PD, kJ/d), and energy deposited as lipid (LD, kJ/d) were determined by a comparative slaughter technique. Data were analyzed by a factorial approach or by multivariate analysis of PD and LD on ME. Maintenance energy requirements (MEm) and efficiency of ME utilization for PD (kp) and LD (kf) were estimated with both approaches. For the multivariate analysis, an additional parameter, the fraction of ME intake above maintenance used for PD (X) was defined as linear function of BW, with slope (d) and intercept (c) estimated simultaneously with the above parameters. Estimates were highly dependent on the approach and assumptions used. The MEm and kp values were higher and less accurate with the factorial approach than with multivariate analysis. The factorial approach estimated unrealistic kf values (kf > 1). With the multivariate analysis, MEm did not differ between species (20 kJ•d–1•kg–0.8). On the other hand, kp was significantly higher (e.g., 0.52 ± 0.06 vs. 0.43 ± 0.06; P < 0.05) for salmon than for trout and independent of diet, but kf was 0.81 (±0.13) regardless of species or diet. The ME intake above MEm used for PD (c) was higher in salmon than trout (57 vs. 55%; P < 0.05). The change in partitioning of ME for PD due to the change in BW was negative for trout (d = –0.18), but positive for salmon (d = 0.16). The d values agreed well with the increase of LD:PD ratio with BW for trout and the decrease of LD:PD with BW for salmon, which may have been related to the maturation status of this fish and the associated loss of body lipid observed by maturing salmon. In conclusion, MEm and cost of LD were similar for rainbow trout and Atlantic salmon, but the cost of PD was lower for salmon than for trout.

Key Words: Energy Efficiency • Energy Requirements • Oncorhynchus mykissSalmo salar


    Introduction
 Top
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 Implications
 Literature Cited
 
Comparative studies have shown that rainbow trout and Atlantic salmon have different G:F when reared under similar experimental conditions and feeding protocol (Azevedo et al., 2004aGo,bGo; Krogdahl et al., 2004Go). The basis for this difference is not clear and this suggests that nutrient utilization differs between these two salmonid species. As shown in pigs, differences in G:F among different pig genotypes (Noblet et al., 1999Go; van Milgen and Noblet, 1999Go; Kolstad et al., 2002Go) were explained in part by differences in the allocation of energy between growth and maintenance. Similar studies have not yet been conducted for salmonid species.

The allocation of dietary energy in animals between maintenance, protein, and lipid growth has often been investigated by a factorial approach. Since its development by Kielanowski (1965)Go, the regression of ME intake (dependent variable) as a function of protein deposition (PD) and lipid deposition (LD) has been very useful to investigate partitioning of ME between maintenance, protein, and lipid growth in various animals (e.g., Klein and Hoffmann, 1989Go; Noblet et al., 1999Go). van Milgen and Noblet (1999)Go have proposed a multivariate approach to overcome some of the limitations of the factorial approach. In this multivariate approach, PD and LD (dependent variables) are considered a function of ME intake. Multivariate analysis allowed more accurate analysis of ME partitioning in pigs compared with the factorial approach (van Milgen and Noblet, 1999Go); this type of analysis has not yet been applied to fish.

The objectives of this study were to investigate the partitioning of ME for maintenance and growth in growing postjuvenile rainbow trout and Atlantic salmon using factorial and multivariate analyses.


    Materials and Methods
 Top
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 Implications
 Literature Cited
 
Diets
Four isoenergetic (DE = 20 MJ/kg, as-fed basis; Table 1Go) diets containing digestible protein (DP) to DE ratios (i.e., 24, 22, 20, and 18 g/MJ) were formulated by decreasing the DP content from 53 to 39% and by increasing the lipid level from 19 to 24% (as-fed basis). Digestibility of energy and nutrients of the experimental diets was determined for rainbow trout and Atlantic salmon in a previous study (Azevedo et al., 2004aGo).


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Table 1. Composition of experimental diets
 
Fish and Experimental Conditions
Rainbow trout (1 yr old; initial BW = 268 g ± 3% [mean ±CV]; Ontario domestic strain; fall spawning) and Atlantic salmon (2 yr old; initial BW = 456 g ± 7% [mean ±CV]; anadromous strain; offspring from captive wild brood stock originating from LaHave River, New Brunswick, Canada) were obtained from the Alma Aquaculture Research Station (Alma, Ontario, Canada) and from the Ontario Ministry of Natural Resources, Ringwood Fish Culture Station (Ringwood, Ontario, Canada), respectively. The animals were kept in accordance with the guidelines of the CCAC (1984)Go and the University of Guelph Animal Care Committee.

Fifty-five fish were randomly allocated to each of 24 rectangular fiberglass tanks (1,087 L), with three tanks per diet per species. Each tank was considered an experimental unit. The aquatic system was supplied with well water at 26 L/min (1.1 turnovers/h). Water temperature averaged 8.5°C (±0.2) throughout the feeding trial. Lighting was programmed to mimic natural photoperiod (Alma Aquaculture Res. Stn., lat 80°26'W, long 43°42'N, February to December). Oxygen and flow rates were measured weekly. Dissolved oxygen never fell below 7 mg/L.

Fish were acclimated to the experimental conditions for a 2-wk period, during which time they were fed a commercial trout diet (Martin Mills, Elmira, Ontario, Canada). Fish were then fed the experimental diets for 308 d. The fish were carefully hand-fed to near satiety the experimental diets twice weekly as two meals a day. During the other days of the week, fish were fed the experimental diets in predetermined rations by belt-feeders programmed to discharge feed twice daily at times similar to hand feeding. Fish were weighed every 28 d.

Fish Sampling and Chemical Analyses
On the first day of the experiment, 12 fish from each species were selected randomly, anesthetized with tricaine methanesulfonate (200 mg/L), killed with a sharp blow to the head, and kept at –20°C until analysis. This procedure was repeated at 84, 168, and 308 d in the feeding trial (5 to 10 fish sampled per tank). Whole fish, dressed carcass, and viscera were weighed, and samples of dressed carcass (including kidney) and of viscera (including liver and gonads) were pooled (per tank) and frozen for analysis of whole-body chemical composition.

Whole fish bodies were cooked in an autoclave. The autoclaved fish carcasses were then ground into a homogeneous slurry in a Waring blender. The ground samples were transferred into shallow dishes, frozen, and subsequently freeze-dried. These samples were subsequently ground again and stored at –20°C before analysis.

Diets and fish carcass were analyzed for DM and ash according to AOAC (1995)Go, for CP (%N x 6.25) with a Kjeltec autoanalyzer (model No. 1030, Tecator, Hoganas, Sweden), for lipid using the method of Bligh and Dyer (1959)Go, and for GE with a Parr 1271 automated bomb calorimeter (Parr Instruments, Moline, IL).

Calculations
Metabolizable energy (kJ/d) was calculated according to the following equation:


where GE intake (IE) and fecal energy losses (FE) were determined and reported by Azevedo et al. (2004a)Go. Urinary and branchial energy losses (UE + ZE) were calculated according to the following equation:


where DN is the digestible N intake; RN is the retained N; and 24.9 kJ/g is the energy loss per gram of N loss in fish (Cho and Kaushik, 1990Go). Retained energy (RE) was calculated as follows:


Mean heat values of protein and lipid combustion used to convert protein and lipid body gain to respective energy gain were 23.6 and 39.5 kJ/g, respectively (Brafield and Llewellyn, 1982Go). The rate of energy deposited as protein was calculated according to the following equation:


and the rate of energy deposited as lipid was calculated as follows:


The exponent for expressing metabolic BW (b) was fixed at 0.8 because this exponent seems valid for many fish species (Hepher, 1988Go; Clarke and Johnston, 1999Go) or alternatively, b was estimated from the model.

Models for Partitioning of ME Utilization
In the factorial approach, the partitioning of ME was represented according to the following model:


where a x BWb = ME for maintenance (MEm) in kJ/d; a = coefficient of MEm in kJ•kg BW–b•d–1; b = metabolic BW exponent; kp = partial efficiency of energy utilization for protein deposition; kf = partial efficiency of energy utilization for lipid deposition; PD = energy deposited as protein, kJ/d; and LD = energy deposited as lipid, kJ/d.

In the multivariate model, the partitioning of ME was represented by a system of two equations:


[1]


[2]

where PD = energy deposited as protein, kJ/d; LD = energy deposited as lipid, kJ/d; ME = ME intake, kJ/d; MEm = maintenance energy requirement (MEm = a x BWb, kJ/d); a = coefficient of maintenance energy requirements (kJ•kg BW–b•d–1); b = metabolic BW exponent; and X = the fraction of ME intake (above maintenance) designated for PD. It was assumed that X decreased linearly with increasing BW (van Milgen and Noblet, 1999Go) according to the following function:


where ci = fraction of ME used for PD at the lowest BW (for fish group i); di = is the change in partitioning of ME toward PD due to the change in BW (kg–1, for group i); and BW0i = smallest BW for fish group i.

Statistical Analyses
The ME, RE, PD, and LD were experimentally measured variables for each experimental unit (tank), but MEm, kp, and kf were parameters estimated either by the simple nonlinear regression, factorial, or multivariate models. Data were analyzed using the NLIN procedure of SAS (SAS Inst., Inc., Cary, NC). A logarithmic transformation of the factorial model and of their dependent variable (ME) was performed to account for heteroscedasticity of the error.

In the multivariate analysis, a statistical weighting scheme (for PD and LD) was adopted so that the weight was inversely proportional to the residual variation. Weighting was required because the magnitudes and residual standard deviations of LD were higher than those of PD and consequently, the residual variances could be different for each equation. Initially, data for each equation were assigned the same weight, after which the residual variances for PD and LD were determined. These variances then served to establish a new weighting scheme. The procedure was repeated until no further changes in the residual variances were observed (van Milgen and Noblet, 1999Go).

Parameter estimates for kp, kf, and MEm by either models and their respective standard errors were obtained using the Gauss-Newton iterative method with a convergence criterion of 10–8.

Hypotheses concerning treatment effect (species) on the estimated parameters by these models were tested by comparing the fits of models using the extra sum of squares principle (Ratkowsky, 1983Go) where F-values were compared with Fc-values for significance at P < 0.05. F-values were calculated according to the following equation:


where RSS1 = residual sums of squares of Model i; RSS2 = residual sums of squares of Model i + 1; dfr1 = residual df (Model i); dfr2 = residual df (Model i + 1); MSE2 = mean square error of Model i + 1; Model i is a simpler model of a more complex Model i + 1 The Fc-values were calculated as Fc = F(dfr1 – dfr2), dfr2. If Fc > F, then the simplified Model i was accepted and the more complex Model i + 1 rejected.


    Results
 Top
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 Implications
 Literature Cited
 
Energy Balance Data and Pearson Correlation Coefficients
The overall mean, standard deviation, minimum and maximum values of ME, average BW, RE, PD, and LD are given in Table 2Go. The Pearson correlation coefficients were obtained to determine the degree of linear relationships between variables ME, average BW, RE, PD, and LD for the dataset of postjuvenile fish (Table 3Go). Linear correlations between ME and RE were above 0.75, indicating a high degree of linear correlation between ME and RE. The linear correlation of ME with LD was above 0.75 (r = 0.759; P < 0.001), but the correlation between ME and PD was low (r = 0.276; P < 0.001). The correlations between BW and PD and LD were lower than 0.5 (P < 0.001). The correlation between PD and LD was not significant (r = –0.102).


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Table 2. Energy balance data for the postjuvenile rainbow trout and Atlantic salmona
 

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Table 3. Pearson correlation coefficients between variablesa
 
Factorial Partitioning of ME for Maintenance and Protein and Lipid Gain
The effect of species and diet on partitioning of ME for MEm, PD, and LD with the factorial model was analyzed according to the extra-sums-squares principle (Ratkowsky, 1983Go) and is presented in Table 4Go and Figure 1Go.


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Table 4. Comparison of fits for postjuvenile rainbow trout and Atlantic salmon to determine species and diet and species and diet effects on maintenance and efficiency of ME for protein deposition (kp)a,b
 


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Figure 1. Energy retained (RE, kJ/d) as protein (PD, kJ/d) or lipid (LD, kJ/d) depending on metabolizable energy intake (ME, kJ/d) for postjuvenile rainbow trout and Atlantic salmon fed four isoenergetic diets with different digestible protein:DE ratios and reared at 8.5°C. {blacktriangledown} = PD for rainbow trout; x = LD for rainbow trout; {triangledown} = PD for Atlantic salmon; + = LD for Atlantic salmon.

 
The simultaneous estimation of MEm, kp and kf for postjuvenile rainbow trout and Atlantic salmon by the factorial approach resulted in kf estimates higher than 1. A kf of 0.9 was assumed for the tests presented in Tables 4Go and 5Go.


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Table 5. Parameter estimates (asymptotic standard errors) for describing ME intake, kJ/d, as a function of metabolic body weight and energy retention (kJ/d) according to a factorial modela
 
When MEm by species was estimated with different kp values for each species and diet combination (eight kp values), with b = 0.8 and kf assumed to be 0.9, this model could be reduced to a simplified model of common MEm and two kp values as reported in Table 5Go. If b were to be estimated, the model did not converge, even when the number of possible iterations was increased from 100 to 10,000. It was therefore decided to fix the value of b at 0.8. In this case, MEm was not affected by species (34.6 ± 3.6 kJ•d–1•kg–0.8; Table 5Go). When kf was assumed to be 0.9, there was a species effect on kp. The efficiency of ME utilization for PD was 0.53 and 0.81 for rainbow trout and Atlantic salmon, respectively. Because there was a significant species effect on kp for a given diet (Test B-A; Table 4Go), the hypothesis that one species was consistently more efficient than the other was tested (Table 4Go) by adding a new parameter "e" and replacing kp2 by e x kp1. The estimate for "e" was 1.53 and kp1 = 0.53, consequently, kp2 = e x kp1 = 1.53 x 0.53 = 0.81, which indicated that regardless of diet, the kp of salmon was on average 53% higher than the kp of trout (Tables4Go and 5Go). Alternatively, a model with kp by species also estimated 0.81 and 0.53, respectively, for kp2 and kp1.

Multivariate Analysis of ME Partitioning for Maintenance and Protein and Lipid Gains
The multivariate analysis procedure allowed accounting for the fact that PD and LD are the result of variation in ME intake and not the converse, as assumed in the factorial approach. This approach, however, required a hypothesis concerning the partitioning of ME intake above maintenance between PD and LD. In the present study, it was assumed that the proportion of ME intake above maintenance for PD decreased linearly with increasing BW (van Milgen and Noblet, 1999Go). Therefore, with increasing BW, less energy was channeled to PD, but this relationship was not always consistent and depended on species (Table 6Go).


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Table 6. Comparison of model fits for postjuvenile rainbow trout and Atlantic salmon for describing protein (PD, kJ/d) and lipid deposition (LD, kJ/d) as a function of satiation metabolic energy intake (kJ/d) and body weight (kg) according to a multivariate modela
 
The MEm was not significantly different between postjuvenile rainbow trout and Atlantic salmon (20 kJ•d–1•kg–0.8, Table 7Go). On the other hand, values for c, d, and kp differed significantly between the two species, independent of diet. The fraction of ME for PD at the lowest BW (ci) for each species was higher for salmon compared with trout (0.57 vs. 0.55; Table 7Go). The change in partitioning of ME toward PD due to the change in BW was negative for trout (d = –0.18), but it was positive for salmon (d = 0.16; Table 7Go). The values of d for these two species agree well with the increase of LD:PD with BW for rainbow trout and the decrease of LD:PD with BW for salmon (Figure 2Go).


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Table 7. Parameter estimates (asymptotic standard errors) for describing protein (PD, kJ/d) and lipid deposition (LD, kJ/d) by postjuvenile rainbow trout and Atlantic salmon as a function of satiation ME intake (kJ/d) and body weight (kg) according to a multivariate modela
 


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Figure 2. Changes of LD:PD ratio (means across diets ± SEM; n = 12) of rainbow trout and Atlantic salmon as fish grew for a period of 308 d at 8.5°C in freshwater when fed diets with different protein:lipid ratios. The LD is the rate of energy deposited as body lipid; PD is the rate of energy deposition as body protein. Live BW is the average weight for fish between two consecutive fish samplings. The first-order polynomial for the change of LD:PD with BW was significant, P < 0.001. There was a linear increase and decrease (P < 0.05) of LD:PD with BW for rainbow trout and Atlantic salmon, respectively. Diet and species x diet interaction did not significantly affect the linear changes of LD:PD with BW. The second-order polynomial was not significant and also not affected by species, diet, and species xdiet effects. {blacktriangledown} = LD:PD for rainbow trout; {square} = LD:PD for Atlantic salmon.

 

    Discussion
 Top
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 Implications
 Literature Cited
 
Partitioning of ME Utilization: Species Effects
Maintenance requirements were comparable to MEm values reported by other studies with salmonids (e.g., Cho and Kaushik, 1990Go; Bureau et al., 2002Go; Storebakken, 2002Go). Although, there is no comparative study between these salmonid species at the sizes used in the present study, the estimates of basal metabolic rate (NRC, 1981Go) for these two species are within the same ranges (e.g., Cho and Kaushik, 1990Go; Grisdale-Helland et al., 2002Go) and this suggests that MEm should be similar between these two fish.

The effect of genotype on partitioning of ME between MEm and energy retained as protein or lipid via a factorial approach has been investigated in pigs (Noblet et al., 1999Go; van Milgen and Noblet, 1999Go; Kolstad et al., 2002Go), in mice and rats (Koong, 1977Go; Pullar and Webster, 1977Go), in broiler chickens (Leclercq and Saadoun, 1982Go), and in marine fish species (Lupatsch et al., 2001Go, 2003Go). The factorial approach has, however, not been used previously to investigate the partitioning of ME in different salmonid species. In most of the above-mentioned studies with pigs, mice and rats, and chicken, the maintenance requirement was assumed to depend on animal genotype, but the kp and kf were assumed to be independent of genotype. This may not be an appropriate assumption if there are differences in protein and/or lipid turnover rates related to the species per se, or if changes in turnover are caused by differences in energy intake. The above assumption may also not be appropriate if there are differences in the metabolic pathways (with different efficiencies) involved in protein and lipid turnover (Klein and Hoffmann, 1989Go; Carter et al., 1998Go; Reeds et al., 1998Go), consequently causing different kp and kf between different genotypes. Differences in biochemical pathways are unlikely to exist among salmonids (Medale and Guillaume, 1999Go). Differences in protein turnover rates may exist among salmonids with different growth rates, but this aspect has not been compared for salmonid species.

Species effect on kp and kf were investigated simultaneously with MEm for sea bream, sea bass, and white grouper by Lupatsch et al. (2003)Go; however, the comparison of MEm and kp and kf in that study was not supported by statistical analysis, but the factorial approach was used for the three species independently of each other. In the present study, the effects of species and diet composition on ME partitioning were analyzed by the extra-sum-of-squares principle (Ratkowsky, 1983Go). The same principle was used in studies of the effect of pig genotypes on partitioning of ME utilization (Noblet et al., 1999Go; van Milgen and Noblet, 1999Go).

The estimates for kp obtained were similar to those obtained in other fish (e.g., Rodehutscord and Pfeffer, 1999Go; Lupatsch et al., 2003Go) and other animals (e.g. Pullar and Webster, 1977Go; van Milgen and Noblet, 1999Go). The kp values obtained in this study were, however, quite variable (0.53 to 0.81). Klein and Hoffmann (1989)Go compared data presented by different authors in 41 articles published from 1977 to 1985, and reported values of kp that varied substantially from 0.38 to 0.63 in chickens and from 0.75 to 0.97 in pigs. Fuller et al. (1979)Go also compared experimental data from several authors working with growing pigs and reported that kp values varied from 0.35 to 0.80, decreasing with BW of the animals, whereas kf varied from 0.70 to 0.91.

Assuming that kf was not affected by species and was equal to 0.9, kp for postjuvenile trout was 0.53 vs. 0.81 for Atlantic salmon, irrespective of diet, suggesting a much greater efficiency of ME utilization for protein growth in salmon than in trout. The lower cost of protein deposition for salmon compared with trout suggests differences in protein metabolism between these two species. It is not clear why the cost of protein deposition would be lower in salmon than in trout. One reason might be that the kp reflects not only the energy cost for protein synthesis, but also other costs associated with body protein turnover, which can contribute considerably to the energy needs for protein deposition (Reeds et al., 1998Go) and therefore contribute to a lower kp in salmon. It is also hypothesized that the difference in the costs of protein deposition between salmon and trout is due to differences in the protein turnover rate and/or differences in the metabolic utilization of nutrients for protein deposition between these species. Testing this hypothesis requires further investigation.

Meyer-Burgdorff and Rosenow (1995)Go suggested that the high protein turnover in carp was likely the main reason for rather low energy efficiency for protein deposition. It is possible that kp differences obtained either between factorial and multivariate models and between different estimates within a model in the current study may not have any biological meaning; they may be the result of methodology, and therefore, the possibility of exclusively statistical meaning is not totally excluded. Further investigation on possible metabolic differences (e.g., protein turnover differences between these two species) will help to gain further insight into the aforementioned issues.

Partitioning of ME Utilization: Metabolic Body Weight
The metabolic rate and therefore the maintenance energy requirements strongly depend on fish BW. Typically, the relationship is expressed as an allometric equation of the form MEm = a x BWb. The scaling exponent (b) is a point of controversy in mammals and in fish. This is particularly true when considering scaling exponent for different BW within a species. For example, in mammals, there is controversy between body scaling exponents of 2/3 (White and Seymour, 2002) or 3/3 (Brody, 1945Go). White and Seymour (2002) found no support for a metabolic scaling exponent of 3/3. These authors reported that basal metabolic rate of 619 mammalian species from 19 orders was proportional to BW2/3.

In fish, reported b values also differ among studies. Clarke and Johnston (1999)Go reported a mean value of scaling exponent b of 0.79 (SE = 0.11, n = 183). This mean was obtained for 69 different postlarval teleost species living in a wide range of water temperatures. Resting metabolic rate (R, mmol of oxygen gas/h) was related to body mass (M = BW, g) by R = a x Mb. The exponent b was obtained after the model was fitted by least squares linear regression after logarithmic transformation of both variables. In all these cases, care was taken that experimental fish were either unfed or postabsorptive, and therefore avoided the effects of feeding on metabolic rate. Using a different approach involving carcass energy loss of fasting fish, Lupatsch et al. (1998)Go obtained an exponent b of 0.82. The use of feed deprivation periods to estimate maintenance requirements and metabolic BW exponent may not be correct as it assumes that the catabolism and metabolism of a fasting fish and fed fish are similar. Although a scaling exponent of approximately 0.8 (Hepher, 1988Go; Cho and Kaushik, 1990Go; Bureau et al., 2002Go) is commonly accepted, there is no generally accepted theoretical explanation for this value. The question of applying a single metabolic BW exponent in fish was considered to be acceptable for the various salmonid species. In fish, metabolic rates, basal metabolic rate, and maintenance requirement (NRC, 1981Go) can be five- to 30-fold lower than those of terrestrial vertebrates (Bureau et al., 2002Go). Given this aspect, together with the fact that the determination of these rates is never very precise, the error is greater than the differences obtained with different BW exponents for fish, making errors in BW exponents relatively inconsequential.

Partitioning of ME Utilization: Approach Differences
The partitioning of ME into MEm and RE assumes that the efficiency of ME utilization for protein retention and lipid deposition are identical, which is not likely to occur because kp should in theory be smaller than kf (ARC, 1981Go; Emmans, 1995Go).

The simultaneous estimation of kp and kf and MEm in the present study resulted in estimates similar to values obtained with other fish studies (e.g., Lupatsch et al., 2003Go). The simultaneous estimation of MEm, kp, and kf for the postjuvenile fish with the factorial approach, however, resulted in unrealistically high kf values (kf > 1). There was no significant linear correlation between PD and LD for the postjuvenile fish. Therefore, it is unlikely to be related to a multicollinearity problem (Roux et al., 1982Go; Slinker and Gliantz, 1985Go). The high interdependency of the estimates MEm, kp, and kf, and the possibility of overestimating MEm may have resulted in overestimation of kf and consequently the kf values were unrealistic. For this reason, the factorial partitioning of ME for MEm, kp, and kf in the current study assumed a kf of 0.9.

The multivariate analysis of PD and LD (dependent variables) on ME (independent variable) allowed for the simultaneous estimation of MEm, kp, and kf for the present data. The MEm and kp estimates with the multivariate model were lower compared with estimates obtained with the factorial approach for the same data-sets. Similar results were reported by van Milgen and Noblet (1999)Go, who also found slightly higher estimates for MEm and kp with the factorial approach (Noblet et al., 1999Go) compared with the multivariate analysis of the same dataset for pigs. Furthermore, these authors found kf in both studies were almost identical (0.83 estimated with the factorial approach [Noblet et al., 1999Go] vs. 0.82 estimated with the multivariate analysis [van Milgen and Noblet, 1999Go]). The kf estimated with the multivariate analysis varied between 0.81 and 0.85. These kf estimates are close to 0.9, supporting the appropriate assumption of a fixed kf of 0.9 in the factorial as kf in factorial approach would be expected to be either almost identical or higher than kf estimated by the multivariate analysis of the same data.

The multivariate analysis depended on the definition of the function of ME utilization above MEm for PD. The fraction X (0 ≤ X ≤ 1) represents the ME intake above maintenance that is used for PD, and the fraction 1 – X is the remaining fraction of ME intake above maintenance used for LD. The parameter X is not a constant; rather, it is affected by variables such as diet composition, feeding level, and degree of maturity of the animal with species and breed differences, and thus is a function of ME intake (Koong, 1977Go).

A Michaelis-Menton type equation was used by Koong (1977)Go to describe the effect of level of ME intake on the proportion of ME above MEm for protein and lipid synthesis. In the study by van Milgen and Noblet (1999)Go, the fraction X for ad libitum-fed pigs was defined as a linear function of the pigs’ BW. In the current study, fish were fed to satiation, and therefore, the effect of feeding level could not be studied as suggested by Koong (1977)Go. In the current study, it was assumed that X was a linear function of BW (van Milgen and Noblet, 1999Go). The linear model for the partitioning of ME above MEm for PD and LD as a function of BW was parameterized to include an intercept (c) within the observed range of BW specific for each dataset. The c and d estimates differed between rainbow trout and Atlantic salmon. The c value for rainbow trout was lower than for Atlantic salmon, suggesting that 55 and 57% of ME above MEm was utilized for PD for trout and salmon, respectively. The d value (i.e., ME above MEm diverted from PD to LD) increased as BW increased for rainbow trout. Similar d values were reported by van Milgen and Noblet (1999)Go for growing pigs. In contrast, postjuvenile Atlantic salmon did not divert ME above MEm from PD to LD, as the d value for this fish was positive. This result is also supported by the fact that the PD:LD ratio increased with BW for this fish, contrary to the other fish groups in the present study. The reason for the increase in PD:LD with increasing BW in postjuvenile Atlantic salmon is not clear, although it could be related to the maturation status of this fish and the associated faster gain of body protein compared with body lipid that is generally observed with maturing salmon (Morkore and Rorvik, 2001Go). In immature growing fish, as is generally the case in mammals, it is expected that PD:LD would decrease with increasing BW, and this situation occurred in the current study for the postjuvenile rainbow trout.

The output from the statistical approaches used in this study can be very useful to current energy requirement systems for fish (e.g., Cho and Bureau, 1998Go) by adding key parameters such as ME intake, MEm, and the efficiencies of ME utilization for protein (kp) and lipid deposition (kf) in a manner similar to the current feed requirement systems (e.g., NRC, 1998Go e.g., NRC, 2001Go).


    Implications
 Top
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 Implications
 Literature Cited
 
Statistical analyses of metabolizable energy partitioning for maintenance and retained energy for protein deposition and lipid deposition is a useful alternative to biochemical analysis of the costs of protein and lipid growth. These models allowed for the study of factors such as species and diet on the partitioning of metabolizable energy utilization. However, results were highly dependent on the model and model assumptions used. For salmonids from 200 to 1,600 g of body weight, efficiencies of metabolizable energy for protein deposition and lipid deposition of 0.51 and 0.81, respectively, are suggested.

1 Correspondence—phone: 519-924-4120, ext. 53668; fax: 519-767-0573; e-mail: dbureau{at}uoguelph.ca).

Received for publication June 9, 2004. Accepted for publication January 4, 2005.


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 Abstract
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 Materials and Methods
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 Literature Cited
 


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