Adaptation of a non-ruminant nutrient-based growth model to rainbow trout (Oncorhynchus mykiss Walbaum)

Journal of Agricultural Science (2010), 148, 17 29. f Cambridge University Press 2009 17 doi:10.1017/s0021859609990037 Printed in the United Kingdom MODELLING ANIMAL SYSTEMS PAPER Adaptation of a non-ruminant nutrient-based growth model to rainbow trout (Oncorhynchus mykiss Walbaum) K. HUA 1 *, S. BIRKETT 2,C.F.M.DELANGE 1 AND D. P. BUREAU 1 1 Department of Animal and Poultry Science, University of Guelph, Guelph, Ontario N1G 2W1, Canada 2 Department of Systems Design Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada (Revised MS received 28 January 2009; First published online 1 June 2009) SUMMARY Models that accurately describe and predict growth and nutrient utilization of fish can be useful in developing strategies to improve the economic and environmental sustainability of aquaculture operations. Current bioenergetics models are not sufficiently flexible to be applied to the wide range of conditions encountered in aquaculture. There is a need to move from bioenergetics approaches to more mechanistic approaches based on nutrient utilization by fish. A non-ruminant nutrient-based growth model has been successfully used in pig production. The model explicitly describes the utilization of energy-yielding nutrients and metabolites for body protein deposition (Pd) and body lipid deposition (Ld) at the whole animal level. Partitioning of intake of energy-yielding nutrients between Pd and Ld is governed by a minimum ratio (minlp) of the body lipid mass (L) to protein mass (P), a maximum daily rate of Pd (PdMax), or maximum efficiency of using intake of the first limiting dietary essential amino acid (AA) for body Pd. The growth model was adapted to rainbow trout (Oncorhynchus mykiss (Walbaum 1792)) through parameterization and various modifications consistent with its framework. The fish nutrient-based model was evaluated by comparing model simulations with data from various experiments carried out with rainbow trout. Significant discrepancies between model predictions and experimental observations were observed. The model predicted energy retention well but did not always accurately predict growth rate, nor Pd and Ld. Overall, the model underestimated growth rate (expressed as thermal-unit growth coefficient (TGC)) by 37% and Pd by 15% and overestimated Ld by 13%. These discrepancies are probably attributable to differences in nutrient utilization and partitioning mechanisms between fish and pigs. The development of more reliable models requires better understanding of the nutritional and endogenous determinants of fish growth. INTRODUCTION Models that accurately describe and predict fish growth and nutrient utilization can provide a means to develop strategies for improving the economic and environmental sustainability of aquaculture operations. A number of bioenergetics models have been developed to predict growth, feed conversion ratio (FCR) and waste outputs of various fish species (Cho 1992; Cho & Bureau 1998; Kaushik 1998; Cui & Xie * To whom all correspondence should be addressed. Email: khua@uoguelph.ca 1999; Bureau et al. 2002, 2003; Lupatsch & Kissil 2005; Zhou et al. 2005). These models are simple and practical, but the limitations of the energetic approach have been increasingly recognized (Birkett & de Lange 2001a; Bureau et al. 2002; de Lange & Birkett 2005; Sandberg et al. 2005a, b). Energy systems simplify the partitioning of dietary components into protein deposition (Pd) and lipid deposition (Ld) on the basis of their heats of combustion; they also disregard specific metabolic roles of different nutrients and their interaction, and ignore significant differences in contribution of protein and lipid towards live weight gain. However, lipid reserves can

18 K. HUA ET AL. be mobilized to support Pd (Black 1974; Campbell 1988; Bureau et al. 2006). Pd and Ld also differ in energetic efficiencies (Emmans 1994; Birkett & de Lange 2001a; Bureau et al. 2002; Lopez & Leeson 2008). Furthermore, live weight gain is driven by Pd due to the close association of water with Pd, whereas Ld results in little or no weight gain (Shearer 1994; Dumas et al. 2007). In other words, combining dietary components solely on the basis of their energy values does not allow a complete evaluation of chemical composition of the feed, or an adequate account of the role of a specific component in the metabolic process, or an assessment of the composition of the biomass gain. Furthermore, these models are empirically based on statistical interpretations of experimental data and, therefore, cannot be legitimately extrapolated to conditions beyond which data are collected (Baldwin 1995; Thornley & France 2007). The current bioenergetics models are not sufficiently flexible to be applied to the wide range of conditions encountered in aquaculture (Bureau & Hua 2008). Biochemical models, based on an explicit representation of biochemical reactions in individual tissues, provide a more accurate representation of nutrient utilization. There are several dynamic fish models explicitly tracking the metabolic use of nutrients, such as that developed by Machiels & Henken (1986) for African catfish (Clarias gariepinus), and subsequent modifications or adaptations for tilapia (Oreochromis niloticus), rainbow trout (Oncorhynchus mykiss) (van Dam & Penning de Vries 1995), African catfish (C. gariepinus) and turbot (Scophthalmus maximus) larvae (Conceic a o et al. 1998). Recently a dynamic growth model was constructed based on explicit representation of metabolic pathways for Atlantic salmon (Salmo salar L.; Bar et al. 2007). These models are useful in understanding biological mechanisms, and can be applied to a wider range of conditions than empirical models. However, mechanistic models are often complex, and dynamic models based on differential nonlinear equations usually require special software; therefore, practical application at the production level can be hindered. Moreover, increased accuracy or precision cannot be guaranteed from increased details in a system (McNamara 2004). Construction of mechanistic models requires adequate knowledge of the system, and relies on sufficient and accurate data to quantify the perceived system (Baldwin 1995). The process of parameterization can be a major bottleneck in the development and application of models, particularly for complex mechanistic models (Kyriazakis 1999). In addition, a very small inaccuracy in one variable that may not be apparent in static models (describing a process at one time), can accumulate significantly over time in dynamic models (McNamara 2004). There is a need for a mechanistic approach to predict growth and nutrient utilization of fish while maintaining the general applicability in practical production systems. A nutrient-based model that combines empirical description of outcomes with conceptual equations provides a useful approach to deal with the main biological and physiological control points of nutrient partitioning in growing animals. Birkett & de Lange (2001a, b, c) suggested using a nutrient flow modelling approach to represent explicitly the material flows of nutrients and the transformations of these nutrients as they are processed by an animal, avoiding the limitations associated with metabolizable energy (ME) or net energy (NE) models of energy utilization. The nutrient-based model for growing non-ruminant animals developed by Birkett & de Lange (2001a, b, c) has been successfully used in pig production. The model describes explicitly the utilization of energy-yielding nutrients and metabolites for body Pd and body Ld at the whole animal level. Key to the model are rules that define partitioning of retained nutrients between Pd and Ld. This partitioning is constrained by three key parameters: an intrinsic upper limit to Pd (maximum daily rate of Pd (PdMax)), a minimum ratio (minlp) of whole body lipid (L) to protein (P) mass, and a maximum efficiency of using intake of the first limiting dietary amino acids (AAs) for Pd. PdMax is a concept that has been widely applied in swine nutrition. If energy intake is adequate, Pd increases with increasing supply of dietary AAs, governed by a maximum marginal efficiency of AA utilization, until reaching PdMax. AAs supplied in excess of requirements for Pd are catabolized. When Pd is below PdMax and is limited by energy intake, partitioning of energy-yielding nutrient intake to Pd and Ld is ruled by minlp. Being non-ruminant vertebrate animals, fish share similarities with pigs in terms of digestive physiology and metabolism, as well as nutrient partitioning and energy utilization. The nutrient partitioning rules in terms of PdMax and minlp employed in the framework of the pig nutrient-based model may be applicable to fish. Azevedo et al. (2004b) present some experimental evidence supporting the existence of PdMax in fish. In large rainbow trout reared at constant temperature, Azevedo et al. (2004b) observed that there was a linear increase of body weight (BW) over time, while body protein concentration remained constant. This resulted in constant Pd per day for fish fed to satiation (Azevedo et al. 2004b). The Pd curve developed for rainbow trout by Dumas et al. (2007) also supports the existence of PdMax in rainbow trout. A few studies support the existence of a minimum ratio of Ld to Pd in fish (Meyer-Burgorff et al. 1989; Azevedo et al. 1998). A constant ratio of Ld to Pd has been observed to be independent of feeding level in juvenile tilapia (initial body weight

Adaptation of a nutrient-based model to fish 19 Feed intake Diet composition Digestible lipid intake Digestible carbohydrate intake Digestible protein intake Fatty acids Starch/Sugars Amino acids Metabolites (NH 3, glucose, acetyl CoA, ATP) Lipid deposition Oxidation Protein deposition Basal ATP requirements Water + ash deposition Body weight gain Require energy (ATP) Produce energy (ATP) Fig. 1. A framework representing nutrient partitioning in growing fish. (IBW)=7 g) (Meyer-Burgorff et al. 1989), and in juvenile rainbow trout growing from 13 to 110 g (Azevedo et al. 1998). The objective of the current study was to investigate the extent to which the nutrient partitioning concepts used in the non-ruminant animal growth model of Birkett & de Lange (2001a, b, c) are applicable to fish by adapting the nutrient-based model to fish and evaluating its performance in predicting growth of rainbow trout (O. mykiss). MATERIALS AND METHODS The nutrient-based growth model presented by Birkett & de Lange (2001a, b, c) was adapted to fish through parameterization and various modifications consistent with its framework (Fig. 1). A detailed description of the complete conceptual and computational framework of the pig nutrient-based model, as well as its calibration procedure, can be found in Birkett & de Lange (2001a, b, c). Briefly, the deterministic and dynamic model with a one-day iteration interval extended the representations of nutrient utilization used in conventional animal growth models. Daily feed intake was characterized by the explicit flows of essential AAs, non-specific nitrogen, crude fat, starch, sugars and fermentable material. Nutrient use is prioritized as follows: (1) a basal (maintenance) requirement for AAs, nitrogen (N) and adenosine triphosphate (ATP) independent of production level; (2) the potential Pd consistent with the remaining available AA intake and the animal s (genetic) performance potential (PdMax); and (3) daily lipid retention as the sink for excess nutrient intake, based on the constraint of mass balances for individual metabolite flows. Additional constraints were imposed on the chemical composition of growth to maintain a minimum L to P ratio when energy intake limits Pd (minlp). The detailed procedures of model adaptation to fish are presented below. Although the model adaptation is intended to be applicable to fish in general, the values of parameters were empirically derived from studies conducted with rainbow trout. New metabolic factors pertinent specifically to fish were incorporated into the model to account for the determinant effect of water temperature on fish metabolism and the limited capacity of fish to utilize carbohydrates (Bureau et al. 1998). The model was then calibrated based on the energetic cost of Pd and Ld in rainbow trout as determined by Azevedo et al. (2005). Model adaptation Since fish are poikilothermic animals, their metabolic rate, growth, energy expenditure and feed intake are highly influenced by water temperature (Bureau et al. 2002). Specific to the fish nutrient-based model, parameters such as PdMax, minlp, maximum utilization of glucose, maintenance AA and N requirements, and basal energy requirements are deemed to be influenced by water temperature. A linear relationship between growth rate, nutrient deposition and temperature was observed in the range of 6 15 xc for rainbow trout (Azevedo et al. 1998; Dumas et al.

20 K. HUA ET AL. 2007). Therefore, a linear water temperature effect was assumed for PdMax, minlp, maximum utilization of glucose, maintenance AA and N requirements. This is deemed reasonable for practical rearing conditions (5 18 xc) for rainbow trout. It has been observed that increasing water temperature results in a curvilinear (almost linear) increase in fasting heat production of fish up to the optimum temperature for growth; thereafter an increase of temperature results in no increase or even depression of fasting heat production (Bureau et al. 2002). Therefore, basal energy requirements as a function of temperature were estimated by an empirical quadratic equation of Cho (1992) for fasting heat production (detailed equation is provided below). AA metabolism and deposition AA metabolism is explicitly represented in terms of maintenance requirements, inevitable catabolism, deposition as protein, catabolism of AAs supplied in excess of requirement and preferential catabolism of AAs for energy use. Essential AAs are individually represented, while non-essential AAs are not differentiated and converted to equivalents of non-specific nitrogen. To account for the effects of metabolic body weight (MBW; kg BW 0.8 ) and water temperature, maintenance essential AA requirements reported in Rodehutscord et al. (1997) were converted to mg/kg MBW/degree day. Maintenance N requirement for rainbow trout is estimated to be 2. 2 mg/kg MBW/ degree day based on data from Fournier et al. (2002). Inevitable AA catabolism is the catabolism of the dietary first-limiting AA, which reflects activity of AA degrading enzymes and is unrelated to energetic need (Moughan 2003). Rodehutscord et al. (2000) reported a marginal efficiency of utilizing lysine for Pd of 0. 71 for rainbow trout fed a high protein diet when lysine was the first limiting AA. Due to lack of specific efficiency data for other AAs conducted with rainbow trout, a 0. 70 marginal efficiency is assumed for all essential AAs in the model, corresponding to a rate of inevitable catabolism of 0. 30 of digestible AA intakes in the model. Deposition of essential AAs is based on the whole body AA profile reported by Guillaume et al. (2001). A temperature-dependent PdMax of 0. 09 g/degree day is used. This value was obtained from a literature survey based on 117 data points from 27 studies that included immature rainbow trout (BW from 3 to 1265 g) fed to near-satiety with nutritionally adequate diets and reared at water temperature within the range of 6 18 xc (Dumas et al. 2007). Carbohydrate metabolism Fish have limited ability to utilize carbohydrates. Excess intake of enzymatically degradable carbohydrates that yield glucose is assumed to be excreted LP 1 00 0 75 0 50 0 25 0 00 0 0 2 5 5 0 7 5 10 0 12 5 15 0 17 5 DEI (kj/kg MBW/degree day) Fig. 2. Relationship between the ratio of whole body lipid to whole body protein (LP) and DEI (kj/kg MBW/degree day): LP=1. 19/(1+9. 06/DEI) (R 2 =0. 81, Sy.x=0. 06). in the urine or eliminated by other processes at no energetic cost (Bureau et al. 1998). Maximum utilizable glucose was estimated to be 0. 67 mmol/kg MBW/degree day on the basis of the experiment by Bureau et al. (1998). The production of volatile fatty acids (VFA) derived from enteric fermentation is assumed to be negligible in fish since enteric microflora are at least ten-fold lower than in pigs (Olsen et al. 2005; Shirkey et al. 2006). Lipid metabolism and deposition Fatty acids (FA) for Ld can be derived from dietary FA or synthesized de novo from glucose or AAs in intermediary metabolism or from mobilization of body fat. When Pd is limited by energy intake, Ld and Pd are constrained by minlp. The minlp is a parameter determined empirically from digestible energy intake (DEI) in rainbow trout using pooled data from studies of Azevedo et al. (1998) and Bureau et al. (2006). In the study by Azevedo et al. (1998), the fish (IBW=13 g) were reared at temperatures between 6 and 15 xc for 12 weeks, whereas in the study of Bureau et al. (2006), the fish (IBW=150 g) were reared at 8. 5 xc for 24 weeks. In these studies, fish were fed diets that were not limiting in essential nutrients. The relationship was significantly (P<0. 05) better represented by an asymptotic equation than a linear equation, as follows (Fig. 2): minlp=119=(1+906=dei) (R 2 =081, Sy:x=006) where minlp=minimum body lipid to protein ratio, DEI=temperature adjusted DE intake, kj/kg MBW/ degree day and Sy.x=standard deviation of the residuals. Energy metabolism Dietary gross energy values of crude protein, fat and starch were assumed to be 23. 6, 39. 5 and 17. 2 kj/g,

Adaptation of a nutrient-based model to fish 21 respectively (Cho & Kaushik 1990). Gross energy content of excreted urinary N compounds was taken to be 24. 9 kj/g N (Cho & Kaushik 1990). There were six calibration parameters related to energy utilization in the pig growth model: ATPd (cost of intake of digestible dry matter (DM)), ATPx (cost of processing of undigested DM), ATPu (cost of N excretion), cost of Pd and related metabolic support processes (ATPp), such as protein turnover, cost of Ld and related metabolic support processes (ATPl) and basal energy requirement (ATPb). These requirements were expressed in terms of mol ATP. In the fish model, only three calibration parameters were used: ATPb, ATPp and ATPl. ATPu was assumed to be nil since N is excreted by fish at no energetic cost (Cho & Kaushik 1990). ATPd and ATPx were also assumed to be nil, since the energy cost of ingesting or egesting feed DM is probably negligible in fish (Cho & Kaushik 1990). Basal energy requirement ATPb was approximated by converting fasting heat production (kj/day) to ATP equivalents (assuming 1 mol ATP=52 kj, Lehninger 2000). The free energy released in vivo by breaking a high energy ATP bond varies somewhat according to thermodynamic conditions relating to temperature and the intercellular concentrations of ATP and ADP, but free energy is generally considered to be 52 kj/mol ATP. ATP energy content varies in the literature, e.g. 74, 78 and 93 kj ME/mol ATP being reported for ATP derived from glucose, FA and VFA, respectively (Armstrong 1969; van Es 1980). This is because it is often given at the DEI level, rather than at the metabolite level, and the nutrient composition of the ME used to generate ATP will affect the energetic efficiency. Fish have a much lower (5 10-fold lower) basal energy metabolism than homeotherms (Bureau et al. 2002), rendering model predictions not sensitive to ATP energy content and estimates of ATPb. Furthermore, water temperature has a major influence on basal metabolism of fish and estimates of fasting heat production (HeE) should take into account this effect. Based on oxygen consumption data of rainbow trout of different weights reared at different temperatures, the following empirical equation was developed to predict fasting heat production (kj/day) of salmonids as a function of water temperature between 5 and 15 xc by Cho (1992): HeE=(x001+326rTx005rT 2 )rmbw where HeE=fasting heat production (kj/day), T= water temperature (xc) and MBW=kg BW 0.8. Therefore, ATP equivalents of ATPb=(x0. 01+3. 26r Tx0. 05rT 2 )rmbw/52. The parameter ATPp was estimated to be 0. 30 mol ATP/g Pd, obtained by model calibration for energetic efficiency of using energy intake for digestible Pd (Kp) of 0. 53 (Azevedo et al. 2005). The parameter ATPl was estimated to be 56 mol ATP/mol triglyceride deposited, obtained from model calibration with an energetic efficiency of Ld (Kf) of 0. 90 (Azevedo et al. 2005). Azevedo et al. (2005) obtained the Kp and Kf values from rainbow trout fed diets containing 20 MJ/kg digestible energy and 300 500 g/kg digestible protein. Prediction of BW and growth Final BW (FBW) was calculated as BW(g)=protein(g)+lipid(g)+water(g)+ash(g) Water and ash contents were related to protein content through allometric equations: Water(g)=534rprotein 0934 (Dumas et al: 2007) Ash(g)=0166rprotein 0933 (Dumas et al: 2007) Gut fill was assumed to be negligible and therefore estimated as nil. Feed intake In the pig growth model, daily DEI is related to BW through empirical equations. Estimates of the feed intakes clearly influence the accuracy of model predictions. Due to the difficulties of accurately predicting feed intake of fish from feed composition, biological and environmental factors (e.g. water temperatures), no attempt has been made to predict intake in the fish model. In simulations of specific experiments for model evaluation, the actual observed feed intakes are used as model inputs. Sensitivity to parameter estimates Sensitivity of model outputs to the key parameters ATPp, ATPl, PdMax, inevitable AA catabolism and parameters in the equation relating minlp to DEI was determined from simulations for fish of different sizes. Growth periods were included for small fish (10 100 g), medium-sized fish (200 300 g) and large fish supposedly having achieved PdMax (500 600 g). Each model parameter was increased by 10%, and the percent change in various predicted primary output variables (growth period, thermal-unit growth coefficient (TGC), feed efficiency (FE), Pd and Ld) was determined as a measure of model sensitivity. Model evaluation The model was evaluated by comparing the results of simulations with observations from various studies conducted with rainbow trout at the University of Guelph (Azevedo et al. 1998; 2004a, b) involving a

22 K. HUA ET AL. Table 1. Sensitivity test of model predictions (percent changes) to 10% increases in parameters* of ATPp, ATPl, PdMax, inevitable AA catabolism, or parameters in the equation relating minlp to DE intake. Model prediction response variables are growth period, TGC, FE, Pd and Ld ATPp ATPl PdMax Inevitable AA catabolism Slope in minlp equation# Plateau in minlp equation# BW between 10 and 100 g Growth period (day) +1. 5 0 0 +3. 0 0 +1. 5 TGC x2. 0 0 0 x2. 8 0 x2. 8 FE x2. 4 0 0 x2. 4 0 x0. 8 Average Pd (g/day) x2. 3 0 0 x4. 1 0 x2. 8 Average Ld (g/day) x3. 9 x1. 5 0 +4. 4 0 x0. 5 BW between 200 and 300 g Growth period (day) 0 0 0 4. 3 0 +8. 7 TGC x1. 2 x0. 4 0 x2. 8 0 x1. 6 FE x0. 9 x0. 9 0 x3. 6 0 x5. 4 Average Pd (g/day) x0. 1 0 0 x3. 9 0 x8. 0 Average Ld (g/day) x6. 4 x1. 1 0 5. 5 0 +8. 7 BW between 500 and 600 g Growth period (day) 0 0 x7. 1 0 0 0 TGC x0. 8 x0. 4 +3. 2 x1. 2 0 0 FE x1. 0 0 +3. 0 x1. 0 0 0 Average Pd (g/day) 0 0 +5. 5 x1. 4 0 0 Average Ld (g/day) x5. 8 x1. 1 x6. 8 1. 1 0 0 * The starting parameter values are presented in the text. # minlp equation: minlp=plateau/(1+slope/dei). wide range of rearing water temperatures, diet compositions, fish sizes and life stages. In Azevedo et al. (1998), rainbow trout were reared at four different temperatures (6, 9, 12 and 15 xc), growing from 13 to 110 g. The fish were fed a practical diet containing 460 g/kg digestible protein and 20 MJ/kg digestible energy. The diet contained fish meal, fish oil, blood meal, maize gluten meal, brewer s dried yeast and whey. In Azevedo et al. (2004a), rainbow trout were reared on four diets growing from 47 to 200 g at a water temperature of 12 xc. In Azevedo et al. (2004b), rainbow trout were reared on the four diets growing from 268 to 1580 g for 44 weeks at a water temperature of 8. 5 xc. The studies of Azevedo et al. (2004 a, b) used four diets containing about 20 MJ/kg digestible energy and 300 500 g/kg digestible protein. The diets contained fish meal, fish oil, blood meal, maize gluten meal, wheat middlings and whey. In all model simulations, diet composition (characterized by digestible nutrients) and observed feed intake (g/100 g BW/day) were used as model inputs. Feed intake was recorded on a weekly basis in the experiments. In model simulations, BWs of fish at the beginning and end of each week were calculated from observed IBW and observed growth rate in the experiments. Daily feed intake was then calculated as g/100 g BW/day and used as model input for each weight period. Model simulations were based on a growth period from observed IBW to observed FBW. Predicted growth rate, Pd, Ld and recovered energy (RE) over the growth period were compared with observed values from the experiments. Model simulations were considered to be significantly different from experimental observations when model simulations did not fall within 95% confidence interval of the experimental observations. RESULTS Table 1 presents the results of the analysis of parameter sensitivity, which is dependent on fish size and life stages. For small and medium-sized fish, the outputs are sensitive to inevitable AA catabolism, ATPp and minlp parameter, whereas for large fish, the greatest sensitivity is to PdMax. Comparisons of model simulations and experimental observations are presented in Tables 2 4. Table 2 compares model simulations with observations from Azevedo et al. (1998). Model predictions tended to underestimate Pd and growth at low water temperature. Table 3 compares model simulations with experimental observations from Azevedo et al. (2004 a). While RE predictions agreed with the observations, there was a tendency for the model to underestimate Pd and overestimate Ld. Table 4

Table 2. Comparison of model simulations with observations from Azevedo et al. (1998). The model simulated growth period (days) from observed IBW to observed FBW. Predicted TGC, Pd, Ld and RE over the growth period were compared with observed values from the experiments 15 xc 12 xc 9xC 6xC Observations Simulations Observations Simulations Observations Simulations Observations Simulations IBW (g) 13. 3 13. 3 13. 3 13. 3 FBW (g) 110. 1 84. 6 60. 7 38. 1 Days 84 87 84 98 84 103 84 106 Total feed intake (g) 84 86 61 66 40 46 22 25 Daily feed intake (g) 1. 0 1. 0 0. 7 0. 7 0. 5 0. 4 0. 3 0. 2 Pd (g/day) 0. 19 0. 007 0. 18 0. 14 0. 009 0. 12 0. 09 0. 002 0. 07 0. 05 0. 002 0. 04 Ld (g/day) 0. 17 0. 007 0. 16 0. 11 0. 005 0. 10 0. 07 0. 002 0. 07 0. 04 0. 001 0. 04 TGC 0. 19 0. 005 0. 19 0. 19 0. 007 0. 17 0. 20 0. 001 0. 17 0. 19 0. 004 0. 16 RE (kj/day) 11. 3 0. 47 10. 7 7. 9 0. 47 6. 7 5. 0 0. 10 4. 3 2. 7 0. 10 2. 2 Table 3. Comparison of model simulations with observations from Azevedo et al. (2004a). The model simulated growth period (days) from observed IBW to observed FBW. Predicted TGC, Pd, Ld and RE over the growth period were compared with observed values from the experiments Diet 1 Diet 2 Diet 3 Diet 4 Observations Simulations Observations Simulations Observations Simulations Observations Simulations IBW (g) 47. 4 47. 4 47. 4 47. 4 FBW (g) 193. 4 199. 4 193. 4 199. 4 Days 84 97 84 104 84 99 84 100 Total feed intake (g) 108 129 116 141 115 140 124 154 Daily feed intake (g) 1. 3 1. 3 1. 4 1. 4 1. 4 1. 4 1. 5 1. 5 Pd (g/day) 0. 32 0. 017 0. 25 0. 31 0. 010 0. 24 0. 29 0. 013 0. 241 0. 30 0. 004 0. 24 Ld (g/day) 0. 13 0. 014 0. 19 0. 18 0. 008 0. 19 0. 18 0. 004 0. 23 0. 26 0. 001 0. 27 TGC 0. 22 0. 003 0. 19 0. 23 0. 002 0. 18 0. 22 0. 006 0. 18 0. 23 0. 000 0. 19 RE (kj/day) 13. 3 1. 04 13. 6 15. 2 0. 55 13. 3 14. 5 0. 11 14. 7 16. 9 0. 13 16. 2 Adaptation of a nutrient-based model to fish 23

Table 4. Comparison of model simulations with observations from Azevedo et al. (2004b). The model simulated growth period (days) from observed IBW to observed FBW. Predicted TGC, Pd, Ld and RE over the growth period were compared with observed values from the experiments Diet 1 Diet 2 Diet 3 Diet 4 Observations Simulations Observations Simulations Observations Simulations Observations Simulations Period of 0 12 weeks IBW (g) 268 268 268 268 FBW (g) 584. 3 574. 3 588. 5 575. 7 Days 84 102 84 104 84 109 84 102 Total feed intake (g) 322 364 327 351 352 375 343 377 Daily feed intake (g/day) 3. 8 3. 6 3. 9 3. 4 4. 2 3. 4 4. 1 3. 7 Pd (g/day) 0. 72 0. 004 0. 50 0. 69 0. 018 0. 49 0. 71 0. 009 0. 47 0. 66 0. 019 0. 47 Ld (g/day) 0. 62 0. 028 0. 69 0. 59 0. 080 0. 58 0. 68 0. 063 0. 64 0. 64 0. 046 0. 729 TGC 0. 27 0. 005 0. 22 0. 26 0. 004 0. 21 0. 27 0. 003 0. 21 0. 26 0. 002 0. 22 RE (kj/day) 43. 7 1. 66 38. 9 40. 2 2. 77 34. 4 44. 5 2. 02 36. 4 41. 6 1. 76 39. 9 Period of 12 24 weeks IBW (g) 584. 3 574. 3 588. 5 575. 7 FBW (g) 940 930 962 957 Days 84 83 84 89 84 86 84 84 Total feed intake (g) 428 448 421 467 452 487 473 500 Daily feed intake (g/day) 5. 1 5. 4 5. 0 5. 2 5. 4 5. 7 5. 6 6. 0 Pd (g/day) 0. 71 0. 016 0. 68 0. 66 0. 017 0. 65 0. 69 0. 025 0. 69 0. 76 0. 037 0. 68 Ld (g/day) 0. 80 0. 190 1. 02 0. 90 0. 154 0. 94 0. 86 0. 088 1. 10 1. 05 0. 083 1. 19 TGC 0. 20 0. 002 0. 20 0. 20 0. 003 0. 192 0. 21 0. 001 0. 20 0. 21 0. 002 0. 21 RE (kj/day) 48. 5 7. 61 56. 5 50. 7 5. 29 52. 4 49. 3 2. 83 59. 6 61. 0 2. 51 63. 0 Period of 24 44 weeks IBW (g) 940 930 962 957 FBW (g) 1518 1506 1579 1575 Days 140 146 140 150 140 150 140 157 Total feed intake (g) 789 806 813 832 854 877 863 919 Daily feed intake (g) 5. 6 5. 5 5. 8 5. 5 6. 1 5. 8 6. 2 5. 9 Pd (g/day) 0. 69 0. 031 0. 69 0. 74 0. 049 0. 67 0. 84 0. 067 0. 71 0. 79 0. 043 0. 67 Ld (g/day) 0. 79 0. 159 0. 79 0. 54 0. 142 0. 76 0. 80 0. 206 0. 86 0. 71 0. 125 0. 86 TGC 0. 14 0. 002 0. 14 0. 14 0. 001 0. 13 0. 15 0. 001 0. 14 0. 15 0. 001 0. 13 RE (kj/d) 50. 2 5. 17 47. 6 41. 3 6. 73 46. 0 57. 2 7. 84 50. 6 51. 4 8. 97 49. 8 Whole period 0 44 weeks IBW (g) 268 268 268 268 FBW (g) 1518 1506 1579 1575 Days 308 331 308 343 Total feed intake (g) 1539 1618 1561 1650 1658 1739 1679 1796 Daily feed intake (g) 5. 0 5. 0 5. 1 4. 8 5. 4 5. 1 5. 5 5. 3 Pd (g/day) 0. 71 0. 019 0. 64 0. 71 0. 025 0. 615 0. 76 0. 037 0. 64 0. 75 0. 013 0. 62 Ld (g/d) 0. 75 0. 040 0. 83 0. 65 0. 038 0. 762 0. 78 0. 087 0. 86 0. 78 0. 069 0. 91 TGC 0. 19 0. 002 0. 19 0. 19 0. 005 0. 179 0. 20 0. 005 0. 19 0. 20 0. 003 0. 19 RE (kj/day) 48. 2 1. 55 47. 7 44. 7 2. 36 44. 6 51. 9 3. 39 49. 2 51. 5 4. 38 50. 7 24 K. HUA ET AL.

Adaptation of a nutrient-based model to fish 25 0 9 y = x 1 4 y = x Simulated Pd (g/d) 0 8 0 7 0 6 0 5 0 4 0 3 0 2 y = 0 8583x 0 0076 R 2 = 0 9191 Simulated Ld (g/d) 1 2 1 0 8 0 6 0 4 y = 1 1312x + 4E-05 R 2 = 0 96 0 1 0 2 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 Observed Pd (g/d) 0 0 0 2 0 4 0 6 0 8 1 1 2 1 4 Observed Ld (g/d) Simulated TGC 0 3 0 25 0 2 0 15 0 1 y = 0 625x + 0 0522 R 2 = 0 7874 y = x Simulated RE (kj/d) 80 70 60 50 40 30 20 y = 1 0134x 0 9259 R 2 = 0 9524 y = x 0 05 10 0 0 0 0 05 0 1 0 15 0 2 0 25 0 3 0 20 40 60 80 Observed TGC Observed RE (kj/d) Fig. 3. Comparison of model simulations with experimental observations of Pd, Ld, TGC and RE. compares model simulations with observations from Azevedo et al. (2004b). For the first 12 weeks, the model tended to underestimate Pd and TGC, and overestimate Ld. For the periods of 12 24 weeks and 24 44 weeks, model predictions were in agreement with observations and none of the model-simulated parameters were significantly different from observed values. For the whole 44-week period, although there were numerical differences between model simulations and experimental observations of Pd, Ld and TGC, the differences were not significant except for TGC of fish fed Diet 4. The model simulations of RE agreed with experimental observations. By pooling all model simulations from Tables 2 4 and comparing them with experimental observations, an overall evaluation of model simulations is illustrated in Fig. 3. The results suggest that, in general, RE simulations were agreeable with observations, but the model underestimated Pd by 15% and TGC by 37% and overestimated Ld by 13%. DISCUSSION The objective of the present study was to investigate if the concepts of nutrient partitioning used in a nonruminant/pig growth model by Birkett & de Lange (2001a, b, c) are applicable to fish. The model is presented as a general nutrient-based growth model supposedly applicable to all non-ruminant animals (Birkett & de Lange 2001a, b), which is then adapted and calibrated for pigs in the final paper (Birkett & de Lange 2001 c). In the present study, the feasibility of incorporating and adapting selected concepts from the pig version of the model to fish was investigated. The nutrient-based model estimates weight gain and composition of weight gain for different animal types

26 K. HUA ET AL. based on nutrient intake and the key factors affecting nutrient and energy partitioning, including the intake and balance of digestible essential AAs, PdMax and minlp. The PdMax concept is well-documented in pigs. In the adapted fish model, a single PdMax value (0. 09 g/ degree day) was used, which was derived from a study of literature survey based on 117 data points from 27 studies (Dumas et al. 2007). In the survey, Pd linearly increased with BW and reached an apparent plateau of Pd at BW between 400 and 1300 g for rainbow trout. Sensitivity analysis showed that the model is moderately sensitive to the adopted PdMax value at higher BW and when PdMax drives growth. PdMax is fundamental to the adaptation of the pig model since it incorporates a degree of maturity into growth predictions. Further studies are necessary to explore variation in PdMax among different groups of fish. Nonetheless, the current adapted fish model is shown to be quite accurate for predicting nutrient partitioning in fish over 500 g and when PdMax drives growth. The independence of the effects of protein intake and energy intake on Pd has been well established for pigs. When AA intake is limiting, additional intake of energy has no effect on Pd and preferential catabolism. In that case, dietary limiting AA is not used to meet energy needs (Moughan 1999). However, contrary to what is seen in pigs, the efficiency of utilization of limiting essential AA was found to be affected by dietary digestible energy level in fish (Encarnação et al. 2004). Furthermore, this effect was dependent on the type of energy-yielding nutrients. The lysine-sparing effect exerted by lipids/ fatty acids was not observed with other energyyielding nutrients (Encarnac ão et al. 2006). Compared with other non-ruminant animals, fish seem to have a more elastic inevitable AA catabolism. This is probably due to fish having limited ability to use carbohydrates as energy sources, and therefore AAs and lipids are effective dietary energy-yielding components for fish. Nutrient metabolism observed in fish might therefore have to be represented dynamically through alternative and competing metabolic pathways. In the nutrient-based model, a high level (whole animal) approach is used to control partitioning of limiting nutrients when competing uses are applicable. A fish model may require a more direct representation of the body s metabolic control mechanism. To do so, it would require a dynamic metabolic model which is beyond the scope of a nutrient-based model such as that described in the current paper. Under the current model framework, imbalanced AA intake is channelled to Ld, which could have resulted in the minor overestimation of Ld, when one or more digestible AA is marginally deficient but without obvious negative impact on fish growth performance in practice. The energy partitioning rule of minlp is central to the nutrient-based model. In pigs, minlp is determined as the ratio of body lipid to protein when energy intake is insufficient to achieve PdMax and AA intake is not limiting Pd. In the current adapted fish model, body composition data from rainbow trout fed at four intake levels (0. 25, 0. 50, 0. 75 and 1. 00 of near-satiation) (Bureau et al. 2006) and three intake levels (0. 70, 0. 85 and 1. 00 of near-satiation) (Azevedo et al. 1998) were used, on the assumption that Pd would have been limited by energy and not by PdMax. This assumption was supported by the linear effect of energy intake on Pd in these experiments. The relationship between DEI and minlp ratio from the pooled data of Azevedo et al. (1998) and Bureau et al. (2006) was best represented by an asymptotic relationship. Even though this asymptotic relationship is a statistically better fit to the data than a linear relationship (i.e. minlp=0. 266+0. 033rDEI (kj/kg MBW/degree day), R 2 =0. 77, Sy.x=0. 07), there was still variance unexplained by the asymptotic equation. Sensitivity analysis also indicates that this is a key parameter for medium-sized fish. The comparison of model simulations and experimental observations suggests that RE is relatively well predicted, while Pd is underestimated and Ld is overestimated. This indicates that the minlp energy partitioning rule makes a significant contribution to the observed discrepancies in the present study and should be explored further. Important first steps are to characterize more accurately at what stages of growth and up to what energy intake level energy intake determines Pd in different fish types and to characterize effects of BW and diet nutrient composition on minlp. In the adaptation of the model, it became apparent that DEI should be expressed as a function of MBW and water temperature when determining its relationship to minlp, rather than using absolute DEI values as in the model by Birkett & de Lange (2001a, b, c). This modification is necessary for fish, because feed intake was influenced not only by fish size but also by temperature. However, in the study of Azevedo et al. (1998), the effects of BW and water temperature may be confounded since fish reared at different temperatures had different FBWs. Eliminating the temperature effect in the minlp to DEI relationship resulted in a similar shape of fitting curve and yielded simulation results similar to those presented in Tables 2 4 (data not shown). On the conceptual grounds that fish are poikilothermic organisms and that temperature has a determinant effect on their growth and metabolism, it was decided to retain temperature in the minlp equation. Future experiments that independently investigate the effects of temperature, as well as BW, on minlp may provide more information on this issue.

Adaptation of a nutrient-based model to fish 27 CONCLUSION The present study investigated the feasibility of adapting selected concepts from a pig growth model to fish through incorporating parameters related to fish metabolic characteristics as well as redetermination of key model parameters. The resulting fish nutrient-based model underestimates Pd and overestimates Ld under PdMax, while it predicts RE well. These results, combined with sensitivity analysis indicate that the primary source of the discrepancies between predictions from the adapted fish model and experimental observations is the rule that governs the partitioning of retained nutrients between Pd and Ld when energy intake is insufficient to reach PdMax, represented by the minlp parameter. As suggested by the variance of the relationship between minlp and DE intake, minlp appears to be also affected by factors other than DEI. Further development of the model should strive to differentiate and quantify these factors. Growth of animals is determined by accretion of the body components water, protein, fat, minerals and a small amount of other components (glycogen, etc.). Growth of body components and the efficiency with which the nutrients are converted are affected by numerous endogenous (species, genetics and life stage) and exogenous (diet composition, feeding level, environment and season) factors. At present, these factors, especially the endogenous determinants of AA utilization and Ld in fish, are not fully understood. Further research is necessary to elucidate these factors and their effects. Model development is limited at present by the lack of experimental data for completely independent parameterization and evaluation. Nevertheless, the current model adaptation and evaluation should be of value for improving understanding of growth and nutrient partitioning processes in fish. 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