The goat requires energy for self-organization, motion, harvesting food, maintenance, growth and/or milk production. Jørgensen  indicated that this is important to distinguish between two forms of energy: energy that can be accumulated to do work and the energy that cannot do work, and is lost as heat to the environment. As the world population continues to grow during this century, livestock must focus on production efficiency to provide an adequate food supply; for instance, milk and dairy foods.
The main feeding systems for dairy goats in the world are Agricultural and Food Research Council  , National Research Council  , the Small Ruminant Nutrition System   and Institute Nationale Recherche Agronomique  . The last two systems included dairy goats’ recommendation but the available information from Spanish dairy goats’ breeds is still scarce. Energy requirements of ruminant have been studied via respiration calorimetry, comparative slaughter technique and feeding trials. Therefore, the different feeding systems compile a wide range of requirements due that different breeds, purposes (milk, meat and fiber) and energy requirements methodologies were combined. Data used in this study comes from the same breed and, the energy balance was quantified using open system indirect calorimetry techniques.
The metabolizable energy (ME) requirements for maintenance (MEm) and the efficiency of utilization of ME for lactation (kl) are two key parameters in the calculation of the energy requirements of dairy goats. When the goat is in positive tissue energy balance, some of the ME intake (MEI) is being directed towards tissue energy retention (Tg) and kg is the efficiency of utilization of MEI for tissue energy gain. When the goat is in zero energy balance, all the MEI is being directed to maintenance and milk production. And when the goat is in negative energy balance, some of the milk energy is derived from body stores (Tl), being kt the efficiency of utilization of tissue energy for milk production.
These parameters have been estimated using a variety of modeling approaches for different livestock species. Historically in lactating cows, Moe et al. (1971)  proposed a multiple linear regression approach for estimating maintenance requirements and partial efficiencies based on the observation of dietary ME. Strathe et al. (2011)  proposed an energy function that generalized the model advocated by  .
Some heat is lost during every energy transformation, and their quantification was some of the main objectives of the present study, combining indirect calorimetry data and linear mixed models. The objective of the present study is to collate data from energy balance studies with lactating dairy goats, and to fit Moe  and Strathe  mathematical functions to estimated parameters of energy metabolism in relation to milk production such us efficiency of utilization of ME for lactation (kl), body weight gain (kg), body tissue mobilization for milk production (kt) and MEm.
2. Material and Methods
2.1. Animals and Feeding
The experimental procedure was approved by the Animal Use and Care Committee of the Universitat Politècnica de València (UPV, Spain) and followed the codes of practice for animals used in experimental works proposed by the European Union (2007)  .
Data from eight energy balance experiments (three unpublished) conducted at the Experimental Farm of the UPV were used to develop the model      . All studies had shown the possibility to replace cereal grain with agricultural fibrous byproducts successfully. The trials encompassed a total of 267 observations from multiparous Murciano-Granadina goats; six studies in mid and two studies in mid-late lactation. The trial  replaced corn grain (37%) with a blend of soy hulls and corn gluten feed and, alfalfa hay was used as forage (forage to concentrate ratio was 45:55) in lactating goats in mid lactation.  with lactating goats in mid lactation, studied the effect of replacing corn grain (60%) with citrus pulp (60%) or soy hulls (60%) in a forage to concentrate ratio of 15:85.  replaced oats (38%) with rice bran with lactating goats in mid-late lactation and alfalfa hay was the forage (35:65).  used the same concentrate and substituted alfalfa hay with maralfalfa hay in goats at mid-late lactation, being the forage to concentrate ratio of 40:60.  , with goats in mid lactation and using alfalfa hay as forage (the forage to concentrate ratio was 33:67), replaced barley grain (60%) with fibrous byproducts such as orange pulp (60%) or soy hulls (60%). The other three unpublished studies, with lactating goats at mid lactation and forage to concentrate ratio of 40:60, replaced cereal grain with lemon pulp, beet pulp and olive pulp. Due to that these experiments were not published, more detailed were required, one replaced 35% of barley grain with lemon pulp and, to reach isoenergetic diets (11 MJ ME/kg dry matter (DM), on average) fat was added to lemon pulp diet (2.5% and 4.1% of ether extract (EE) for cereal and lemon pulp, respectively). The neutral detergent fiber (NDF) ranged from 31% to 37% and crude protein (CP) was 18% on average. The second experiment replace 31% of corn with beet pulp and no fat was added (2.7% and 1.9% EE for corn and beet pulp, respectively), and the energy value was 13 and 12 MJ ME/kg DM). Corn diet had 31% NDF and mixed diet with beet pulp 56%, and the CP content was 15% on average. The third experiment replaced 25% of barley with olive pulp and due that olive pulp has oil, the EE content of barley diet was 2.2% and olive pulp diet 4.3%, therefore, the energy content was 11 and 12 MJ ME/kg DM, respectively. The olive pulp mixed diet had greater NDF (33%) than barley diet (28%) and different CP content was observed as well; 18% and 15% for olive pulp and barley diets, respectively.
Therefore, goats were fed mixed diets with an average value of 17 MJ of gross energy/kg DM (11 MJ ME/kg DM) and CP ranged from 14% to 18.7% DM basis. The NDF ranged from 23% to 59% (DM basis) and the starch content from 2% to 42% (DM basis). Due that some experiments replaced cereal with fibrous byproduct, in order to reach isoenergetic diets, lipids were added to some diets and the EE content ranged from 2% to 6%. Intake was ad libitum with diets offered at 110% of consumption on the preceding few days and goats had free access to water. Half the daily ration was offered at 08:00 and the other half at 16:00, respectively.
Briefly, within each study, total energy intake and output of fecal, urinary and milk were recorded. ME intake was calculated as the difference between energy intake and the losses in feces, urine and methane. Energy recovered or loss was estimated by subtracting heat production and milk energy from ME intake. Heat production was measured by indirect calorimetry in open circuit respiration head hood system described by   . Descriptive statistic of the range of calorimetric data included in database is summarized in Table 1.
2.2. Studies Origin
The database contained energy balance inputs and outputs from eight studies conducted at UPV, running between 2013 and 2016. In some instances, multiple observations were made on the same goat at different studies. We used a linear regression with fixed effect of study in an attempt to extract quantitative
Table 1. Summary statistics of the calorimetry data (n = 267).
DM = dry matter; CP = crude protein of diet; NDF = neutral detergent fiber; EE = ether extract; ME = metabolizable energy; BW = body weight.
relationships that best explain the observations.
where Yij was the dependent variable, ∂ was the intercept, Si was the fixed effect of ith study, Xij was the value of the continuous predictor variable of the jth observation in the ith study and εij was the residual deviation of the jth observation in the ith study. The continuous predictor variable used was the ratio energy in milk to MEI, both expressed in kJ/kg BW0.75.
On the other hand, in order to avoid ignoring the fact that observations within a given study have more in common than observations across studies, random effect of study was used for mixed model analysis. The linear mixed model was detailed as follow:
where Yij was the dependent variable, ∂ was the intercept, Si was the random effect of ith study, Xij was the value of the continuous predictor variable, and εij was the residual deviation of the jth observation in the ith study. The continuous predictor variable used was the same as that above.
To account for the study effect, we have adjusted the individual measurements with respect to the study mean to remove variation among studies. Each residual was added to its corresponding Y predicted value to generate adjusted Y values   .
2.3. Model Description
Two models were used to describe energy utilization by lactating goats in the present work. Both models belong to the family of univariate models because the response represents a single energy trait. That is, the response variable was regressed on a set of independent variables. Historically, energy balance data from lactating dairy cows were analyzed using the classical linear regression approach of Moe  :
where MEI, Tg and Tl were expressed in kJ/kg BW0.75 per day, MBW was metabolic body weight (kg of BW0.75) and, El was the energy in milk (kJ/kg BW0.75 per day). The intercept α was the regression constant, which was assumed to represent the amount of MEI that was not attributable to any specific variable in the model. β1, β2, and β3 represent the unit amount of ME required for maintenance, milk production and body gain, respectively, β4 was the amount of dietary ME which is spared per unit of body tissue energy loss, and ε was the error. The reciprocals 1/β2 and 1/β3 represent the efficiency of milk production (kl) and body gain (kg) from dietary MEI. The ratio β4/β2 represents the efficiency of use of body tissue for milk production (kt). Moe  reported that β1 cannot be interpreted independent of the regression constant (α) and, it appears most logical to assign this amount of energy to the maintenance term:
The energy model function proposed by Strathe  was described as:
where El, MEI, Tg and Tl were described above (kJ/kg BW0.75 per day). β0 was the intercept and β1, β2 and β3 were the parameters describing the change in El with unit change in MEI, Tg and Tl, respectively and ε was the error. In this model, NEm = −β0, MEm = −(β0/β1), kl = β1, kt = β3, and kg = (β1/β2).
2.4. Parameter Estimation and Goodness of Fit
Univariate relationships between dependent and independent variables were fitted to data using lm and lme functions, from the library nlme, of the Statisitical package of R  , considering goat as random in both models. In the Moe  model MEI was the dependent variable and, EI was the dependent variable by the  model. Parameter estimation in these linear mixed effect models were performed by maximizing the log likelihood function (logL). A general method for comparing nested models fit by maximum likelihood is the likelihood ratio test. And, one statistical model is said to be nested within another model if it represents a special case of the other model. The likelihood ratio test gives a p-value from a chi-square distribution. The following goodness of fit indicator was used; Bayesian information criterion (BIC). If we use BIC to compare the models, we prefer the model with the lowest BIC.
Primary, model (3) and (4) were adjusted by linear model. Then, Models (3) and (4) were run as mixed model with goat as random effect; we called now Models (5) and (6), respectively. Afterwards, mixed models included variance and correlation structure. The variance functions are specified in the lme function using the weight argument. The varPower was the variance weight used here which is a power of the absolute value of the variance covariate given by the fitted values. Correlation structure is used to model dependence among observations. The correlation structure used was an autoregressive structure of order 1 (corAR1). Therefore, Models (5) and (6) were converted to (7) and (8), respectively. Likelihood ratio test was used to model comparison and, plotting the residuals against predicted values was used for model diagnostics, and the quantile-quantile plot was used for normality test of residuals.
3. Results and Discussion
This work gathered data from eight studies and, observation across studies was not balanced. Considering the study effect as fixed effect while performing the regression analysis led to poorer adjust than when the study effect was considered as random. So, the goodness of fit indicators BIC was lower when the study was taken as random effect instead than fixed; 2740 vs 2757, respectively. And maximum logL was greater with random than fixed study effect model (Table 2). Based on the BIC and logL criteria, the model with study as random effect fitted the data better. Figure 1 illustrates the boxplot of energy balance for the eight studies adjusted for Y, according to the mixed model corrected with study effect taken as random. Visual assessment suggests that the effect of MEI on the energy outputs were consistent across studies.
Table 3 shows the parameters estimates and goodness of fit from Moe  and
Table 2. Goodness of fit from the models used to correct the study effect.
BIC = Bayesian information criterion; logL = log likelihood function. 1Linear model (1) , Study (S) as fixed effect; 2 Linear model (2) , Study (S) as random effect.
Figure 1. Boxplot of energy balance (EI/MEI) for the eight studies, on other hands, the linear mixed model. EIs energy in milk (kJ/kg BW0.75 and day); MEI, metabolic energy intake (kJ/kg BW0.75 and day). Study A (López and Fernández, 2013), B (López et al., 2014), C (Criscioni and Fernández, 2016), E (Ibáñez et al., 2016) and F, G, H (unpublished).
Table 3. Parameters estimates and goodness of fit.
BIC = Bayesian information criterion; logL = log likelihood function. 1Energy function proposed by Moe et al., 1971 ( ): (3) linear; (5) mixed; (7) mixed with variance and correlation structure. 2Energy function proposed by Strathe et al., 2011 ( ): (4) linear; (6) mixed; (8) mixed with variance and correlation structure.
Strathe  models. Based on BIC criterion, energy balance data were better described by Models (7) than (5) and (3) for Moe and, for the Strathe model better fit with (8) than (6) and (4) were found. The Moe model had produced a value of logL of −1457, −1453 and −1446 for (3), (5) and (7) respectively. Model (7) was considerably greater than (3) and (5). The likelihood ratio statistic comparing the mixed model with the mixed model than included correlation and a variance function was large (13.87) and the p-value for the test was essentially zero (p = 0.001), so we preferred Model (7). The Strathe model had produced a value of logL of −1352, −1345 and −1338 for (4), (6) and (8) respectively. Because the larger likelihood ratio (14.68) and significant (p < 0.0001) differences for the test comparing Models (6) and (8), we found that Model (8) is significantly better than (6).
Figure 2 showed the standardized residual and quantile plots; for Moe and Strathe models. We presented only the model with better goodness of fit described in Table 3; Model (7) and (8). The residuals are symmetrically distributed around zero, with approximately constant variance. Figure 2 showed the normal plots of residuals by the quantile-quantile plot as well. Distribution of the within goat errors has heavier tails in both but is also symmetry around zero.
Consequently, BIC criterion was smaller for Strathe than Moe model. And, within Strathe model, smaller BIC and maximum logL were found in (8) model than (4) and (6), with a larger likelihood ratio test. Thus, the goodness of fit indicated a preference for Model (8).
Efficiencies of conversion of ME to net energy, according to the two models tested, were shown in Table 4. Due to that better goodness of fit with (8) model, our discussion was based on those estimated parameters.
The NEm obtained from Model (8) was of 283 kJ/kg BW0.75 per day. Estimation of maintenance energy requirements of goats in the literature is scarce and, includes animals from different breeds in different physiological stages. Nine estimates of fasting heat production of adult goats were used by AFRC  , ranged from 212 to 403 kJ NEm/kg BW0.75 per day. A mean value of 315 kJ NEm/kg BW0.75 per day was recommended by AFRC  . This is very similar to the value in ARC  of 319 kJ /kg BW0.75 for the fasting metabolism of adult cattle. Thus, the fasting metabolism of both cattle and goat appears to be higher than that of the sheep, for which ARC  gave values of 230 kJ/kg BW0.75. On the other hand, the NRC  proposed the same value than AFRC  while the SRNS   proposed a value for dairy goats of 338 kJ NEm/kg BW0.75 per day. Energy requirements of lactating dairy goats recommended by NRC  are based on the study of  involving a database of treatment from the literature, database that did not have in consideration factors such as dietary concentrate level. The INRA  system is based on material balance studies on goats in the descending phase of lactation, integrated with information obtained by the other feeding systems. The value proposed by INRA  was lower than our study; 265 kJ/kg BW0.75 per day. Other studies conducted with Murciano-Granadina goats by
Figure 2. Diagnostics of the models proposed by Moe et al. (1971) and Strathe et al. (2011) , using a mixed model with autocorrelation structure of order 1. Where MEI was the metabolizable energy intake, EI the net energy in milk and, β0, β1, β2 and β3 were the parameters, Tg was tissue energy retention and Tl the milk energy derived from body stores.
Table 4. Energy parameters obtained in dairy goats.
MEm = metabolizable energy for maintenance (kJ/kgBW0.75); kl = efficiency of use of ME for lactation; kg = efficiency of use of ME for gain; kt = efficiency tissue energy mobilization; NEm = net energy for maintenance (kJ/kgBW0.75). 1Energy function proposed by Moe et al., 1971 ( ): (3) linear; (5) mixed; (7) mixed with variance and correlation structure. 2Energy function proposed by Strathe et al., 2011 ( ): (4) linear; (6) mixed; (8) mixed with variance and correlation structure.
 , reported a value of 324 kJ/kg BW0.75 per day, greater than the value obtained at the present work, but we must indicate that these authors used castrate males for the calculation.  , with the same goat breed than our work but 27 years before, estimated the ENm during lactation by regression and obtained a value of 268 kJ/kg BW0.75 per day, slightly lower than our value obtained with Model (8).  found a fasting heat production of 310 kJ/kg BW0.75 per day, obtained by indirect calorimetry in female’s Murciano-Granadina dry goat. The MEm obtained with (8) model was 460 kJ/kg BW0.75 per day. Seventeen estimates of the MEm of goat derived from feeding trials were found by AFRC  , and the average value proposed was 438 kJ/kg BW0.75 per day. According to literature, the variation between estimates was considerable; ranged from 365 to 530 kJ/kg BW0.75 per day. So,  estimated MEm from several energy metabolism studies conducted with goats, and it varies widely; from 422 to 501 kJ/kg BW0.75 per day. The NRC  for goats, adopted  estimated maintenance requirements, which they were obtained for three breed groups (dairy, meat and indigenous, and Angora goats) and various animal categories (growing animals, dry animals and wethers, lactating goats, intact males). INRA  with a qm (ME to gross energy in the diet) of 0.64 recommended 441 kJ/kg BW0.75 per day, value 19 kJ/kg BW0.75 per day lower than the value estimated in this study.  obtained a value of 443 kJ MEm/kg BW0.75 per day with adult castrated males’ goats and  obtained a value of 401 kJ/kg BW0.75 per day, both authors using indirect calorimetry and regression techniques.  reported, in cow of high genetic merit, higher gross energy efficiency than cows of low genetic merit. Concomitantly, genetic selection has increased fasting heat production and energy maintenance requirements in lactating cows  because genetic selection chose leaner animals (larger proportions of body protein mass, enlarged organ size and lower backfat thickness) than fatter. Bigger organ size means greater energy expenditure to sustain transport, digestion and absorption. Therefore, the increase in maintenance requirements found in our work was consistent with the literature that describes increased fasting heat production in animals of higher genetic merit (for instance, genetic merit improved from the previous study of   .
Differences in ME requirements for milk production are due to variations in the conversion efficiency from ME to NE, depending on whether the energy comes from feed or body fat mobilization. Our work shown a kl value of 62%, within the range of the feeding system reported below. The kl used by AFRC  and NRC  was 63% and 61%, respectively (with a qm of 0.64 from our database). The SRNS for goats   proposed a value of 64%. INRA  proposed an efficiency of ME to milk only that included maintenance (kls), and this efficiency for a qm of 0.64 was 65%.  proposed a kl of 67%, which is very similar to those suggested by INRA  for high-quality diets.  found an average kl value of 67% for Saanen goat fed silage-based forage diet and non-forage diet in mid lactation. And  fed Alpine goats during mid lactation with 60% of concentrate found a kl of 63%.
Interpreting BW changes is often difficult because of the related variations in volume and content of the digestive tract system. The AFRC  method deals with BW changes only for growing animals and lactating goats. AFRC considers a kg value of 60% and, the conversion efficiency of NE from body reserves to milk production was 84%, which is slightly higher than that of INRA (ktg = 80%). For INRA  , the efficiency of ME to store energy reserves (ktg) is significantly higher with a difference with kls which is almost constant; therefore, it is calculated from kls (ktg = kls + 15 = 80%). The NRC  proposed a kg value of 70% and adopted the efficiency of mobilization NE to milk production (El) equal to the 84%, values proposed by ARC  . The kg value obtained in our study (83%) was similar than INRA  and greater than NRC  . The efficiency kt was 78%, lower than the main feeding systems discussed here, although INRA  proposed that the ktg was also the efficiency of utilization of body energy reserve for lactation (80%), similar that the value obtained with our model.
All feeding system reviewed here for dairy goats shown kt greater than kg, in our study it was opposed and, INRA  gave the same value for kt and kg, and close to our model. If we moved to dairy cow’s literature we found the same results from  where kg was greater than kt.  discussed this topic in their paper, suggested that in US Holstein cows, the efficiency of producing milk from body store reserves is substantially higher than the efficiency of utilizing dietary ME for tissue energy gain, as initially proposed by  .  suggested that body growth was limited and hypothesized that the higher kg, in comparison with values from  , was a consequence of the gain being mostly replenishment of body lipids mobilized at early lactation. Therefore, differences in kg by  may be a result of the gain composition and different degrees of cattle maturity at the start of lactation. In our study, goats were in mid and mid-late lactation suggesting than both, kg and kt, could be not constant during lactation, showing variation from early though mid to late lactation. Peak lactation is accomplished with lipid mobilization whereas that mid to late lactation favoring the utilization of metabolic fuels for body reserves recovery rather than milk production.
Likewise, kg is theoretically affected by the diet composition and differences in the nutrient fractions comprising dietary ME have the potential to alter the efficiency of dietary energy utilization. The increase in the efficiency of utilizing dietary energy could be partially attributed to the changes in diet composition (from forage diets to mixed diets with dietary ether extract levels higher and increased amount of cereals). During the last 30 years, dairy goat feeding systems in Spain have passed from grazing to have the animals confined on the barn, feeding with mixed diets rich in concentrates; mainly cereals and increasing the amount of fat added too  . Table 1 summarized that starch ranged from 1.5% to 41.6% and EE ranged from 1.9% to 5.7% in mixed diets used in this compilation. The composition of a diet can shift the microbial population in the rumen and consequence of the production of volatile fatty acids. The rumen volatile fatty acids can alter energy partition between milk and body tissue; molar proportions of acetic and butyric acids are positively related to milk fat concentration and, as indicated  in their review, increasing propionic acid proportion can result in more energy partitioned into body tissue and less into milk. Furthermore, changing diet composition can influence partitioning of nutrients towards body tissues rather than mammary gland. In an investigation of the effect of lipogenic and glucogenic feeds on nutrient partitioning and energy balance,  showed that cows fed a lipogenic diet partitioned more energy to milk than cows fed a glucogenic diet. The energy mobilized from body fat tended to be higher in cows fed a lipogenic diet than cows fed the glucogenic diet. Lipogenic nutrients originate either from fibre or dairy fat or from body reserves while glucogenic nutrients originate from starch escaped from rumen degradation or gluconeogenesis. Our study used mixed diets based on cereal suggesting that glucogenic nutrients stimulate body fat deposition and the partitioning of ME into body tissues. When the mixed diets replaced cereal with fibrous by product, greater fat was added to reach isoenergetic diets and, consequently, the lipogenic nutrients increased. However, no effect on efficiencies was found, probably since that dietary fat decrease the heat increment due that the relatively low energy cost of the transfer of absorbed fatty acids to milk when compared with the cost of the novo synthesis of fatty acids  . These discovered, in common with the stage of lactation, could explain the higher kg than kt observed in our study, agreeing with the efficiencies proposed by  . Likewise, INRA  proposed the same value of kg and kt; ktg = 80%, being this value the average between kg (83%) and kt (78%) obtained in our study.
Two models were proposed to analyze energy balance data from lactating goats fed mid and mid-late lactation; Moe  and Strathe  . The better fitted was obtained with Strathe model and NEm was 283 kJ/kg BW0.75 per day, and kl, kg and kt were 62%, 83% and 78%, respectively. The increase in the efficiency of utilizing dietary energy for gain was partially attributed to the stage of lactation (mid-late) and the use of cereal in the mixed diets.
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