Joint analysis of longitudinal feed intake and single recorded production traits in pigs using a novel Horizontal model.

A novel Horizontal model is presented for multitrait analysis of longitudinal traits through random regression analysis combined with single recorded traits. Weekly ADFI on test for Danish Duroc, Landrace, and Yorkshire boars were available from the national test station and were collected from 30 to 100 kg BW. Single recorded production traits of ADG from birth to 30 kg BW (ADG30), ADG from 30 to 100 kg BW (ADG100), and lean meat percentage (LMP) were available from breeding herds or the national test station. The Horizontal model combined random regression analysis of feed intake (FI) with single recorded traits of ADG100, LMP, and ADG30. In the Horizontal model, the FI data were horizontally structured with FI on each week as a "trait." The additive genetic and litter effects were modeled to be common across different FI records by reducing the rank of the covariance matrices using second- and first-order Legendre polynomials of age on test, respectively. The fixed effect and random residual variance were estimated for each weekly FI trait. Residual feed intake (RFI) was derived from the conditional distribution of FI given the breeding values of ADG100 and LMP. The heritability of FI varied by week on test in Duroc (0.12 to 0.19), Landrace (0.13 to 0.22), and Yorkshire (0.21 to 0.23). The heritability of RFI was lowest and highest in wk 6 (0.03) and 10 (0.10), respectively, in Duroc and wk 7 (0.04 and 0.02) and 1 (0.09 and 0.20), respectively, in Landrace and Yorkshire. The proportion of FI genetic variance explained by RFI ranged from 20 to 75% in Duroc, from 19 to 75% in Landrace, and from 11 to 91% in Yorkshire. Average daily gain from 30 to 100 kg BW and ADG30 heritabilities were moderate in Duroc (0.24 and 0.22, respectively), Landrace (0.34 and 0.25, respectively), and Yorkshire (0.34 and 0.22, respectively). Lean meat percentage heritability was moderate in Duroc (0.37) and large in Landrace (0.62) and Yorkshire (0.60). The genetic correlation of FI with ADG100 increased by week on test followed by a 32% decrease from wk 7 in Duroc and a 7% decrease in dam line breeds. Defining RFI as genetically independent of production traits leads to consistent and easy interpretable breeding values. The genetic parameters of traits in the feed efficiency complex and their dynamics over the test period showed breed differences that could be related to the fatness and growth potential of the breeds. The Horizontal model can be used to simultaneously analyze repeated and single recorded traits through proper modeling of the environmental variances and covariances.

Reproductive performance of "nurse sows" in Danish piggeries.

The use of nurse sows in Danish piggeries is common practice because of large litter sizes; however, the effect of being selected as a nurse sow on subsequent reproductive performance is unknown. Therefore, the aim of this study was to quantify a nurse sow's reproductive performance in the subsequent litter. Nurse sows were defined as sows weaning their own litter at least 18 days postpartum and thereafter nursing another litter (nurse litter) before service. Data (2012-2013) from 20 piggeries with more than 14.5 live born piglets per litter and a stable distribution of sows among parities over time were selected. Records from 79,864 litters were obtained and analyzed using mixed linear and logistic regression models. The average lactation lengths were 40.3 days for nurse sows and 27.8 days for non-nurse (normal) sows. Nurse sows weaned on average 12.4 piglets and subsequently 11.5 nurse piglets, whereas non-nurse weaned 11.7 piglets in their single weaning. There was no difference in re-service rate between nurse and non-nurse sows in the subsequent reproductive cycle. Subsequent litter size in the next reproductive cycle was higher for nurse sows than that for non-nurse sows (18.69 vs. 18.11 total born piglets; P < 0.001). Nurse sows were of a slightly lower parity than non-nurse sows (3.12 vs. 3.27, P < 0.001), and nurse sows had an increased weaning to estrus interval compared to non-nurse sows (4.23 vs. 4.19 days, P < 0.001). The results indicate that nurse sows were selected among sows nursing large litters and could therefore suggest that these sows represent the best percentile of sows in a given piggery. In conclusion, this survey indicated no negative effects of being selected as a nurse sow on the subsequent reproductive performance. On the contrary, nurse sows gave birth to more piglets compared to non-nurse sows in their subsequent litter.

A dynamic growth model for prediction of nutrient partitioning and manure production in growing-finishing pigs: Model development and evaluation.

Nutrient loading and air emissions from swine operations raise environmental concerns. The objective of the study was to describe and evaluate a mathematical model (Davis Swine Model) of nutrient partitioning and predict manure excretion and composition on a daily basis. State variables of the model were AA, fatty acids, and a central pool of metabolites that supplied substrate for lipid synthesis and oxidation. The model traced the fate of ingested nutrients and water through digestion and intermediary metabolism into body protein, fat, water, and ash, where body protein and fat represented the body constituent pools. It was assumed that fluxes of metabolites follow saturation kinetics, depending on metabolite concentrations. The main inputs to the model were diet nutrient composition, feed intake, water-to-feed ratio, and initial BW. First, the model was challenged with nutrient partitioning data and then with excretion data. The data had 48 different feeding regimes with contrasting energy and lysine intakes at 2 different stages of growth. The overall observed and predicted mean were 109 and 112 g/d for protein deposition and 132 and 136 g/d for lipid deposition respectively, suggesting minor mean bias. Root mean square prediction error (RMSPE) was used in evaluation of the model for its predictive power. The overall RMSPE was 2.2 and 4.1 g/d for protein and lipid deposition, respectively. The excretion database used for evaluation of the model was constructed from 150 digestibility trials using growing-finishing pig diets that had a wide range of nutrient chemical composition. Nutrient and water excretion were quantified using the principle of mass conservation. The average daily observed and predicted manure production was 3.79 and 3.99 kg/d, respectively, with a RMSPE of 0.49 kg/d. There was a good agreement between observed and predicted mean fecal N output (9.9 and 9.8 g/d, respectively). Similarly, the overall observed and predicted mean urine N output was 21.7 and 21.3 g/d, respectively, suggesting minor mean bias. The RMSPE was 1.9 and 4.1 g/d for fecal and urinary N, respectively. Evaluation of the model showed that the model predicts manure excretion and N content well and can be used to assess environmental mitigation options from swine operations.

Determination of protein and amino acid requirements of lactating sows using a population-based factorial approach.

Determination of appropriate nutritional requirements is essential to optimize the productivity and longevity of lactating sows. The current recommendations for requirements do not consider the large variation between animals. Therefore, the aim of this study was to determine the amino acid recommendations for lactating sows using a stochastic modeling approach that integrates population variation and uncertainty of key parameters into establishing nutritional recommendations for lactating sows. The requirement for individual sows was calculated using a factorial approach by adding the requirement for maintenance and milk. The energy balance of the sows was either negative or zero depending on feed intake being a limiting factor. Some parameters in the model were sow-specific and others were population-specific, depending on state of knowledge. Each simulation was for 1000 sows repeated 100 times using Monte Carlo simulation techniques. BW, back fat thickness of the sow, litter size (LS), average litter gain (LG), dietary energy density and feed intake were inputs to the model. The model was tested using results from the literature, and the values were all within ±1 s.d. of the estimated requirements. Simulations were made for a group of low- (LS=10 (s.d.=1), LG=2 kg/day (s.d.=0.6)), medium- (LS=12 (s.d.=1), LG=2.5 kg/day (s.d.=0.6)) and high-producing (LS=14 (s.d.=1), LG=3.5 kg/day (s.d.=0.6)) sows, where the average requirement was the result. In another simulation, the requirements were estimated for each week of lactation. The results were given as the median and s.d. The average daily standardized ileal digestible (SID) protein and lysine requirements for low-, medium- and high-producing sows were 623 (CV=2.5%) and 45.1 (CV=4.8%); 765 (CV=4.9%) and 54.7 (CV=7.0%); and 996 (CV=8.5%) and 70.8 g/day (CV=9.6%), respectively. The SID protein and lysine requirements were lowest at week 1, intermediate at week 2 and 4 and the highest at week 3 of lactation. The model is a valuable tool to develop new feeding strategies by taking into account the variable requirement between groups of sows and changes during lactation. The inclusion of between-sow variation gives information on safety margins when developing new dietary recommendations of amino acids and protein for lactating sows.

Multivariate and univariate analysis of energy balance data from lactating dairy cows.

The objectives of the study were to develop a multivariate framework for analyzing energy balance data from lactating cows and investigate potential changes in maintenance requirements and partial efficiencies of energy utilization by lactating cows over the years. The proposed model accounted for the fact that metabolizable energy intake, milk energy output, and tissue energy balance are random variables that interact mutually. The model was specified through structural equations implemented in a Bayesian framework. The structural equations, along with a model traditionally used to estimate energetic parameters, were fitted to a large database of indirect calorimetry records from lactating cows. Maintenance requirements and partial efficiencies for both models were similar to values reported in the literature. In particular, the estimated parameters (with 95% credible interval in parentheses) for the proposed model were: net energy requirement for maintenance equal to 0.36 (0.34, 0.38) MJ/kg of metabolic body weight·day; the efficiency of utilizing dietary energy for milk production and tissue gain were 0.63 (0.61, 0.64) and 0.70 (0.68, 0.72), respectively; the efficiency of utilizing body stores for milk production was 0.89 (0.87, 0.91). Furthermore, additional analyses were conducted for which energetic parameters were allowed to depend on the decade in which studies were conducted. These models investigated potential changes in maintenance requirements and partial efficiencies over the years. Canonical correlation analysis was used to investigate the association between changes in energetic parameters with additional dietary and animal characteristics available in the database. For both models, net energy requirement for maintenance and the efficiency of utilizing dietary energy for milk production and tissue gain increased in the more recent decades, whereas the efficiency of utilizing body stores for milk production remained unchanged. The increase in maintenance requirements in modern milk production systems is consistent with the literature that describes increased fasting heat production in cows of higher genetic merit. The increase in utilization of dietary energy for milk production and tissue gain was partially attributed to the changes in dietary composition, in particular to the increase in dietary ether extract to levels closer to currently observed in modern milk production systems. Therefore, the estimated energetic parameters from this study can be used to update maintenance requirements and partial efficiencies of energy utilization in North American feeding systems for lactating cows.

Energy and nutrient deposition and excretion in the reproducing sow: model development and evaluation.

Air and nutrient emissions from swine operations raise environmental concerns. During the reproduction phase, sows consume and excrete large quantities of nutrients. The objective of this study was to develop a mathematical model to describe energy and nutrient partitioning and predict manure excretion and composition and methane emissions on a daily basis. The model was structured to contain gestation and lactation modules, which can be run separately or sequentially, with outputs from the gestation module used as inputs to the lactation module. In the gestating module, energy and protein requirements for maintenance, and fetal and maternal growth were described. In the lactating module, a factorial approach was used to estimate requirements for maintenance, milk production, and maternal growth. The priority for nutrient partitioning was assumed to be in the order of maintenance, milk production, and maternal growth with body tissue losses constrained within biological limits. Global sensitivity analysis showed that nonlinearity in the parameters was small. The model outputs considered were the total protein and fat deposition, average urinary and fecal N excretion, average methane emission, manure carbon excretion, and manure production. The model was evaluated using independent data sets from the literature using root mean square prediction error (RMSPE) and concordance correlation coefficients. The gestation module predicted body fat gain better than body protein gain, which was related to predictions of body fat and protein loss from the lactation model. Nitrogen intake, urine N, fecal N, and milk N were predicted with RMSPE as percentage of observed mean of 9.7, 17.9, 10.0, and 7.7%, respectively. The model provided a framework, but more refinements and improvements in accuracy of prediction (particularly urine N) are required before the model can be used to assess environmental mitigation options from sow operations.

Genetic parameters for male fertility and its relationship to skatole and androstenone in Danish Landrace boars.

Concerns have been raised regarding selection against the boar taint compounds, androstenone and skatole, due to potential unfavorable genetic correlations with important male fertility traits (i.e., selection of boars with low levels of these boar taint compounds might also reduce male fertility). Hence, the objective of this investigation was to study the genetic association between direct measures of male fertility and the boar taint compounds in Danish Landrace pigs. Concentrations of skatole and androstenone in the back fat were available for approximately 6,000 and 1,000 Landrace boars, respectively. The litter size traits, such as total number born, live piglets at d 5, and piglet survival until d 5 on relatives of the slaughter boars, were extracted from the Danish Landrace breeding program, yielding 35,715 records. Semen volume, sperm concentration, subjective sperm quality score, and total number of sperm were available from 95,267 ejaculates. These ejaculates were collected between 2005 and 2012 and originated from 3,145 Landrace boars from 12 AI stations in Denmark. The traits were analyzed using single and multitrait animal models including univariate random regression models. Skatole and androstenone concentrations were moderate to highly heritable (i.e., 0.33 and 0.59, respectively). The genetic correlation between the two compounds was moderate (0.40). Genetic variance of sperm production per ejaculate increased during the productive life of the boar, resulting in heritability estimates increasing from 0.18 to 0.31. Genetic correlations between sperm production per ejaculate at different ages were high and generally larger than 0.8, indicating that later genetic merit can be predicted from records at an early age. The heritability (based on service-sire genetic component) of both total number of piglets born and survival to d 5 were 0.02, and the correlation between these effects and the additive genetic effect on boar taint ranged from 0.05 to -0.40 (none of these correlations were significantly different from zero). Most importantly, the genetic correlations between skatole and androstenone and the different semen traits tended to be more favorable with increase in age of the boars. In conclusion, these data suggest that concentrations of skatole and androstenone can be reduced through genetic selection without negatively affecting important male fertility traits in Danish Landrace pigs.

Genetic parameters for different measures of feed efficiency and related traits in boars of three pig breeds.

Residual feed intake (RFI) is commonly used as a measure of feed efficiency at a given level of production. A total of 16,872 pigs with their pedigree traced back as far as possible was used to estimate genetic parameters for RFI, growth performance, food conversion ratio (FCR), body conformation, and feeding behavior traits in 3 Danish breeds [Duroc (DD), Landrace (LL), and Yorkshire (YY)]. Two measures of RFI were considered: residual feed intake 1 (RFI1) was calculated based on regression of daily feed intake (DFI) from 30 to 100 kg on initial test weight and ADG from 30 to 100 kg (ADG2). Residual feed intake 2 (RFI2) was as RFI1, except it was also regressed with respect to backfat (BF). The estimated heritabilities for RFI1 and RFI2 were 0.34 and 0.38 in DD, 0.34 and 0.36 in LL, and 0.39 and 0.40 in YY, respectively. The heritabilities ranged from 0.32 (DD) to 0.54 (LL) for ADG2, from 0.54 (DD) to 0.67 (LL) for BF, and from 0.13 (DD) to 0.19 (YY) for body conformation. Feeding behavior traits including DFI, number of visits to feeder per day (NVD), total time spent eating per day (TPD), feed intake rate (FR), feed intake per visit (FPV), and time spent eating per visit (TPV) were moderately to highly heritable. Residual feed intake 2 was genetically independent of ADG2 and BF in all breeds, except it had low genetic correlation to ADG2 in YY (0.2). Residual feed intake 1 was also genetically independent of ADG2 in DD and LL. Both RFI traits had strong genetic correlations with DFI (0.85 to 0.96) and FCR (0.76 to 0.99). They had low or no genetic correlations with feeding behavior traits. Unfavorable genetic correlations were found between ADG2 and both BF and DFI. Among feeding behavior traits, DFI had low genetic correlations to other traits in all breeds. High and negative genetic correlations were also found between TPD with FR (-0.79 in YY to -0.88 in DD), NVD, and TPD (-0.91 in DD to -0.94 in YY) and between NVD and FPV (-0.83 in DD to -0.91 in YY) in all breeds. The genetic trend for feed efficiency was favorable in all breeds regardless of the definition of feed efficiency used. In summary, RFI1 and RFI2 were heritable and selection for reduced RFI2 can be performed without adversely affecting ADG and BF and could replace FCR in the selection index for the Danish pig breeds. Selection could also be based on RFI1 for breeds with fewer concerns about a negative effect of BF or for breeds that do not have BF records.

Anti-methanogenic effects of monensin in dairy and beef cattle: a meta-analysis.

Monensin is a widely used feed additive with the potential to minimize methane (CH4) emissions from cattle. Several studies have investigated the effects of monensin on CH4, but findings have been inconsistent. The objective of the present study was to conduct meta-analyses to quantitatively summarize the effect of monensin on CH4 production (g/d) and the percentage of dietary gross energy lost as CH4 (Ym) in dairy cows and beef steers. Data from 22 controlled studies were used. Heterogeneity of the monensin effects were estimated using random effect models. Due to significant heterogeneity (>68%) in both dairy and beef studies, the random effect models were then extended to mixed effect models by including fixed effects of DMI, dietary nutrient contents, monensin dose, and length of monensin treatment period. Monensin reduced Ym from 5.97 to 5.43% and diets with greater neutral detergent fiber contents (g/kg of dry matter) tended to enhance the monensin effect on CH4 in beef steers. When adjusted for the neutral detergent fiber effect, monensin supplementation [average 32 mg/kg of dry matter intake (DMI)] reduced CH4 emissions from beef steers by 19±4 g/d. Dietary ether extract content and DMI had a positive and a negative effect on monensin in dairy cows, respectively. When adjusted for these 2 effects in the final mixed-effect model, monensin feeding (average 21 mg/kg of DMI) was associated with a 6±3 g/d reduction in CH4 emissions in dairy cows. When analyzed across dairy and beef cattle studies, DMI or monensin dose (mg/kg of DMI) tended to decrease or increase the effect of monensin in reducing methane emissions, respectively. Methane mitigation effects of monensin in dairy cows (-12±6 g/d) and beef steers (-14±6 g/d) became similar when adjusted for the monensin dose differences between dairy cow and beef steer studies. When adjusted for DMI differences, monensin reduced Ym in dairy cows (-0.23±0.14) and beef steers (-0.33±0.16). Monensin treatment period length did not significantly modify the monensin effects in dairy cow or beef steer studies. Overall, monensin had stronger antimethanogenic effects in beef steers than dairy cows, but the effects in dairy cows could potentially be improved by dietary composition modifications and increasing the monensin dose.

Genetic parameters for androstenone and skatole as indicators of boar taint and their relationship to production and litter size traits in Danish Landrace.

Boar taint is an offensive odor that affects the smell and taste of cooked pork, resulting mainly from the accumulation of skatole and androstenone in the back fat of intact males. The aim of the study was to estimate genetic parameters for skatole and androstenone and their genetic relationship to production and litter size traits. Concentrations of skatole and androstenone in the back fat were available for approximately 6,000 and 1,000 Landrace boars, respectively. The concentrations were log-transformed to align phenotypic measures to a normal distribution. Heritability estimates for Log(skatole) and Log(androstenone) were 0.33 and 0.59, respectively. The genetic correlation between the 2 measures of boar taint was 0.37, suggesting that genetic selection against boar taint based on only 1 of the chemical compounds could be insufficient. The boar taint compounds had low and mostly favorable genetic correlations with the production traits. Most noticeable, a favorable genetic correlation of -0.20 between meat percentage and Log(skatole) was estimated and hence continued selection for lean pigs can also slowly reduce the level of boar taint if the desired carcass weight is kept constant. The relationship between litter size traits (measured on sows related to boars) and boar taint compounds was low and not significantly different from 0. In conclusion, skatole and androstenone can be reduced through selection without affecting important economical production and litter size traits. Therefore, animal breeding offers an effective and sustainable solution to surgical castration of male piglets.

Late gestation undernutrition can predispose for visceral adiposity by altering fat distribution patterns and increasing the preference for a high-fat diet in early postnatal life.

We have developed a sheep model to facilitate studies of the fetal programming effects of mismatched perinatal and postnatal nutrition. During the last trimester of gestation, twenty-one twin-bearing ewes were fed a normal diet fulfilling norms for energy and protein (NORM) or 50% of a normal diet (LOW). From day 3 postpartum to 6 months (around puberty) of age, one twin lamb was fed a conventional (CONV) diet and the other a high-carbohydrate-high-fat (HCHF) diet, resulting in four groups of offspring: NORM-CONV; NORMHCHF; LOW-CONV; LOW-HCHF. At 6 months of age, half of the lambs (all males and three females) were slaughtered for further examination and the other half (females only) were transferred to a moderate sheep diet until slaughtered at 24 months of age (adulthood). Maternal undernutrition during late gestation reduced the birth weight of LOW offspring (P<0·05), and its long-term effects were increased adrenal size in male lambs and adult females (P<0·05), increased neonatal appetite for fat-(P=0·004) rather than carbohydrate-rich feeds (P<0·001) and reduced deposition of subcutaneous fat in both sexes (P<0·05). Furthermore, LOW-HCHF female lambs had markedly higher visceral:subcutaneous fat ratios compared with the other groups (P<0·001). Postnatal overfeeding (HCHF) resulted in obesity (.30% fat in soft tissue) and widespread ectopic lipid deposition. In conclusion, our sheep model revealed strong pre- and postnatal impacts on growth, food preferences and fat deposition patterns. The present findings support a role for subcutaneous adipose tissue in the development of visceral adiposity, which in humans is known to precede the development of the metabolic syndrome in human adults.

A methodological approach to estimate the lactation curve and net energy and protein requirements of beef cows using nonlinear mixed-effects modeling.

The objective of this study was to evaluate methods to predict the secretion of milk and net energy and protein requirements of beef cows (Bos indicus and B. taurus) after approximately 1 mo postpartum using nonlinear mixed-effect modeling (NLME). Twenty Caracu × Nellore (CN) and 10 Nellore (NL) cows were inseminated to Red Angus bulls, and 10 Angus × Nellore (AN) were bred to Canchim bulls. Cows were evaluated from just after calving (25 ± 11 d) to weaning (220 d). Milk yield was estimated by weighing calves before and after suckling (WSW) and by machine milking (MM) methods at 25, 52, 80, 109, 136, 164, 193, and 220 ± 11 d of lactation. Brody and simple linear equations were consecutively fitted to the data and compared using information criteria. For the Brody equation, a NLME model was used to estimate all lactation profiles incorporating different sources of variation (calf sex and breed of cow, cow as a nested random effect, and within-cow auto-correlation). The CV for the MM method (29%) was less than WSW (45%). Consequently, the WSW method was responsible for reducing the variance about 1.5 times among individuals, which minimized the ability to detect differences among cows. As a result, only milk yield MM data were used in the NLME models. The Brody equation provided the best fit to this dataset, and inclusion of a continuous autoregressive process improved fit (P < 0.01). Milk, energy and protein yield at the beginning of lactation were affected by cow genotype and calf sex (P < 0.001). The exponential decay of the lactation curves was affected only by genotype (P < 0.001). Angus × Nellore cows produced 15 and 48% more milk than CN and NL during the trial, respectively (P < 0.05). Caracu × Nellore cows produced 29% more milk than NL (P < 0.05). The net energy and net protein requirements for milk yield followed a similar ranking. Male calves stimulated their dams to produce 11.7, 11.4, and 11.9% more milk, energy and protein, respectively (P < 0.05). The MM method is better than the WSW technique to detect genetic or environmental differences in milk yield among beef cows. The data obtained by the MM method and analyzed by NLME models allows the inclusion of fixed effects, random effects and an auto-regressive process in lactation equations to describe lactation curves and net energy and protein requirements. The NLME is a powerful tool to describe differences in the secretion of milk due to heterosis and cell mammary external stimulus in beef cows.

Characterizing bovine adipocyte distribution and its relationship with carcass and meat characteristics using a finite mixture model.

The appreciation of adipose tissue complexity has initiated a new era of multifaceted investigations that continue to provide findings in adipocyte biology, but quantitative descriptions of adipocyte distribution are lacking. The first objective was to develop a finite mixture model to model adipocyte bimodal distribution and to correlate these estimates with carcass and meat characteristics. A secondary objective was to demonstrate within-animal observed variability in adipocyte cellularity. Steers were finished on a high-grain diet (n = 14) or grass (n = 16). One 12-cm thick LM steak from each steer was collected during harvest. A probability density function was developed that partitioned the cell diameter population into small and large populations and described the relative proportions of cells for each animal in these 2 distinct populations. Five parameters were estimated through the finite mixture model: the means (µ(1) and µ(2)) and SD (σ(1) and σ(2)) for the small and large adipocyte populations, respectively, and a proportion parameter (p) describing the proportion of the distribution of the smaller adipocyte populations. The proportion parameter for all animals tended to be different (P = 0.07) between groups with the grain presenting a p of 22.5 ± 12.5% and grass 16.2 ± 4.7%. The µ(2) was correlated with yield grade (YG, P = 0.04), and σ(2) with final BW, HCW, dressing percentage, YG, and quality grade score (P = 0.01). When correlating these parameters with the sensory data, µ(2) and σ(2) were correlated with tenderness (P ≤ 0.05), σ(1) and p with juiciness (P ≤ 0.05), and p with overall palatability (P = 0.01). Adipocyte cellularity variability was measured by examining the results from 5 randomly chosen steers from each group (grain and grass). In this subset, the µ(1) and p ranged from 32.1 to 46.1 µm and 1 to 27% for grass-finished steers, and ranged from 33.7 to 41.0 µm and 10 to 48% for grain-finished steers. The µ(2) and (1 - p) ranged from 75.0 to 105.1 µm and 73 to 99% for grass-finished steers, respectively, and ranged from 84.8 to 124.0 µm and 52 to 90% for grain-finished steers, respectively. The finite mixture model provides a quantitative description of the distribution of adipocytes and contributes to explaining adipocyte biology. Adipocyte cellularity variability among samples within an animal is a topic that should be further evaluated, as well as its correlation with other factors, such as gene expression and hormone secretion.

Predicting milk yield and composition in lactating sows: a Bayesian approach.

The objective of this study was to develop a framework describing the milk production curve in sows as affected by parity, method of milk yield (MY) determination, litter size (LS), and litter gain (LG). A database containing data on LS, LG, dietary protein and fat content, MY, and composition measured on more than 1 d during lactation and method for determining MY from peer reviewed publications and individual sow data from 3 studies was constructed. A Bayesian hierarchical model was developed to analyze milk production data. The classical Wood curve was used to model time trends in MY during lactation, and it was re-parameterized expressing the natural logarithm of MY values at d 5, 20, and 30 as functional parameters. The model incorporated random effects of experiment, sow nested within experiment, and fixed effects of LS, LG, parity, and method through the functional parameters of the Wood curve. A second set of models were constructed to analyze milk composition data, including day in milk, LS, dietary protein, and fat contents. Four scenarios with different LG and LS were constructed using the framework to estimate the energy output in milk at different days during lactation. The estimated energy output was compared with energy output values calculated using the 1998 NRC method. Milk yield was underestimated by approximately 20% with the weigh-suckle-weigh technique compared with the deuterium oxide dilution technique (P < 0.001). The mean LG and LS for the dataset were 2.05 kg/d (1.0; 3.3) and 9.5 piglets (5; 14), respectively. The MY was affected by LS on d 5 and 20 (P < 0.001) and by LG on d 20 (P < 0.001) and d 30 (P = 0.004). The mean time to peak lactation was 18.7 d (SD = 1.06) postpartum and mean MY at peak lactation was 9.23 kg (SD = 0.14). The average protein, lactose, and fat content of milk was 5.22 (SD = 0.06), 5.41 (SD = 0.08), and 7.32% (SD = 0.17%), respectively. The NE requirement for lactation increased from d 5 to 20 because of increased MY. Requirements also increased with increasing LG and LS. The framework could be used to predict energy and protein requirements for lactation under different production expectations and can be incorporated into a whole animal model for determination of energy and nutrient requirements for lactating sows, which can optimize sow performance and longevity.

Estimating digestible methionine requirements for laying hens using multivariate nonlinear mixed effect models.

The purpose of this paper was to develop a unified framework for analyzing dose-response data in farm animals and apply it to meta-analysis of digestible Met requirement studies in laying hens. A database containing Met dose-response data from 23 trials originating from 15 peer-reviewed publications was constructed. A multivariate nonlinear mixed effects model was chosen as the statistical framework to model egg mass (g/d) and feed utilization (%) responses simultaneously. The framework accounted for responses being correlated in both the random effects and the errors, which provided a superior fit to data compared with modeling these separately. The framework was implemented in the NLMIXED procedure in SAS and could accommodate different dose-response functions per response. Three different dose-response functions-the linear broken line, quadratic plateau, and monomolecular functions-were used to identify the best-performing function. The statistical model, which used the quadratic plateau as the functional base for both responses, provided the best fit to data; hence, it was used for biological inference. Effects of secondary covariates of nutritional, genetic, and experimental design origin were investigated, and a systematic trend across studies was detected. The BW of the hens accounted for the majority of the between-study variability by allowing the asymptotic responses to be dependent on the BW. The final estimate of the Met requirement for maximizing egg mass was 356 (SE = 6.1) mg/d, whereas the corresponding Met requirement for maximizing feed utilization was significantly higher (P < 0.001), at 390 (SE = 11) mg/d. Thus, it can be concluded that the biological requirement for digestible Met is at least 356 mg/d. When multiple responses are collected in dose-response studies, these should preferably be analyzed simultaneously because the requirements are established within the same statistical model that accounts for correlation among the errors and among the random effects associated with distinct responses in the model.

Modeling the efficiency of phosphorus utilization in growing pigs.

Microbial phytase has been used to reduce P excretion from swine to mitigate environmental pollution. The objective of the study was to quantify the effect of feeding a low-P phytase-supplemented diet on growth and P utilization in growing pigs using mathematical models. A total of 20 weaned piglets (BW = 6.5 kg) housed in metabolism cages were randomly assigned to a standard diet (STD) or P-amended diet containing reduced P content and supplemented with phytase (AMN) with 10 pigs/diet. Body weight and feed consumption were recorded weekly so complete growth and cumulative P intake (cPI) curves could be modeled. A function with fixed point of inflexion (Gompertz) and a variable point of inflexion (generalized Michaelis-Menten) were considered in determining bioequivalence by analyzing BW vs. age relationships, whereas the monomolecular function was used to describe BW vs. cPI. All functions were incorporated into a nonlinear mixed effects model, and a first-order autoregressive correlation structure was implemented to take into account repeated measures. There was no difference between the 2 groups in final BW when the Gompertz equation was fitted (176 vs. 178 kg with SE of 7 kg for the STD and AMN, respectively) or the rate parameter (0.0140 vs. 0.0139 with SE of 0.0004 for the STD and AMN, respectively). The generalized Michaelis-Menten equation also showed a similar trend. When BW was expressed as a function of cPI the derivative with respect to cPI represented P efficiency, so it was possible to analyze the expected difference of the 2 diets in using P for BW gain and express it as a continuous function of cPI. The analysis showed through the entire growth period the difference in P efficiency was different from zero. On average, 56 g of supplemented inorganic P was consumed by a pig fed the AMN to reach market weight. In contrast, 309 g of supplemented inorganic P was consumed by the group fed the STD to reach similar BW. It would depend on other factors, but feeding pigs the AMN can result in economic benefit. Pigs fed the AMN excreted 19% less P compared with those fed the STD. In conclusion, nonlinear mixed model analysis (with repeated measures) was suitable for growth and efficiency analysis and showed that pigs fed the AMN consumed less than 20% of the inorganic P and performed as well as those fed the traditional inorganic P supplemented diet. The implications for mitigating P pollution, especially in areas where P loading is already problematic, are substantial.

A Bayesian approach to analyze energy balance data from lactating dairy cows.

The objective of the present investigation was to develop a Bayesian framework for updating and integrating covariate information into key parameters of metabolizable energy (ME) systems for dairy cows. The study addressed specifically the effects of genetic improvements and feed quality on key parameters in current ME systems. These are net and metabolizable energy for maintenance (NE(M) and ME(M), respectively), efficiency of utilization of ME for milk production (k(L)) and growth (k(G)), and efficiency of utilization of body stores for milk production (k(T)). Data were collated from 38 studies, yielding 701 individual cow observations on milk energy, ME intake, and tissue gain and loss. A function based on a linear relationship between milk energy and ME intake and correcting for tissue energy loss or gain served as the basis of a full Bayesian hierarchical model. The within-study variability was modeled by a Student t-distribution and the between-study variability in the structural parameters was modeled by a multivariate normal distribution. A meaningful relationship between genetic improvements in milk production and the key parameters could not be established. The parameter k(L) was linearly related to feed metabolizability, and the slope predicted a 0.010 (-0.0004; 0.0210) change per 0.1-unit change in metabolizability. The effect of metabolizability on k(L) was smaller than assumed in present feed evaluation systems and its significance was dependent on collection of studies included in the analysis. Three sets of population estimates (with 95% credible interval in parentheses) were generated, reflecting different degrees of prior belief: (1) Noninformative priors yielded 0.28 (0.23; 0.33) MJ/(kg(0.75)d), 0.55 (0.51; 0.58), 0.86 (0.81; 0.93) and 0.66 (0.58; 0.75), for NE(M), k(L), k(G), and k(T), respectively; (2) Introducing an informative prior that was derived from a fasting metabolism study served to combine the most recent information on energy metabolism in modern dairy cows. The new estimates of NE(M), k(L), k(G) and k(T) were 0.34 (0.28; 0.39) MJ/(kg(0.75)d), 0.58 (0.54; 0.62), 0.89 (0.85; 0.95), and 0.69 (0.60; 0.79), respectively; (3) finally, all informative priors were used that were established from literature, yielding estimates for NE(M), k(L), k(G), and k(T) of 0.29 (0.11; 0.46) MJ/(kg(0.75)d), 0.60 (0.54; 0.70), 0.70 (0.50; 0.88), and 0.80 (0.67; 0.97), respectively. Bayesian methods are especially applicable in meta-analytical studies as information can enter at various stages in the hierarchical model.

A multivariate nonlinear mixed effects method for analyzing energy partitioning in growing pigs.

Simultaneous equations have become increasingly popular for describing the effects of nutrition on the utilization of ME for protein (PD) and lipid deposition (LD) in animals. The study developed a multivariate nonlinear mixed effects (MNLME) framework and compared it with an alternative method for estimating parameters in simultaneous equations that described energy metabolism in growing pigs, and then proposed new PD and LD equations. The general statistical framework was implemented in the NLMIXED procedure in SAS. Alternative PD and LD equations were also developed, which assumed that the instantaneous response curve of an animal to varying energy supply followed the law of diminishing returns behavior. The Michaelis-Menten function was adopted to represent a biological relationship in which the affinity constant (k) represented the sensitivity of PD to ME above maintenance. The approach accommodated inclusion of a PD potential (PD(Potential)) concept. This was described by a Gompertz function, which was parameterized in terms of the maximum rate of PD (PD(Max)) and corresponding BW (BW(PDMax)) at that point. Metabolizable energy for LD was equated to the difference between ME intake and the sum of ME used for maintenance and PD. Metabolizable energy designated for PD and LD was used, with efficiencies k(p) and k(f), respectively. The new equations were compared with the van Milgen and Noblet (1999) equations using 2 comprehensive data sets on energy metabolism in growing pigs. The 2 equation sets were evaluated using information criteria, which showed that the new equations performed best for data set II, whereas the reverse was true for the first. For the data set I population, estimates for k(p) and k(f) were 0.57 (SE = 0.05) and 0.84 (SE = 0.03), respectively. Maintenance was quantified as 1.10 (SE = 0.08) MJ/d*kg(0.55). The animal variation in the parameter k(p) was estimated to be 6% CV. The animal variation in PD(Max) and k(f) was estimated to be 9 and 10% of the population estimates, respectively. It was concluded that application of the MNLME framework was superior to the multivariate nonlinear regression model because the MNLME method accounted for correlated errors associated with PD and LD measurements and could also include the random effect of animal. It is recommended that multivariate models used to quantify energy metabolism in growing pigs should account for animal variability and correlated measurement errors.

Flexible alternatives to the Gompertz equation for describing growth with age in turkey hens.

A total of 49 profiles of growing turkey hens from commercial flocks were used in this study. Three flexible growth functions (von Bertalanffy, Richards, and Morgan) were evaluated with regard to their ability to describe the relationship between BW and age and were compared with the Gompertz equation with its fixed point of inflection, which might result in its overestimation. For each function, 4 ways of analysis were implemented. A basic model was fitted first, followed by implementation of a first-order autoregressive correlation structure. A model that considered only mature BW varied with year and another that considered only the rate coefficient varied with different years were applied. The results showed that the fixed point of inflection of the Gompertz equation can be a limitation and that the relationship between BW and age in turkeys was best described using flexible growth functions. However, the Richards equation failed to converge when fitted to the turkey growth data; therefore, it was not considered further. Inclusion of an autoregressive process of the first order rendered a substantially improved fit to data for the 3 growth functions. The Morgan equation provided the best fit to the data set and was used for characterizing mean growth curves for the 7 yr of production. It was estimated that the maximum growth rate occurred at 3.74, 3.65, 3.99, 4.18, 4.05, 4.01, and 3.77 kg BW for production years from 1997 to 2003, respectively. It is recommended that flexible growth functions should be considered as an alternative to the simpler functions (with a fixed point of inflection) for describing the relationship between BW and age in turkeys because they were easier to fit and very often gave a closer fit to data points because of their flexibility, and therefore a smaller residual MS value, than simpler models. It can also be recommended that studies should consider adding a first-order autoregressive process when analyzing repeated measures data with nonlinear models.

A multilevel nonlinear mixed-effects approach to model growth in pigs.

Growth functions have been used to predict market weight of pigs and maximize return over feed costs. This study was undertaken to compare 4 growth functions and methods of analyzing data, particularly one that considers nonlinear repeated measures. Data were collected from an experiment with 40 pigs maintained from birth to maturity and their BW measured weekly or every 2 wk up to 1,007 d. Gompertz, logistic, Bridges, and Lopez functions were fitted to the data and compared using information criteria. For each function, a multilevel nonlinear mixed effects model was employed because it allowed for estimation of all growth profiles simultaneously, and different sources of variation (i.e., sex, pig, and litter effects) were incorporated directly into the parameters. Furthermore, variance in-homogeneity and within-pig correlation were introduced to the functions. Inclusion of a variance of power function and a continuous autoregressive process of first order rendered a substantially improved fit to data for all 4 growth functions. The Lopez function provided the best fit to the data set and was used for characterizing mean growth curves for the 3 sexes (barrows, boars, and gilts). It was estimated that the maximum growth rate occurs at 117, 134, and 96 kg of BW for barrows, boars, and gilts, respectively. Hence, the gilts reached their maximum growth rate at an earlier stage in life compared with boars. Mature size of pigs varied systematically with sex and was estimated to be 466, 537, and 382 kg of BW for the barrows, boars, and gilts, respectively. These estimates are significantly affected by the duration of the experimental period, and it is recommended that future studies looking at estimating the mature size in animals are conducted long enough so that the BW visually stabilizes. Furthermore, studies should consider adding continuous autoregressive process when analyzing nonlinear mixed models with repeated measures.