Marcio Antonio Dornelles Goncalves

An update on modeling dose-response relationships: Accounting for correlated data structure and heterogeneous error variance in linear and nonlinear mixed models.

Advanced methods for dose-response assessments are used to estimate the minimum concentrations of a nutrient that maximizes a given outcome of interest, thereby determining nutritional requirements for optimal performance. Contrary to standard modeling assumptions, experimental data often present a design structure that includes correlations between observations (i.e., blocking, nesting, etc.) as well as heterogeneity of error variances; either can mislead inference if disregarded. Our objective is to demonstrate practical implementation of linear and nonlinear mixed models for dose-response relationships accounting for correlated data structure and heterogeneous error variances. To illustrate, we modeled data from a randomized complete block design study to evaluate the standardized ileal digestible (SID) Trp:Lys ratio dose-response on G:F of nursery pigs. A base linear mixed model was fitted to explore the functional form of G:F relative to Trp:Lys ratios and assess model assumptions. Next, we fitted 3 competing dose-response mixed models to G:F, namely a quadratic polynomial (QP) model, a broken-line linear (BLL) ascending model, and a broken-line quadratic (BLQ) ascending model, all of which included heteroskedastic specifications, as dictated by the base model. The GLIMMIX procedure of SAS (version 9.4) was used to fit the base and QP models and the NLMIXED procedure was used to fit the BLL and BLQ models. We further illustrated the use of a grid search of initial parameter values to facilitate convergence and parameter estimation in nonlinear mixed models. Fit between competing dose-response models was compared using a maximum likelihood-based Bayesian information criterion (BIC). The QP, BLL, and BLQ models fitted on G:F of nursery pigs yielded BIC values of 353.7, 343.4, and 345.2, respectively, thus indicating a better fit of the BLL model. The BLL breakpoint estimate of the SID Trp:Lys ratio was 16.5% (95% confidence interval [16.1, 17.0]). Problems with the estimation process rendered results from the BLQ model questionable. Importantly, accounting for heterogeneous variance enhanced inferential precision as the breadth of the confidence interval for the mean breakpoint decreased by approximately 44%. In summary, the article illustrates the use of linear and nonlinear mixed models for dose-response relationships accounting for heterogeneous residual variances, discusses important diagnostics and their implications for inference, and provides practical recommendations for computational troubleshooting.

Effects of amino acids and energy intake during late gestation of high-performing gilts and sows on litter and reproductive performance under commercial conditions

The objective of this study was to determine the effects of AA and energy intake during late gestation on piglet birth weight and reproductive performance of high-performing (14.5 total born) gilts and sows housed under commercial conditions. At d 90 of gestation, a total of 1,102 females (PIC 1050) were housed in pens by parity group (gilts or sows) with approximately 63 gilts and 80 sows in each pen, blocked by BW within each pen, and each female was randomly assigned to dietary treatments within BW block. Dietary treatments consisted of combinations of 2 standardized ileal digestible (SID) AA intakes (10.7 or 20.0 g/d SID Lys and other AA met or exceeded the NRC [2012] recommendations) and 2 energy intakes (4.50 or 6.75 Mcal/d intake of NE) in a 2 × 2 factorial arrangement. Data were analyzed using generalized linear mixed models specified to recognize pen as the experimental unit for parity and the individual female as the experimental unit for dietary treatments. Results indicate an overall positive effect of high energy intake on BW gain during late gestation, although this effect was more manifest under conditions of high, as opposed to low, AA intake (interaction, < 0.001). Furthermore, the magnitude of BW gain response to increased energy intake was greater ( < 0.001) for sows compared with gilts. Sows fed high energy intake had a reduced probability of piglets born alive ( < 0.004) compared with those fed low energy, but no evidence for differences was found in gilts. This can be explained by an increased probability ( = 0.002) of stillborns in sows fed high energy intake vs. sows fed low energy intake. There were no evidences for differences among dietary treatments in litter birth weight and individual piglet birth weight of total piglets born. However, individual born alive birth weight was approximately 30 ± 8.2 g heavier ( = 0.011) for females fed high, as opposed to low, energy intake. Furthermore, piglets born alive were approximately 97 ± 9.5 g heavier ( < 0.001) for sows than for gilts. Preweaning mortality was decreased ( = 0.034) for females fed high AA intake compared with females fed low AA intake regardless of energy level. In conclusion, 1) BW gain of gilts and sows depended not only on energy but also on AA intake, 2) sows fed increased amount of energy had an increased stillborn rate, and 3) increased energy intake during late gestation had a positive effect on individual piglet birth weight with no evidence for such an effect for AA intake.

Effects of standardized ileal digestible tryptophan: lysine ratio on growth performance of nursery pigs.

Two experiments were conducted to estimate the standardized ileal digestible (SID) Trp:Lys ratio requirement for growth performance of nursery pigs. Experimental diets were formulated to ensure that lysine was the second limiting AA throughout the experiments. In Exp. 1 (6 to 10 kg BW), 255 nursery pigs (PIC 327 × 1050, initially 6.3 ± 0.15 kg, mean ± SD) arranged in pens of 6 or 7 pigs were blocked by pen weight and assigned to experimental diets (7 pens/diet) consisting of SID Trp:Lys ratios of 14.7%, 16.5%, 18.4%, 20.3%, 22.1%, and 24.0% for 14 d with 1.30% SID Lys. In Exp. 2 (11 to 20 kg BW), 1,088 pigs (PIC 337 × 1050, initially 11.2 kg ± 1.35 BW, mean ± SD) arranged in pens of 24 to 27 pigs were blocked by average pig weight and assigned to experimental diets (6 pens/diet) consisting of SID Trp:Lys ratios of 14.5%, 16.5%, 18.0%, 19.5%, 21.0%, 22.5%, and 24.5% for 21 d with 30% dried distillers grains with solubles and 0.97% SID Lys. Each experiment was analyzed using general linear mixed models with heterogeneous residual variances. Competing heteroskedastic models included broken-line linear (BLL), broken-line quadratic (BLQ), and quadratic polynomial (QP). For each response, the best-fitting model was selected using Bayesian information criterion. In Exp. 1 (6 to 10 kg BW), increasing SID Trp:Lys ratio linearly increased ( 0.05) ADG and G:F. For ADG, the best-fitting model was a QP in which the maximum ADG was estimated at 23.9% (95% confidence interval [CI]: [<14.7%, >24.0%]) SID Trp:Lys ratio. For G:F, the best-fitting model was a BLL in which the maximum G:F was estimated at 20.4% (95% CI: [14.3%, 26.5%]) SID Trp:Lys. In Exp. 2 (11 to 20 kg BW), increasing SID Trp:Lys ratio increased ( 0.05) ADG and G:F in a quadratic manner. For ADG, the best-fitting model was a QP in which the maximum ADG was estimated at 21.2% (95% CI: [20.5%, 21.9%]) SID Trp:Lys. For G:F, BLL and BLQ models had comparable fit and estimated SID Trp:Lys requirements at 16.6% (95% CI: [16.0%, 17.3%]) and 17.1% (95% CI: [16.6%, 17.7%]), respectively. In conclusion, the estimated SID Trp:Lys requirement in Exp. 1 ranged from 20.4% for maximum G:F to 23.9% for maximum ADG, whereas in Exp. 2 it ranged from 16.6% for maximum G:F to 21.2% for maximum ADG. These results suggest that standard recommendations may underestimate the SID Trp:Lys requirement for nursery pigs from 11 to 20 kg BW.

Effects of pelleting conditioner retention time on nursery pig growth performance.

A total of 180 nursery pigs (PIC 327 × 1050; initially 12.6 kg) were used in an 18-d study to determine the effects of pellet mill conditioning parameters and feed form on pig performance. All diets were similar, and different feed processing parameters were used to create experimental treatments. Factors considered were conditioning time (15, 30, or 60 s) and feed form (mash or pelleted). To remove the confounding factor of feed form, pelleted samples were reground to a similar particle size as the mash diet. Treatments included: 1) mash diet without thermal processing (negative control), 2) pelleted diet conditioned for 30 s (positive control), 3) pelleted diet conditioned for 15 s and reground, 4) pelleted diet conditioned for 30 s and reground, and 5) pelleted diet conditioned for 60 s and reground. Pigs were weaned and fed a common acclimation diet for 21 d before the start of the experiment. Growth and feed disappearance were then measured for 18 d. All diets had similar levels of percentage total starch, but thermally processed diets had a 1.67 to 1.87-fold increase in percentage gelatinized starch compared to the mash diet. Average daily gain and G:F did not differ between treatments overall, but pigs fed the positive control pelleted diet had decreased ADFI ( < 0.05) compared to pigs fed all other diets. Preplanned contrasts revealed that pigs fed mash diets tended to have greater ADG ( < 0.10) compared to those fed pelleted and reground diets. This suggests that processing may have had a negative influence on feed utilization, which is further supported by the finding that pigs fed mash diets tended to have greater ADG ( < 0.10) compared to those fed diets that were thermally processed, regardless of regrinding. Considering these results, it was not surprising that pigs fed mash diets had greater ADG and ADFI ( < 0.05) than those fed pelleted diets. When directly comparing diets conditioned at 60 rpm, fed either as whole pellets or reground to mash consistency, pigs fed pelleted diets had improved G:F ( < 0.05) due to lower ADFI ( < 0.05) but similar ADG. The expected improvement in G:F from pelleting (6.8%) was observed but lost when diets were reground to near original mash particle size. This may indicate that diet form from the actual pelleting process impacts G:F more than conditioner retention time.

Effects of dietary calcium to phosphorus ratio and addition of phytase on growth performance of nursery pigs1

Two studies were conducted to evaluate the growth performance and percentage bone ash of nursery pigs fed various combinations of Ca and P provided by inorganic sources or phytase. In Exp. 1, pens of pigs (n = 720, initially 6.1 ± 0.98 kg) were blocked by initial BW. Within blocks, pens were randomly assigned to one of six treatments (12 pens per treatment) in a three-phase diet regimen. Treatments were arranged in a 2 × 3 factorial with main effects of Ca (0.58% vs. 1.03%) and standardized total tract digestible (STTD) P (0.33% and 0.45% without phytase, and 0.45% with 0.12% of the P released by phytase). During treatment period, Ca × P interactions were observed for all growth criteria (P < 0.05). When diets had low Ca, pigs fed 0.45% STTD P with phytase had greater (P < 0.01) ADG and ADFI than those fed 0.33% or 0.45% STTD P without phytase. When high Ca was fed, ADG and ADFI were similar among pigs fed 0.45% STTD P with or without phytase and were greater than those fed 0.33% STTD P. Gain:feed was reduced (P < 0.01) when high Ca and low STTD P were fed relative to other treatments. On d 21, radiuses were collected from 1 pig per pen for bone ash analysis. Pigs fed 0.33% STTD P had decreased (P < 0.05) percentage bone ash than those fed 0.45% STTD P with or without phytase when high Ca was fed, but this P effect was not observed for low Ca diets (Ca × P interaction, P = 0.007). In Exp. 2, 36 pens (10 pigs per pen, initially 6.0 ± 1.08 kg) were used in a completely randomized design. Treatments were arranged in a 2 × 3 factorial with the main effects of STTD P (at or above NRC [NRC. 2012. Nutrient Requirements of Swine. 11th rev. ed. Washington (DC): National Academic Press.] requirement estimates) and total Ca (0.65, 0.90, and 1.20%). Experimental diets were fed during phases 1 and 2, followed by a common phase 3 diet. Diets at NRC (2012) P level contained 0.45% and 0.40% STTD P, compared with 0.56% and 0.52% for diets greater than the NRC (2012) estimates, in phase 1 and 2, respectively. During treatment period, increasing Ca decreased (linear, P = 0.006) ADG, but increasing STTD P marginally increased (P = 0.084) ADG, with no Ca × P interaction. When diets contained NRC (2012) P levels, pigs fed 1.20% Ca had decreased (P < 0.05) G:F than those fed 0.65% or 0.90% Ca; however, when high STTD P were fed, G:F was not affected by Ca (Ca × P interaction, P = 0.018). In conclusion, excess Ca decreased pig growth and percentage bone ash when diets were at or below NRC (2012) requirement for STTD P, but these negative effects were alleviated by adding monocalcium P or phytase to the diet.

Standardized ileal digestible valine:lysine dose response effects in 25- to 45-kg pigs under commercial conditions

Two experiments were conducted to estimate the standardized ileal digestible valine:lysine (SID Val:Lys) dose response effects in 25- to 45-kg pigs under commercial conditions. In experiment 1, a total of 1,134 gilts (PIC 337 × 1050), initially 31.2 kg ± 2.0 kg body weight (BW; mean ± SD) were used in a 19-d growth trial with 27 pigs per pen and seven pens per treatment. In experiment 2, a total of 2,100 gilts (PIC 327 × 1050), initially 25.4 ± 1.9 kg BW were used in a 22-d growth trial with 25 pigs per pen and 12 pens per treatment. Treatments were blocked by initial BW in a randomized complete block design. In experiment 1, there were a total of six dietary treatments with SID Val at 59.0, 62.5, 65.9, 69.6, 73.0, and 75.5% of Lys and for experiment 2 there were a total of seven dietary treatments with SID Val at 57.0, 60.6, 63.9, 67.5, 71.1, 74.4, and 78.0% of Lys. Experimental diets were formulated to ensure that Lys was the second limiting amino acid throughout the experiments. Initially, linear mixed models were fitted to data from each experiment. Then, data from the two experiments were combined to estimate dose-responses using a broken-line linear ascending (BLL) model, broken-line quadratic ascending (BLQ) model, or quadratic polynomial (QP). Model fit was compared using Bayesian information criterion (BIC). In experiment 1, ADG increased linearly (P = 0.009) with increasing SID Val:Lys with no apparent significant impact on G:F. In experiment 2, ADG and ADFI increased in a quadratic manner (P < 0.002) with increasing SID Val:Lys whereas G:F increased linearly (P < 0.001). Overall, the best-fitting model for ADG was a QP, whereby the maximum mean ADG was estimated at a 73.0% (95% CI: [69.5, >78.0%]) SID Val:Lys. For G:F, the overall best-fitting model was a QP with maximum estimated mean G:F at 69.0% (95% CI: [64.0, >78.0]) SID Val:Lys ratio. However, 99% of the maximum mean performance for ADG and G:F were achieved at, 68% and 63% SID Val:Lys ratio, respectively. Therefore, the SID Val:Lys requirement ranged from73.0% for maximum ADG to 63.2% SID Val:Lys to achieve 99% of maximum G:F in 25- to 45-kg BW pigs.

Regression Analysis to Predict the Impact of High Neutral Detergent Fiber Ingredients on Carcass Yield

Research has shown that carcass yield is reduced when feeding distillers dried grains with solubles (DDGS) or other high fiber ingredients. Considering the financial implications of changing carcass yield, the objective of this project was to develop regression equations to accurately estimate carcass yield from dietary NDF withdrawal strategies. Data from 8 trials originating from 5 journal articles, 2 theses, and 1 technical memo were used to develop a regression equation to predict carcass yield. The regression analysis showed that number of days in the withdrawal period (WP), NDF level in the dietary phase prior to the final phase (NDF1), NDF level in the last dietary phase before marketing (NDF2), and the interaction between NDF2 and WP (NDF2 × WP), were the most important variables in the dataset to predict carcass yield. The resulting regression equation: carcass yield, % = 0.03492 × WP (d) – 0.05092 × NDF1 (%) – 0.06897 × NDF2 (%) – 0.00289 (NDF2 (%) × WP (d)) + 76.0769 may be used to predict the influence of dietary NDF and NDF withdrawal strategy on carcass yield.

Optimizing Dietary Net Energy for Maximum Profitability in Growing- Finishing Pigs

Feed accounts for a significant portion of swine production cost, with dietary energy alone representing more than half of the total cost. Considering the financial implications of determining the energy content of the diet, the objective of this research project was to develop a tool to accurately estimate the dietary NE content that yields maximum profitability for growing-finishing pigs. A Microsoft Excel®-based model was developed to contrast dietary NE defined by the user with recommended concentrations that are intended to maximize profitability in user defined production and economic scenarios. To calculate pig performance, the model uses prediction equations for ADG and feed efficiency. In addition, the model also uses the NDF content of the diet because of its effect on dressing percentage. For profitability calculations, a non-linear mathematical programming model was designed to select the optimum dietary NE content that yields the greatest income over total cost per pig on a live or carcass basis. The model can be used to predict dietary NE content that yields the highest economic benefit considering dynamic productive and economic scenarios. The model can be downloaded at www.ksuswine.org.

Effects of Standardized Total Tract Digestible Phosphorus on Growth Performance, Carcass Characteristics, Bone Mineralization, and Economics of 53- to 287-lb Pigs

A total of 1,130 barrows and gilts (PIC; 359 × Camborough, initial pen average BW of 53.2 ± 1.61 lb) were used in a 111-d growth trial to determine the standardized total tract digestible (STTD) P requirement of growing-finishing pigs from 53 to 287 lb. Pens of pigs were randomly assigned to 1 of 6 dietary treatments in a randomized complete block design with BW as a blocking factor. There were 7 replicate pens per treatment and 26 to 27 pigs per pen (at least 13 barrows and gilts per pen). The experimental diets were corn-soybean meal-based and were fed in 4 phases. The 6 dietary treatments were formulated to contain 80, 90, 100, 115, 130, and 150% of the NRC publication STTD P requirement for growingfinishing pigs within each phase. The STTD P levels were achieved by increasing the amount of limestone and monocalcium phosphate at the expense of corn, maintaining a similar 1.14 to 1.16:1 total Ca:P ratio across treatments, with no added phytase. Overall, increasing STTD P resulted in a quadratic response in ADG, F/G, and final BW (P < 0.05). The greatest improvement was observed with STTD P at 130% of NRC for ADG and final BW and 115% STTD P of the NRC recommendation for F/G. Average daily feed intake increased linearly with the inclusion of STTD P (P < 0.05). Increasing STTD P resulted in a linear increase in fat-free bone ash weight and percentage ash (P < 0.05). Barrows had significantly higher percentage ash compared to gilts (P < 0.05). Increasing STTD P resulted in an increase in HCW and carcass ADG, with the greatest response observed with STTD P at 130% of NRC (quadratic, P < 0.05). There was a marginally significant quadratic response in carcass F/G, with the greatest improvement with STTD P at 115% of NRC (P < 0.10). Carcass yield decreased with increasing STTD P (linear, P < 0.05), while there was a marginally significant decrease in backfat and increase in fat-free lean (linear, P < 0.10). No difference was observed for loin depth (P > 0.05). Feed cost per pig increased linearly with increasing STTD (P < 0.05). Contrarily, gain value per pig and IOFC increased quadratically, with the greatest profit observed with STTD P at 130% of NRC (P < 0.05). For ADG and feed efficiency, the quadratic model demonstrated the best fit. The maximum response in ADG was estimated at 122% of NRC STTD P, and the maximum response in feed efficiency was estimated at 116% of NRC STTD P. The broken-line linear model best fitted the data for ash as a percentage of fat-free dried bone, with a plateau achieved at 131% of the NRC STTD P requirement. In conclusion, the estimated STTD P requirement for growing-finishing pigs from 53 to 287 lb ranged from 116 to 131% of the NRC publication recommendations for each phase, depending on the response criteria and statistical model.

Effects of Crude Protein and Amino Acid to Lysine Ratio on Finishing Pig Growth Performance and Carcass Characteristics

The increased availability of synthetic amino acids has reduced the amount of intact protein sources used in swine diets. The objective of this study was to determine the effects of different CP levels and AA to Lys ratios on growth performance and carcass characteristics in late finishing pigs. A total of 1,682 pigs (327 × 1050, PIC, Hendersonville, TN; initially 252.7 lb BW) were used in a 25-d growth trial arranged in an unbalanced randomized complete block design with 25 pigs per pen and initially 8 or 16 pens per treatment. Dietary treatments were arranged in a 2 × 2 + 1 factorial consisting of combinations of 10.3 or 13.5% CP and 2 AA to Lys ratios plus a control diet (13.5% CP from soybean meal). The standardized ileal digestible (SID) ratios to Lys were 55% Met+Cys, 68% Thr, 17% Trp, 65% Val, 56% Ile, and 32% His for PIC (2013) and 60% Met+Cys, 68% Thr, 20% Trp, 72% Val, 55% Ile, and 37% His for the Modified ratio. Overall, from d 0 to 25, pigs fed the control diet had increased ADG (P < 0.001) compared with pigs fed diets formulated with the PIC or Modified AA:Lys ratios. There were no statistical differences in ADFI observed between the treatments. For F/G, there was a 2-way marginally significant interaction (P = 0.066) where F/G was improved for pigs fed the PIC AA:Lys ratios with 13.5% CP compared to those fed diets with 10.3% CP; however, there were no statistical differences in F/G between CP levels in pigs fed Modified AA:Lys ratios. Final BW was increased in pigs fed the control compared to pigs fed diets formulated with the PIC (P = 0.017) or Modified (P < 0.001) AA:Lys ratios. Pigs fed 10.5% CP provided by glutamic acid and glycine, regardless of AA:Lys ratio, had increased (P = 0.031) carcass yield; however, there was no statistical differences between the dietary treatments regarding HCW, backfat, loin depth, and percentage lean. In conclusion, reducing intact protein (soybean meal) decreased growth performance and the inclusion of a nitrogen source (glycine and glutamic acid) was not able to recover growth performance in this commercial study. The 2 amino acid ratios in the low crude protein diets evaluated in this study did not improve growth performance or carcass characteristics.