Modeling the Impact of Birth and Twenty-Day Body Weight on the Postweaning Growth of Pigs

The Professional Animal Scientist 23 (2007):211–223

Modeling the Impact of Birth and Twenty-Day Body Weight on the Postweaning Growth of Pigs A. P. Schinckel,*1 PAS, R. Cabrera,†2 R. D. Boyd,†3 S. Jungst,† C. Booher,† M. Johnston,†3 P. V. Preckel,‡ and M. E. Einstein* *Department of Animal Sciences, Purdue University, West Lafayette, IN 47907; †PIC North America, Hendersonville, TN 37075; and ‡Department of Agricultural Economics, Purdue University, West Lafayette, IN 47907

ABSTRACT A stochastic pig BW growth model was developed to reproduce the nonlinear relationships between birth, weaning, and nursery exit BW to later grow-finish BW. Serial grow-finish BW measurements of barrows and gilts were fitted to mixed model generalized Michaelis-Menten equations. Two random effects of the generalized Michaelis-Menten equations were predicted as linear-quadratic functions of birth and 20-d weaning BW. Equations were developed to produce a population of pigs that reproduced the variances and covariance of the random effects. The stochastic model reproduced the variances of the random effects, serial BW, and days to achieve 125 kg BW. The simulation model also reproduced the nonlinear relationships of 20-d and 70-d BW with days to achieve 125 kg and 168-d BW. The simulation data slightly over-predicted 168-d BW and under-predicted days to reach 125-kg BW of barrows with 20-d BW less than 5 kg. Overall, the relationships between

1

Corresponding author: aschinck@ purdue.edu 2 Present address: Ralco Nutrition, Marshall, MN 56258. 3 Present address: Hanor Company, Inc., Franklin, KY 42134.

days to achieve 125 kg BW and 168-d BW with 70-d BW were similar for the actual and simulated data. The sorting of pigs into light and heavy groups based on weaning or nursery exit BW was evaluated. Sorting based on nursery exit BW was more effective in producing groups of pigs with large differences in days to 125 kg BW than sorting based on weaning BW. The model could be used to identify the optimal management of pigs to reduce variation in BW growth. Key words: pig growth, growth equations, stochastic model

INTRODUCTION Variability in the growth rates of pigs is important to the economic costs and income of both the producer and processor (King, 1999; Patience et al., 2002; Patience and Beaulieu, 2006). The optimization of pork production systems requires knowledge of the betweenpig variation in BW and carcass composition in order to develop the most beneficial strategy (King, 1999; Le Dividich, 1999). Mixed model nonlinear analysis software is available which accounts for the underlying variance-covariance structure of serial BW data (Craig and Schinckel, 2001; Schinckel and

Craig, 2002) and it can be used to develop a stochastic pig growth model to predict the variation in BW to target market BW (Schinckel et al., 2003). Some of the variation in age to achieve target market BW is due to variation in birth BW and growth rate from birth to weaning at 14 to 28 d of age (Le Dividich, 1999; Wolter and Ellis, 2001; Klindt et al., 2003). Some production systems have considered separating the smallest pigs from the remaining pigs and rearing the 2 groups of pigs on different finishing sites (Tokach, 2004). Early BW from birth to 70 d of age have nonlinear relationships with subsequent BW and the age to achieve target market BW (Schinckel et al., 2007). The use of nonlinear analyses to account for the nonlinear relationships between the early BW on postweaning BW growth has not been evaluated. The objective of this research was to evaluate the use of mixed model nonlinear analysis to parameterize and model the variation in postweaning BW growth in relationship to the variation in birth and weaning BW.

MATERIALS AND METHODS Data from a weaning management research trial were used to

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evaluate the relationships of early BW growth with postweaning BW growth (Schinckel et al., 2007). The BW data included pigs that had been sow-reared to weaning. Each pig was weighed at birth and weaning at approximately 20 d of age. The pigs were then moved from the farrowing building to the nursery building, where the pigs were allotted to pens by gender and size. The pigs remained in the nursery facility for approximately 7 wk and then were moved into the finish building. They were phase-fed 4 nursery diets based on a feed budget, irrespective of BW. The target on-test BW was 32 kg. Each pig was individually weighed and ear tagged with a transponder for feed intake evaluation with individual feed intake recording equipment feeders (Osborne Industries Inc., Osborne, KS). The pigs were fed using a 4-phase diet program (22 to 41 kg, 41 to 73 kg, 73 to 95 kg, and 95 kg to market). The diets were corn-soybean meal based. Each pig was reweighed every 2-wk period until the pigs reached 122.5 kg. The BW data taken when the pigs entered the nursery were adjusted for age using the PROC GLM procedure of SAS (SAS Inst. Inc., Cary, NC). The final model, which included the effects of weaning treatment, age, and weaning treatment by age, was used to adjust the nursery entry BW to 20 d of age. The grow-finish BW data was fitted to a generalized Michaelis-Menten (GMM) equation (Lopez et al., 2000). The equation has 2 alternative forms: WTi,t = [(WT0 × KC) + (WF × tC)]/(KC + tC) or WTi,t = WT0 + [(WF − WT0) × (t/K)C)]/[1 + (t/ K)C)] where WTi,t is the BW of the ith pig at t days of age, WTo is the mean birth BW, WF is mean mature BW, K is a parameter equal to the days of age in which one-half WF is achieved, and C is a unitless parameter related to changes in proportional growth and shape of the growth curves (Lopez et al., 2000).

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In this function, each pig’s actual birth BW (WTi,o) was used. This function has an inflection point (IP) characterized by age, IP = K × [(C-1)/(C + 1)](1/C) and BW, IP = [(1 + (1/C)) × WT0 + (1 − (1/C)) × WF]/ 2.

Estimation The BW data from each sex of pigs were fitted to the fixed effects GMM function using the nonlinear mixed (NLMIXED) procedure of SAS. The 3 alternative single random effects models were evaluated based on the Akaike’s Information Criteria (AIC). Then additional random effects were added in a stepwise order based on AIC values. The significance of this additional parameter was determined by comparing the AIC values. The R2 values were calculated as squared correlation between the predicted and actual observations. The relative standard deviation (RSD) was calculated with the equation RSD = ⎡T I ⎤ ⎢ ∑∑(ei,t)2/(n − p) ⎥1/2 where ei,t is ⎣ t=1i=1 ⎦ the residual value of the ith pig at age t, n is the number of observations, and p is the number of parameters in the model. The NLMIXED procedure provided predicted values for the random effect of each pig, variance estimates for each random effect, the covariance between the 2 random effects, and the residual variance. The BW of each pig was predicted for the GMM function at 70, 126, and 168 d of age. The ages to achieve 105 and 125 kg BW were predicted for each pig. The between pig variation in these target BW are important parameters when evaluating alternative marketing strategies.

Simulation of 20-d BW and Birth BW For pigs of each sex, birth BW was simulated as follows: birth BWi = mean birth BW + 0.38z1

where birth BWi is the birth BW of the ith pig, 0.38 is the birth BW SD, and z1 has a standard normal distribution. The 20-d BW data of each sex group was fitted to a regression equation including birth BW, (birth BW)2, and (birth BW)3. Variables that had probability values greater than 0.10 were deleted from the regression equation. This regression equation was used to predict 20-d BW from birth BW. The 20-d BW was simulated as follows: 20-d BWi = 20-d BW predicted from birth BWi + z2 × RSD, where z2 is a value sampled from a standard normal distribution and RSD is the sex-specific RSD from the equation predicting 20-d BW from birth BW.

Simulation of wfi and ci To simulate a growth curve for each pig, WF is replaced by (WF + wfi) and C is replaced by (C + ci) where wfi and ci are values for the ith pig. The ci and wfi values were simulated to have a bivariate normal distribution. For each sex group, the wfi and ci values were fitted to regression equations including birth BW, (birth BW)2, 20d BW, and (20-d BW)2 using the GLM procedure of SAS. Variables with probability values greater than 0.10 were deleted. The prediction equations for wfi and ci were substantially different in terms of the variables included in the regression equations, the R2 values, and RSD values.

Simulation of the Distribution of the wfi and ci Random Effects Equations were developed to reproduce the total variance in random effects of the GMM function and their covariance. The equations developed for each sex group were as follows: wfi = predicted (wfi) + b3z3 + b4z4; ci = predicted ci + b5z3 + b6z6, where the predicted values for wfi and ci are the values predicted by the regression equations including birth and 20-d BW

variables b3, b4, b5, and b6 are linear regression coefficients; and z3, z4, z5, and z6 are variables produced by sampling independent standard normal distributions. The correlation of the predicted wfi and ci variables was calculated for pigs of each sex group. The covariance of wfi and ci is the sum of the covariance of the predicted wfi and ci values and b3b5. The values for b3 and b5 were calculated such that the covariances for wfi and ci were reproduced. The relative value of b3 to b5 was set to be proportional to the ratio of the SD of wfi to the SD of ci. The variance in wfi equals the sum of the variance of the predicted values of wfi, b32 and b42. The variance in ci equals the sum of the variance of the predicted values for ci, b52 and b62. Thus, the values of b4 and b6 were calculated to reproduce the total variances of wfi and ci.

Evaluation of the Simulation Model to Reproduce the Original Data The simulation program was used to produce BW data from birth to approximately 125 kg BW for 1,000 barrows and 1,000 gilts. The means, SD, skewness, and Shapiro-Wilk statistic for normality (Univariate Procedure of SAS) were evaluated for birth, 70-, 126-, and 168-d BW. The same statistics were calculated for the random effects (ci and wfi) and the IP variables. The correlation between the ran-

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dom effects was calculated. Also, the correlations between the random effects and the serial BW and days to attain 125 kg were evaluated for the actual and simulated data. The simulation model should reproduce the nonlinear relationships between birth, 20-d, and 70-d BW and the late finishing BW. Therefore, the actual and simulated 168-d BW and days to 125 kg BW values were fitted to regression equations including 3 sets of variables: the linear, quadratic, and cubic effects of either birth, 20-d, or 70-d BW. Nonsignificant variables (P > 0.10) were deleted from each regression equation.

nursery. Three levels of sorting were evaluated: 1) splitting the pigs in upper and lower 50th percentile groups, 2) sorting out the lower 15% of the pigs, and 3) sorting out the lower 5% of the pigs based on BW.

Sorting Simulation A set of 7,000 barrows and 7,000 gilts were simulated. The pigs were simulated to have been farrowed over a 7-d period with a mean weaning age of 20 d (range of 17 to 23 d), and 1,000 pigs of each sex farrowed each day. Each pig’s weaning weight was simulated as its 20d BW adjusted to its actual weaning age. The pigs were simulated to be moved from the nursery to the grow-finish facility at a mean age of 70 d. The simulation program was used to model 4 sorting strategies: 1) sorting within sex at weaning, 2) sorting across sexes at weaning, 3) sorting within sex at movement from the nursery, and 4) sorting across sexes at movement from the

RESULTS AND DISCUSSION Model Relationship to 20-d BW to Birth BW The relationship of 20-d BW to birth BW was evaluated by regression analyses (Table 1). Separate equations were developed for each sex due to significant (P < 0.10) sex by birth BW and sex by (birth BW)2 interactions. The regression equation for the barrows had lower R2 and greater RSD than the gilts. These results suggest that sex-specific equations need to be utilized in modeling the relationship between 20-d and birth BW.

Modeling the Relationship Between Early and Subsequent BW Growth The parameter estimates of the GMM function are shown in Table 2. The WF and C parameters were the 2 parameters considered as random effects. The C parameter primarily determines the percentage of mature BW (WF) at which maximal ADG is achieved (Lopez et al., 2000; Schinckel et al., 2006). The gilts had a greater predicted WF and C value than barrows.

Table 1. Regression of 20-d BW on birth weight1 b1 Treatment Barrows Gilts

b2

b3

b0

Estimate

SE

P

Estimate

SE

P

Estimate

SE

P

R2

RSD2

−1.05 8.58

10.0 −9.8

5.1 6.0

0.05 0.10

−4.6 8.3

2.8 3.7

0.09 0.03

0.79 −1.88

0.5 0.7

0.10 0.01

0.245 0.324

1.14 1.01

1 Adjusted 20-d BW, (in kg) = b0 + b1 × (birth BW) + b2 × (birth BW)2 + b3 × (birth BW)3 where b0, b1, b2, b3, and b4 are regression coefficients. 2 RSD = relative standard deviation.

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Table 2. Parameter estimates and approximate SE for generalized Michaelis-Menten equation1 Barrows

WF K C Var (e) Var (wfi) Var (ci) Cov (wfi, ci)

Gilts

Estimate

SE

RSD,2 kg

R2

Estimate

SE

RSD, kg

R2

361.3 227.3 1.964 4.92 936 0.0155 0.965

15.4 8.2 0.027 0.27 171 0.0025 0.46

2.08 — — — — — —

0.9961 — — — — — —

425.7 277.7 1.861 4.87 1981 0.018 2.28

21.3 11.7 0.024 0.24 387 0.0026 0.74

2.07 — — — — — —

0.9960 — — — — — —

1 The equation has the form WTi.t = [(WTo × KC) + (WF × tC)]/(KC + tC), where WTi,t is the BW of the ith pig at t days of age, WTo is birth BW, WF is mature BW, and C and K are growth parameters. The Var (e) is the predicted residual variance, var (wfi) is the variance of the random effects for WF, and var (ci) is the variance of the random effects for C. The cov (wfi, ci) is the covariance between the 2 random effects. 2 RSD = relative standard deviation.

The regression equations that were used to predict the random effects of the GMM function from birth and 20-d BW are shown in Table 3. The R2 values for the equations ranged from 0.039 to 0.191. The prediction equations for ci and wfi for the barrows only included the linear 20-d BW variable with a negative regression coefficient for ci and positive regression coefficient for wfi. Thus for the barrows, the correlation between the predicted wfi and ci values had a value of −1. The gilt’s prediction equations for ci and wfi were quite different. The gilt’s prediction equation for wfi in-

additional data. These regression equations relating later BW growth to early BW are potentially affected by weaning management, season, and health status. Thus, these values are likely to be farm-genetic, population-sex, and possibly season specific. The least-squares means and SD for the predicted BW at the biweekly ages and predicted ages to achieve 105 and 125 kg BW are shown in Table 4. Overall, the simulation model reproduced the variances of the random effects and the correlation between the random effects. The simulation model repro-

cluded both birth BW and (birth BW)2. The gilt’s regression equation for ci included 20-d BW and (20-d BW)2. These regression equations are very important as they determine the ability of the stochastic model to reproduce the actual nonlinear relationships of birth and weaning BW to later BW. The data must have sufficient observations to identify the best form of the equations (linear, polynominal, nonlinear) and to include the truly important independent variables into the regression equations. Additional variables such as litter size and parity might become significant with

Table 3. Regression equations that predict the values of wfi and ci from birth and 20-d BW b1 Sex

b0

Estimate SE

b2 P

Estimate

SE

b3 P

Estimate

SE

b4 P

Estimate

SE

P

Equations for wfi2 Barrows −29.3 — — — — — — 4.52 2.2 0.04 — — — Gilts −131.1 136.6 56 0.02 30.9 17.0 0.08 — — — — — — Equations for ci Barrows 0.253 — — — — — — −0.393 0.008 0.001 — — — Gilts 0.782 — — — — — — −0.235 0.07 0.001 0.017 0.005 0.003 1

R2

RSD1

0.039 29.4 0.130 40.7 0.191 0.111

0.105 0.122

RSD = relative standard deviation. Values wfi or ci = b0 + b1 × (birth BW, kg) + b2 × (birth BW)2 + b3 × (birth BW)3 where b0, b1, b2, and b3 are the regression coefficients.

2

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Table 4. Statistics for the BW growth curve variables from the fitting of the actual and simulated data1 Actual

Simulated

Mean

SD

Skewness

P2

Mean

SD

Skewness

P2

Gilts Birth BW, kg 20-d BW, kg 70-d BW, kg 126-d BW, kg 168-d BW, kg Days to 105 kg Days to 125 kg wfi, kg ci r (wfi, ci) Age IP, d BW IP, kg ADG IP, kg/d

1.50 6.12 31.8 80.2 120.0 153.3 175.0 −0.42 −0.001 0.338 144.5 99.2 0.966

0.38 1.2 4.8 8.5 11.6 12.6 15.7 43.3 0.128 — 14.4 14.6 0.107

0.59 0.24 −0.40 −0.67 −0.78 2.12 2.65 −0.66 0.44 — 0.02 0.58 −0.58

0.01 0.17 0.10 0.05 0.03 0.001 0.001 0.007 0.07 — 0.95 0.01 0.01

1.49 6.19 32.0 80.3 120.2 153.9 174.7 −0.86 0.0 0.328 144.3 98.9 0.965

0.38 1.2 5.4 9.0 12.0 12.4 15.4 43.2 0.129 — 14.4 14.6 0.107

0.25 −0.04 0.22 0.06 0.02 0.52 0.72 −0.10 0.03 — −0.43 −0.06 0.02

0.01 0.25 0.04 0.48 0.97 0.001 0.001 0.93 0.70 — 0.001 0.31 0.99

Barrows Birth BW, kg 20-d BW, kg 70-d BW, kg 126-d BW, kg 168-d BW, kg Days to 105 kg Days to 125 kg wfi, kg ci r (wfi, ci) Age IP, d BW IP, kg ADG IP, kg/d

1.62 6.46 34.0 87.3 129.1 144.3 164.8 −0.19 0.00 0.199 127.6 89.6 1.020

0.38 1.3 4.4 7.7 10.5 9.5 11.9 29.8 0.117 — 9.6 9.8 0.092

0.52 0.26 −0.27 −0.24 −0.26 1.17 1.71 −0.35 0.56 — 0.0 0.52 −0.51

0.06 0.46 0.58 0.29 0.46 0.001 0.001 0.13 0.01 — 0.99 0.06 0.06

1.61 6.44 34.6 87.3 129.1 144.0 164.5 −0.64 0.00 0.190 128.0 89.6 1.020

0.37 1.3 4.5 2.9 10.8 9.34 11.9 29.7 0.116 — 9.5 9.8 0.089

0.10 −0.16 0.18 0.09 −0.02 0.24 0.39 −0.07 0.07 — −0.30 −0.11 −0.09

0.03 0.22 0.06 0.57 0.27 0.003 0.001 0.03 0.61 — 0.001 0.43 0.12

1

Values wfi and ci are random effects for the generalized Michaelis-Menten equation. r (wfi, ci) is the correlation of wfi and ci. IP = inflection point, the day in which maximum ADG is achieved. The ADG IP is the pig’s maximal ADG. 2 Probability that the values were sampled from a normal distribution based on Shapiro-Wilk Statistic.

duced the actual data set in terms of the means and SD for the serial BW, days to achieve 105 and 125 kg, and IP variables. The magnitude of skewness differed between the actual and simulated data for several variables. The values of wfi were not normally distributed for the actual data for the gilts (P = 0.007) and simulated data for the barrows (P = 0.03). Previous research has shown that the wfi values were normally distributed for pigs with high health status (Schinckel and Craig, 2002). However, the wfi values were significantly skewed and deviated from a normal distribution when pigs were reared under

average to below-average health status commercial environments. The values for days to achieve 105 and 125 kg BW were not normally distributed for either sex for the simulated or actual BW data. The equations for these variables can result in some level of skewness even when the random effects are normally distributed (Schinckel et al., 2005). The means and standard deviations for the predicted maximum ADG and age and BW at maximum ADG (IP) are also presented in Table 4. The actual values for the predicted BW and ADG at the IP variables had greater absolute values for

skewness than the simulated data. These variables were not normally distributed (P = 0.01 for the gilts, 0.06 for the barrows) for the actual data. In contrast, the values of the predicted age at IP variable were normally distributed (P = 0.95) for actual data and not normally distributed for the simulated data set (P = 0.001). In theory, the distribution of variables which are functions of wfi and ci including the BW, days to market BW, and IP variables should be reproduced if the distribution of the wfi and ci values and relationship between the wfi and ci values were reproduced by the stochastic model. The distribution of

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Table 5. Correlations of the values for the random effects of the generalized Michealis-Menten equation with BW and days to 125 kg BW1 Gilts

20-d BW 70-d BW 126-d BW 168-d BW Days to 125 kg

Simulated Actual Simulated Actual Simulated Actual Simulated Actual Simulated Actual

Barrows

wfi

ci

wfi

ci

0.193 0.213 0.296 0.329 0.679 0.712 0.878 0.898 −0.899 −0.891

−0.260 −0.238 −0.733 −0.767 −0.445 −0.415 −0.144 −0.106 0.084 0.077

0.197 0.196 0.480 0.455 0.818 0.826 0.948 0.962 −0.956 −0.940

−0.423 −0.436 −0.731 −0.772 −0.429 −0.385 −0.176 −0.091 0.178 0.060

1

Values wfi and ci are random effects for the generalized Michaelis-Menten equation.

the wfi and ci values and relationship between the wfi and ci values (linear or nonlinear) deserves further investigation on larger data sets. It is possible that environmental conditions which affect individual pigs differently, such as disease exposure, may affect the distribution of the wfi and ci values (Schinckel and Craig, 2002). Overall, the simulation model reproduced the correlations between the random effects and serial BW (Table 5). The correlation of the ci values with 168-d BW (−0.091 vs

Figure 1. Relationship of 168-d BW to birth BW for gilts as predicted by analyses of the actual and simulated data.

−0.176) and days to 125 kg BW (0.060 vs 0.178) were slightly greater in absolute value for the simulated data than the actual data. The regressions of 168-d BW and days to 125 kg BW on earlier BW are shown for the simulated and actual data sets in Table 6. The predicted values from the equations are shown in Figures 1 to 12. The stochastic model tended to over-predict the 168-d BW and under-predict the days to 125 kg BW of barrows with birth BW less than 1.2 kg. There are 2 possible reasons for these differences between the actual and simulated data. The first is that regression equations to predict the wfi and ci values only included the linear effects of 20-d BW. The relationships between birth BW and later BW predicted by the GMM were only indirectly predicted through the modeled relationship of 20-d BW and birth BW. The second reason is that the regression equation predicting wfi from 20-d BW only had an R2 of 0.039. The simulation program slightly over-predicted the 168-d BW and under-predicted the days to 125 kg BW of gilts with 1.9 to 2.5 kg birth BW. The regression equations of 168-d BW and days to 125 kg on

birth BW included a significant (birth BW)3 variable that was not significant for the simulated data. Overall, the simulation reproduced the nonlinear relationships of 168-d BW and days to 125 kg BW to 20-d and 70-d BW. The R2 of the prediction equations including 70-d BW were greater than the equations including either birth or 20-d BW. In some cases, the actual data resulted in regression equations with significant cubic effects when regression analysis of the simulated data did not find significant cubic effects.

Modeling the Impact Sorting Based on Weaning BW The results of sorting pigs within sex at weaning are shown in Table 7. Sorting the barrows into 2 50th percentile groups at weaning resulted in 2 groups of pigs with a 5.5 d difference in days to 125 kg BW and approximately equal SD (10.7 vs 10.8 d). Sorting the gilts into 2 50th percentile groups based on weaning BW resulted in a 17.0 d difference in days to 125 kg BW. The light gilts had a greater SD for days to 125 kg BW than the heavy group (14.1 vs. 11.8 d). The lightest 15% of gilts at weaning had a reduced SD in 20-d BW and greater SD for days to 125 kg BW than the heavy 85% of the gilts at weaning. The simulation model predicted that the lightest 5% of the barrows and lightest 5% of the gilts had substantially reduced SD in weaning BW with no reduction in their SD for days to 125 kg or 168-d BW. This result would not have been predicted by linear models. With linear models, the variance in the dependent variable (Y) = b2 variance (x) + residual variance, where b is the regression coefficient. The simulation model predicted that sorting of the lightest pigs at weaning results in a group of pigs that are relatively more uniform at weaning. However, the simulation model predicted that the light pigs’ growth rates are more

Barrows

Gilts

Barrows

Gilts

Barrows

Gilts

Barrows

Gilts

Barrows

Gilts

Barrows

Gilts

Sex

Actual Simulated Actual Simulated Actual Simulated Actual Simulated

Actual Simulated Actual Simulated Actual Simulated Actual Simulated

Actual Simulated Actual Simulated Actual Simulated Actual Simulated

Data

2

74.7 78.0 88.3 103.7 221.0 216.4 210.0 189.9

34.1 80.5 −4.8 67.0 284.4 219.8 299.8 228.9

b0

25.3 50.0 367.1 66.5 303.4 243.0 −126.9 219.8

b0, b1, b2, and b3 are the regression coefficients. RSD = relative standard deviation.

1

Days to 125 kg

Regression on 70-d BW 168-d BW, kg

Days to 125 kg

Regression on 20-d BW 168-d BW, kg

Days to 125 kg

Regression on birth BW 168-d BW, kg

Dependent Variable

4.38 2.88 −26.4 2.11 −6.25 −2.82 31.6 −1.78

11.7 11.0 10.2 5.57 −11.5 −10.7 −11.8 −5.37

131.9 41.0 224.0 107.1 −168.5 −47.3 −225.0 −110.5

Estimate

1.5 0.42 12.4 0.47 2.3 0.55 14.0 0.53

6.3 2.2 4.9 1.8 1.6 2.6 5.6 1.3

65.0 5.8 69.0 29.0 83.0 6.7 80.0 30.0

SE

b1

0.005 0.001 0.04 0.001 0.007 0.001 0.03 0.007

0.06 0.001 0.04 0.002 0.05 0.001 0.04 0.004

0.04 0.001 0.002 0.001 0.06 0.001 0.006 0.003

P

−0.0426 −0.0204 0.876 −0.0077 0.67 0.0197 −1.03 0.0043

−0.656 −0.635 −0.573 −0.24 0.60 0.59 0.70 0.21

−63.3 −8.74 −121.0 −60.7 81.1 10.4 122.0 62.4

Estimate

SE

0.025 0.006 0.38 0.004 0.04 0.008 0.46 0.002

0.40 0.17 0.26 0.14 0.28 0.21 0.42 0.11

37.0 1.8 39.0 18.0 43.0 2.2 45.0 18.0

b2

0.09 0.002 0.02 0.06 0.07 0.02 0.03 0.05

0.09 0.001 0.03 0.09 0.03 0.004 0.09 0.05

0.09 0.001 0.003 0.001 0.06 0.001 0.008 0.001

P

— — −0.0039 — — — 0.0105 —

— — — — — — — —

10.0 — 21.5 11.4 −12.9 — −21.6 −11.7

Estimate

— — 0.004 — — — 0.005 —

— — — — — — — —

4.6 — 7.0 3.7 6.4 — 8.1 3.3

SE

b3

— — 0.02 — — — 0.03 —

— — — — — — — —

0.03 — 0.003 0.002 0.04 — 0.09 0.002

P

Table 6. Regression of days to 125 kg BW and 168-d BW on birth, 20- or 70-d BW from the actual and simulated data set1

0.513 0.514 0.484 0.533 0.412 0.386 0.425 0.446

0.141 0.119 0.125 0.095 0.099 0.100 0.095 0.102

0.175 0.214 0.14 0.038 0.15 0.20 0.113 0.03

R2

8.2 8.3 7.7 7.5 12.1 12.3 9.1 8.8

10.9 11.2 10.0 10.3 15.0 14.8 11.4 11.3

10.7 10.6 9.9 11.9 14.6 14.0 11.3 11.7

RSD2

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Table 7. Effect of sorting at weaning within each sex1 Gilts Heavy 50% (> 6.18 kg)

Light 50% (< 6.18 kg)

Variable

Mean

SD

Birth BW, kg Weaning BW, kg Nursery BW, kg 168-d BW, kg Days to 105 kg Days to 125 kg % less than 105 kg % less than 90 kg Pigs less than 105 kg Pigs less than 90 kg

1.67 7.23 34.0 124.1 148.9 160.0 3.86 0.11 135 4

0.33 0.80 5.1 10.7 9.8 11.8 — — — —

Heavy 85% (> 4.83 kg) Mean Birth BW, kg Weaning BW, kg Nursery BW, kg 168-d BW, kg Days to 105 kg Days to 125 kg % less than 105 kg % less than 90 kg Pigs less than 105 kg Pigs less than 90 kg

1.55 6.54 32.9 122.3 150.8 172.1 6.5 0.034 387 20

Birth BW, kg Weaning BW, kg Nursery BW, kg 168-d BW, kg Days to 105 kg Days to 125 kg % less than 105 kg % less than 90 kg Pigs less than 105 kg Pigs less than 90 kg

1.52 6.32 32.5 121.5 151.5 172.9 7.7 0.38 514 25

Mean 1.33 5.5 30.5 117.8 155.4 177.0 14.2 0.71 497 25

SD 0.33 0.74 5.3 11.8 11.7 14.1 — — — —

Heavy 50% (> 6.47 kg) Mean 1.76 7.57 36.6 132.3 141.0 161.3 0.51 0.0 18 0

Light 15% (< 4.83 kg) SD

0.36 1.05 5.3 11.3 10.7 12.9 — — — —

Heavy 95% (> 4.09 kg) Mean

Barrows

SD 0.37 1.18 5.4 11.5 10.9 13.2 — — — —

Mean 1.20 4.21 27.3 113.4 159.9 181.6 23.3 0.86 245 9

1.12 3.62 25.0 110.1 163.2 185.1 33.7 1.1 118 4

0.34 0.84 5.1 10.7 8.8 10.7 — — — —

Heavy 85% (> 5.04 kg) SD

0.29 0.5 4.3 11.2 11.3 13.5 — — — —

Mean

SD 0.26 0.42 4.2 10.7 10.9 13.1 — — — —

0.35 1.11 5.3 10.8 9.0 10.8 — — — —

Heavy 95% (> 4.19 kg) Mean

SD

1.66 6.62 34.6 130.1 143.2 163.6 0.92 0.0 61 0

Mean 1.50 5.37 32.0 127.1 146.3 166.8 1.66 0.0 58 0

SD 0.36 0.83 4.6 10.5 8.9 10.8 — — — —

Light 15% (< 5.04 kg) SD

1.68 6.85 35.1 130.6 142.7 163.1 0.11 0.0 48 0

Light 5% (< 4.09 kg) Mean

SD

Light 50% (< 6.47 kg)

0.36 1.25 5.3 10.8 9.1 10.9 — — — —

Mean 1.34 4.33 30.0 124.6 149.0 169.5 2.7 0.0 28 0

SD 0.35 0.60 4.3 10.2 8.8 10.7 — — — —

Light 5% (< 4.19 kg) Mean 1.19 3.63 28.4 122.1 151.4 172.0 4.3 0.0 15 0

SD 0.32 0.50 4.0 10.0 8.9 10.9 — — — —

1

At 168 d of age, a total of 708 pigs (632 gilts, 76 barrows) were under 105 kg BW at 168 d of age. A total of 29 gilts and 0 barrows were under 90 kg BW at 168 d of age.

variable relative to weaning weight such that their SD for days to 125 kg BW is equal to or greater than the heavy pigs at weaning. It should be noted that the lightest 5 or 15% of the pigs at 20-d of age had substantially lighter birth BW than the heavy 85 or 95% of

the pigs at 20-d of age. It has been recognized that pigs with light birth BW have reduced growth performance and that the biological basis for this reduced growth is reduced prenatal myogenesis (Foxcroft et al., 2006; Rehfeldt and Kuhn, 2006). Also, pigs with light birth BW con-

sume less colostrum and may not be able to compete at the udder especially when litter size is greater than 12 pigs (LeDividich, 1999). The simulation program resulted in a total of 708 pigs (632 gilts, 76 barrows) with BW less than 105 kg at 168 d of age. The simulation pro-

219

Modeling the Impact of Early Body Weight

Table 8. Effect of sorting across sexes at weaning Heavy 50% (> 6.31 kg) Mean

Figure 2. Relationship of 168-d BW to birth BW for barrows as predicted by analyses of the actual and simulated data.

% barrows Birth BW, kg Weaning BW, kg Nursery BW, kg 168-d BW, kg Days to 105 kg Days to 125 kg % less than 90 kg1 % less than 105 kg1 Pigs less than 105 kg BW Pigs less than 90 kg BW

54.3 1.72 7.41 35.5 128.5 144.6 165.3 1.95 0.03 137 2

SD — 0.34 0.83 5.3 11.3 9.9 11.9 — — — —

Heavy 85% (> 4.93 kg) Mean % barrows Birth BW, kg Weaning BW, kg Nursery BW, kg 168-d BW, kg Days to 105 kg Days to 125 kg % less than 90 kg1 % less than 105 kg1 Pigs less than 105 kg BW Pigs less than 90 kg BW

51.1 1.62 6.69 34.0 126.6 146.6 167.4 3.5 0.14 415 17

Figure 3. Relationship of days to 125 kg to birth BW for gilts as predicted by analyses of the actual and simulated data.

% barrows Birth BW, kg Weaning BW, kg Nursery BW, kg 168-d BW, kg Days to 105 kg Days to 125 kg % less than 90 kg1 % less than 105 kg1 Pigs less than 105 kg BW Pigs less than 90 kg BW 1

Figure 4. Relationship of days to 125 kg to birth BW for barrows as predicted by analyses of the actual and simulated data.

50.3 1.59 6.47 33.5 125.9 147.3 168.2 4.3 0.18 569 24

Mean 45.7 1.41 5.25 31.1 122.2 155.1 172.2 11.4 0.38 571 27

SD — 0.35 0.79 5.1 12.0 11.3 13.5 — — — —

Light 15% (< 4.93 kg) SD

— 0.36 1.09 5.5 11.7 10.6 12.6 — — — —

Heavy 95% (> 4.14 kg) Mean

Light 50% (< 6.31 kg)

Mean 43.6 1.26 4.26 28.5 118.3 155.1 176.3 14.0 0.57 293 12

SD — 0.33 0.55 4.7 12.3 11.6 13.8 — — — —

Light 5% (< 4.14 kg) SD

0.37 1.22 5.5 11.9 10.8 12.9 — — — —

Mean 44.8 1.15 3.62 26.5 115.5 158.1 179.2 19.9 0.71 139 5

SD 0.29 0.46 4.3 11.9 11.7 13.9 — — — —

At 168 d of age.

gram predicted 29 gilts and no barrows had 168-d BW less than 90 kg. Sorting pigs at weaning within sex resulted in most of the slower growing pigs being in the group of half of the gilts with the lesser weaning weights. More intense sorting (5 or 15%) resulted in the smaller groups

of pigs with lesser weaning BW. The percentage of pigs not achieving the target 90 and 105 kg BW increased as the sorting of light weaning pigs was intensified. However, the percentage of all pigs with BW less than 90 or 105 kg BW that were included in the light BW

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Table 9. Effect of impact sorting based on nursery exit BW within each sex Gilts Heavy 50% (> 31.89 kg)

Birth BW, kg 20-d BW, kg Nursery BW, kg 168-d BW, kg Days to 105 kg Days to 125 kg % less than 105 kg1 % less than 90 kg1 Pigs less than 105 kg Pigs less than 90 kg

1

Heavy 50% (> 34.02 kg)

Light 50% (< 34.02 kg)

SD

Mean

SD

Mean

SD

Mean

SD

1.61 6.55 36.5 127.3 146.0 167.2 1.02 0.0 36 0

0.34 1.04 3.6 9.6 8.6 10.9 — — — —

1.38 5.84 27.6 114.6 158.2 179.8 17.0 0.83 596 29

0.36 1.31 3.1 10.1 10.2 12.9 — — — —

1.72 6.97 38.6 135.6 138.4 158.5 0.03 0.0 1 0

0.36 1.2 3.7 9.2 7.3 9.1 — — — —

1.55 5.96 30.0 123.9 148.8 169.5 2.1 0.0 75 0

0.37 1.2 2.9 9.2 8.0 10.1 — — — —

Light 15% (< 26.35 kg)

Heavy 85% (> 28.75 kg)

Light 15% (< 28.75 kg)

Mean

SD

Mean

SD

Mean

SD

Mean

SD

1.54 6.35 33.6 123.2 150.0 171.3 4.1 0.07 243 4

0.36 1.2 4.6 10.6 10.0 12.2 — —

1.25 5.29 23.7 108.1 164.4 186.3 37.0 2.4 389 25

0.34 1.3 2.2 9.3 10.2 13.1 — —

1.66 6.64 35.7 131.7 141.9 162.2 2.2 0.0 13 0

0.36 1.2 4.6 10.0 8.4 10.2 — — — —

1.46 5.49 26.4 118.6 153.5 174.4 6.0 0.0 63 0

0.36 1.3 2.0 8.6 7.9 10.2 — — — —

Heavy 95% (> 23.20 kg)

Birth BW, kg 20-d BW, kg Nursery BW, kg 168-d BW, kg Days to 105 kg Days to 125 kg % less than 105 kg1 % less than 90 kg1 Pigs less than 105 kg Pigs less than 90 kg

Light 50% (< 31.89 kg)

Mean

Heavy 85% (> 26.35 kg)

Birth BW, kg 20-d BW, kg Nursery BW, kg 168-d BW, kg Days to 105 kg Days to 125 kg % less than 105 kg1 % less than 90 kg1 Pigs less than 105 kg Pigs less than 90 kg

Barrows

Light 5% (< 23.20 kg)

Heavy 95% (25.77 kg)

Light 5% (< 25.77 kg)

Mean

SD

Mean

SD

Mean

SD

Mean

SD

1.52 6.26 32.7 121.9 151.2 172.6 6.6 0.14 437 9

0.37 1.2 5.1 11.1 10.6 12.8 — — — —

1.17 4.91 21.1 103.6 168.7 190.8 55.7 5.7 195 20

0.33 1.4 1.7 8.8 10.4 13.4 — — — —

1.65 6.53 34.8 130.5 142.9 163.3 0.50 0.0 33 0

0.37 1.28 5.0 10.5 8.8 10.6 — — — —

1.37 5.18 24.1 114.8 156.7 178.0 12.3 0.0 43 0

0.38 1.29 1.6 8.1 7.9 10.3 — — — —

At 168 d of age.

groups of barrows and gilts decreased. Sorting across sexes at weaning tended to select a higher percentage of the barrows in the heavy group (Table 8). The 3 levels of sorting (50 to 50, 85 to 15, 95 to 5%) resulted in 2 groups with 6.9-, 8.9-, and 11.0-d differences in days to 125 kg

BW. Sorting pigs across sexes at weaning into 2 halves resulted in the light group of pigs having slightly lesser SD for nursery BW (5.1 vs 5.3 kg) and substantially greater SD for days to 105 and 125 kg BW (11.3 vs 9.9 d and 13.5 vs 11.9 d, respectively). The simulation program predicted that the lightest

5 or 15% of the pigs at weaning would have lesser SD than the heavier groups of pigs for weaning BW and greater SD for days to 105 and 125 kg BW. Sorting the pigs into 2 equally sized groups based on weaning BW resulted in the majority of the pigs with 168 d BW less than 90 kg (27

Figure 5. Relationship of 168-d BW to 20d BW for gilts as predicted by analyses of the actual and simulated data.

Modeling the Impact of Early Body Weight

221

Figure 8. Relationship of days to 125 kg to 20-d BW for barrows as predicted by analyses of the actual and simulated data.

Figure 11. Relationship of days to 125 kg to 70-d BW for gilts as predicted by analyses of the actual and simulated data.

of 29) and less than 105 kg (571 out of 708) sorted into the light BW group. More intense sorting of the lightest 5 or 15% of the pigs based on weaning weight resulted in less of the total number of light BW pigs at 168 d of age being sorted into the light BW groups.

Modeling the Impact of Sorting Based on Nursery Exit BW

Figure 6. Relationship of 168-d BW to 20d BW for barrows as predicted by analyses of the actual and simulated data.

Figure 9. Relationship of 168-d BW to 70d BW for gilts as predicted by analyses of the actual and simulated data.

Figure 7. Relationship of days to 125 kg to 20-d BW for gilts as predicted by analyses of the actual and simulated data.

Figure 10. Relationship of 168-d BW to 70-d BW for barrows as predicted by analyses of the actual and simulated data.

The effect of sorting pigs within each sex based on nursery exit BW is shown in Table 9. Sorting pigs based on nursery BW had a greater impact on 168-d BW and days to target market BW than sorting on weaning BW. The 3 levels of sorting

Figure 12. Relationship of days to 125 kg to 70-d BW for barrows as predicted by analyses of the actual and simulated data.

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Table 10. Effect of sorting based on nursery exit BW across sexes Heavier 50% (> 32.97 kg)

% barrows Birth BW, kg 20-d BW, kg Nursery BW, kg 168-d BW, kg Days to 105 kg Days to 125 kg % less than 105 kg1 % less than 90 kg1 Pigs less than 105 kg Pigs less than 90 kg

Mean

SD

Mean

SD

57.2 1.67 6.76 37.7 132.0 141.7 162.3 0.29 0.0 20 0

— 0.35 1.14 3.7 9.9 8.4 10.4 — — — —

42.8 1.46 6.90 28.7 118.7 154.1 175.2 9.8 0.41 688 29

— 0.37 1.27 3.1 10.4 10.1 12.5 — — — —

Heavy 85% (> 27.42 kg)

% barrows Birth BW, kg 20-d BW, kg Nursery BW, kg 168-d BW, kg Days to 105 kg Days to 125 kg % less than 105 kg1 % less than 90 kg1 Pigs less than 105 kg Pigs less than 90 kg

1

Light 15% (< 27.42 kg)

Mean

SD

Mean

SD

53.4 1.61 6.49 34.6 127.7 145.7 166.4 1.67 0.02 199 2

— 0.36 1.21 4.7 10.9 9.7 11.8 — — — —

30.7 1.33 5.43 24.8 111.8 160.5 182.1 24.2 1.3 509 27

— 0.36 1.31 2.2 9.8 10.3 13.0 — — — —

Heavy 95% (> 24.4 kg)

% barrows Birth BW, kg 20-d BW, kg Nursery BW, kg 168-d BW, kg Days to 105 kg Days to 125 kg % less than 105 kg1 % less than 90 kg1 Pigs less than 105 kg Pigs less than 90 kg

Lighter 50% (< 32.97 kg)

Light 5% (< 24.4 kg)

Mean

SD

Mean

SD

51.4 1.58 6.39 33.8 126.3 147.0 167.8 3.14 0.05 418 7

— 0.37 1.24 5.1 11.5 10.4 12.5 — — — —

23.4 1.22 5.02 22.3 107.2 164.9 186.7 41.4 3.1 290 22

— 0.33 1.32 1.8 9.5 10.6 13.3 — — — —

At 168 d of age.

(50 to 50, 85 to 15, 95 to 5%) produced groups of gilts with 12.6-, 15.0-, and 18.2-d differences and barrows with 11.0-, 12.2-, and 14.7d differences in days to 125 kg BW, respectively. Sorting pigs within each sex based on nursery BW into

2 halves resulted in the majority of the 708 pigs with BW less than 105 kg at 168 d of age to be sorted into either the light BW gilts (n = 596) or light BW barrow (n = 75) groups. More intense sorting of the pigs within sex based on nursery BW re-

sulted in the light BW groups having a greater percentage of light BW pigs but a decreased percentage of the total number of light BW pigs at 168 d of age. The effect of sorting pigs based on nursery BW across sexes is shown in Table 10. Sorting pigs across sexes based on nursery BW into 2 equally sized groups was successful in sorting the majority of pigs with 168-d BW less than 90 (29 of 29) or 105 kg (688 of 708) into the light BW group. Sorting the pigs of the 3 levels (50 to 50, 85 to 15, 95 to 5%) produced 12.9-, 15.7-, and 18.9-d differences in days to 125 kg BW. Thus, such sorting could be used to market the pigs with greater nursery BW 2 to 3 wk sooner than the group with below average nursery BW. More intense sorting (50 to 50, 85 to 15, 95 to 5%) increased the percentage of pigs in the light BW group with 168-d BW less than 105 kg from 9.8 to 24.2 and 41.4%, respectively. Also, the more intense sorting decreased the percentage of the total pigs with 168-d BW less than 105 kg included in the light BW groups from 92.2 to 71.9 and 41.0%, respectively. As the sorting intensity based on nursery BW increased, the differences between the groups for birth, 20-d, and 168-d BW increased and days to 105 and 125 kg BW increased. However, with more intense sorting, the SD for nursery BW for the light pigs was smaller than the SD of the heavy pigs. The SD for days to 105 and 125 kg BW were greater for the light BW groups of pigs at each level of sorting. Also, as the intensity of sorting increased, the SD of nursery BW for the light group of pigs decreased and the SD of days to 125 BW increased. The lightest pigs at 70-d of age had below average birth BW. Some of the pigs with light birth BW have reduced muscle growth potential due to limited prenatal nutrition (Foxcroft et al., 2006; Rehfeldt and Kuhn, 2006).

Modeling the Impact of Early Body Weight

IMPLICATIONS The nonlinear relationships of birth and weaning BW with postweaning BW make the modeling of the variation of pigs growth from birth to target market BW complex. This stochastic model can be used to reproduce the nonlinear relationships of birth and weaning BW to later grow-finish BW. Further research is needed to evaluate the impact of the assumption of normality of the random effects of the mixed model nonlinear equations. This stochastic model is a tool with which to evaluate strategies to sort pigs at early ages to reduce variation in ages to achieve target market BW.

LITERATURE CITED Craig, B. A., and A. P. Schinckel. 2001. Nonlinear mixed effects model for swine growth. Prof. Anim. Sci. 17:256. Foxcroft, G. R., W. T. Dixon, S. Novak, C. T. Putman, S. C. Town, and M. D. A. Vinsky. 2006. The biological basis for prenatal programming of postnatal performance in pigs. J. Anim. Sci. 84(E. Suppl.):E105.

King, R. H. 1999. A Review — Nutritional constraints to pig performance and pig variability. Page 245 in Manipulating Pig Production VII. P.D. Cranwell, ed. Aust. Pig Sci. Assoc., Werribee, Victoria, Australia. Klindt, J. 2003. Influence of litter size and creep feeding on preweaning gain and influence of preweaning growth on growth to slaughter in barrows. J. Anim. Sci. 81:2434. Le Dividich, J. 1999. A Review — Neonatal and weaner pig: Management to reduce variation. Page 135 in Manipulating Pig Production VII. P.D. Cranwell, ed. Aust. Pig Sci. Assoc., Werribee, Victoria, Australia.

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day weight to the postweaning growth of pigs with different weaning management. Prof. Anim. Sci. (In press) Schinckel, A. P., and B. A. Craig. 2002. Evaluation of alternative nonlinear mixed effects models of swine growth. Prof. Anim. Sci. 18:219. Schinckel, A. P., S. Pence, M. E. Einstein, R. Hinson, P. V. Preckel, J. S. Radcliffe, and B. T. Richert. 2006. Evaluation of different mixed model nonlinear functions on pigs fed low-nutrient excretion diets. Prof. Anim. Sci. 22:401.

Lopez, S., J. France, W. J. J. Gerrits, M. S. Dhanoa, D. J. Humphries, and J. Dijkstra. 2000. A generalized Michaelis-Menten equation for the analysis of growth. J. Anim. Sci. 78:1816.

Schinckel, A. P., M. E. Einstein, and D. Miller. 2005. Evaluation of a method to analyze pig live weight data from animal sorting technologies. Prof. Anim. Sci. 21:50.

Patience, J. F., and A. D. Beaulieu. 2006. Variation in the finishing barn. Page 129 in Proc. Manitoba Swine Seminar. Vol. 20. Manitoba Agric. Food and Rural Initiatives, Manitoba, Canada.

Schinckel, A. P., J. Ferrel, M. E. Einstein, S. M. Pearce, and R. D. Boyd. 2004. Analysis of pig growth from birth to sixty days of age. Prof. Anim. Sci. 20:79.

Patience, J. F., R. T. Zijlstra, and D. Beaulieu. 2002. Feeding growing and finishing pigs to maximize net income. Page 61 in Advances in Pork Prod. Vol. 13. Banff Pork Seminar Proc., Banff, Alberta, Canada. Rehfeldt, C., and G. Kuhn. 2006. Consequences of birth weight for postnatal growth performance and carcass quality in pigs as related to myogenesis. J. Anim. Sci. 84(E. Suppl.):E113. Schinckel, A. P., R. Cabrera, R. D. Boyd, S. Jungst, C. Booher, M. Johnson, and M. E. Einstein. 2007. Impact of birth and twenty-

Schinckel, A. P., N. Li, P. V. Preckel, M. E. Einstein, and D. Miller. 2003. Development of a stochastic pig compositional growth model. Prof. Anim. Sci. 19:255. Tokach, M. 2004. Dealing with variation in market weight. Page 281 in Advances in Pork Prod. Vol. 15. Banff Pork Seminar Proc., Banff, Alberta, Canada. Wolter, B. F., and M. Ellis. 2001. The effects of weaning weight and rate of growth immediately after weaning on subsequent pig growth performance and carcass characteristics. Can. J. Anim. Sci. 81:363.