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Evaluation of a Method to Analyze Pig Live Weight Data from Animal Sorting Technologies1
The Professional Animal Scientist 21 (2005):50–58
Evaluation of a Method to Analyze Pig Live Weight Data from Animal 1
Sorting Technologies
A. P. SCHINCKEL*,2, PAS, M. E. EINSTEIN*, and D. MILLER† *Department of Animal Sciences and †Department of Agricultural Economics, Purdue University, West Lafayette, IN 47907
Abstract A method to analyze pig BW data collected by an animal sorting technology scale without individual pig identification was evaluated. Data for ten 1000pig grow-finish barns were simulated by a stochastic model. The BW at each age was modeled as a predicted BW plus a daily residual error (mean = 0; SD = 1.4 kg) and a within-day residual error (mean = 0; SD = 0.98 kg). The number of times each pig was weighed was simulated to vary among pigs and to vary daily for each pig. The number of daily BW measurements taken per pig had an overall mean of 5.40 and SD of 1.23. Two types of data sets were simulated. A complete data set had biweekly data from 70 to 196 d of age. A truncated data set was simulated to reflect typical serial marketing of pigs and included biweekly data from 70 to 154 d of age and weekly truncated data from 161 to 175 d of age. The percentile means of the BW data were calculated and assigned a percentile identification of 1 to 100. The percentile means were fit to a mixed model nonlinear function (Bridges) with two random effects predicted
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Purdue Agriculture Research Program No. 17412. 2 To whom correspondence should be addressed: [email protected]
for each percentile. The fitting of either the complete or truncated data sets reproduced the mean and variance of BW at each age and predicted age to achieve 120 kg of BW. The serial marketing of pigs may produce small biases in the prediction of the actual percentile means. The fitting of the mean percentile data can be used to model the underlying mean and variation of BW growth. (Key Words: Mixed Effects Model, Nonlinear Growth Functions, Swine Growth.)
Introduction Variability in the growth rates of pigs is important to the economic costs and returns of both the pork producer and processor (Patrick et al., 1993; King, 1999). Pork processors have the objective to market lean pork products that are uniform in BW and composition (Boland et al., 1993). The optimization of pork production systems, including the evaluation of alternative management and marketing strategies, requires knowledge of the between-pig variation in BW and carcass composition (King, 1999; Le Dividich, 1999). Recently, mixed model nonlinear analysis software has been made available, which accounts for the underlying variancecovariance structure of serial BW data
(Craig and Schinckel, 2001; Schinckel and Craig, 2002) and has led to the development of a stochastic pig growth model (Schinckel et al., 2003). Recently, scales have been developed that can automatically weigh individual pigs. Pigs are trained to individually enter and walk through an electronic scale and to subsequently exit into a pen with a bank of feeders. Producers can monitor the distribution of BW data and set a sort BW for marketing. Pigs above the sort BW are released into a market pen. These animal sorting technologies (AST) reduce the amount of labor required to sort pigs for marketing and reduce the discounts caused by over- and underweight carcasses. The AST also can increase returns when used to target the optimal Paylean威 (Elanco, Greenfield, IN) use and marketing strategy (Li, 2003). These electronic scales can collect the BW data over any specific period of time. Pigs may be weighed several times per day. However, without individual pig identification, conventional pig random effects models cannot be fit to the BW data, and, subsequently, the BW growth of individual pigs cannot be modeled. Alternative data analyses must be considered to predict the mean and variation of the BW values. The objectives of this study were 1) to develop and evaluate an alternative method of analyzing the BW
Evaluation of Pig Growth
data collected by an AST system and 2) to evaluate the impact of the serial marketing of pigs on the predicted BW growth rates and predicted days to achieve a specific market BW.
Materials and Methods Data from a Purdue University research trial were used as the example data set. High lean gain gilts were reared via all-in all-out procedures (Schinckel and Craig, 2002). A total of 96 gilts were weighed and measured via real-time ultrasound at 49, 70, 104, 132, and 153 d of age. The 42 slowest-growing gilts had an additional BW measurement at 174 d of age. The BW data were fitted to alternate mixed nonlinear models using the nonlinear mixed (NLMIXED) procedure of SAS威 (SAS Institute, Cary, NC; Schinckel and Craig, 2002). The best model of the Bridges function (Bridges et al., 1986), based on residual standard deviation (RSD) and Akaike’s Information Criteria values, was BWit = (C + ci)(1 − exp (− exp (M′ + m′i) tA)) + birth BW + eit, where C, M′, and A are fixed population mean parameters, ci and m′i are random effects for pig i, t is days of age, birth BW is a constant (1.4 kg), and eit is the residual error. The estimated values for C, M, and A were 216.27, −9.124, and 1.755 with SE of 11.5, 0.077, and 0.028, respectively (Schinckel and Craig, 2002). The equation had an R2 of 0.998 and a RSD of 1.70 kg. The NLMIXED procedure estimated a value of ci and m′i for each individual pig. By using these values, the predicted age required to reach a specific target BW can be calculated. Predicted days of age at 110 and 120 kg of BW were used as a measure of overall growth rate. The ci values had a SD of 20.75. The m′i values had a SD of 0.0968. The ci and m′i values also exhibited a negative correlation (r = −0.658; P<0.001). Simulation of the Variation in BW Growth. A set of 1000 ci and m′i values were sampled from a large sam-
ple of ci and m′i values with the same bivariate normal distribution as the observed values. These values, when used in the nonlinear BW function, reproduce a population of pigs with a distribution of individual live growth curves. The BW at each specific age is the predicted BW (BWit) plus two residual error terms, a daily residual error (mean = 0; SD = 1.4 kg) and a within-day residual error (mean = 0; SD = 0.098 kg; Ramaekers, 1996). Based on previous data, the number of meals consumed varies among pigs and varies daily for individual pigs. The number of times each pig was weighed was modeled by the equation Nit = µ + pi + pit, where µ is the mean (5.4), pi is the random effect for the variation between pigs during their postweaning growth (mean = 0; SD = 1.0), and pit is the normally distributed random effect (mean = 0; SD = 0.70) for the variation among days for each individual pig. The value of Nit was rounded to the nearest whole number. This procedure simulated BW data for 1000 individual pigs with a distribution of live growth curves and a varying number of times weighed per day. The process was repeated to simulate data for ten 1000-head grow-finishers. To evaluate the use of AST, these BW data were considered to be measurements for unidentified, random pigs. Daily BW data, biweekly from 70 to 196 d of age and weekly from 154 to 175 d of age, were sorted into percentile groups. The mean of each percentile group was calculated, and the percentile rank (1 to 100) was assigned to the mean value. The percentile means for the 10 biweekly BW from each of the ten 1000-head grow-finishers were fitted to the mixed model nonlinear Bridges function using the nonlinear mixed (NLMIXED) procedure of SAS. The function had the form MBWit = (C + ci){1 − exp [−exp (M′ + m′i) tA]} + birth BW + eit, where MBWit is the mean BW of percentile i at t days of age; C, M′, and A are fixed population mean parameters; ci and m′i are
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random effects for percentile I; t is days of age; birth BW is a constant (1.4 kg); and eit is the residual error. The random effects ci and m′i are assumed to be multivariate normal with means equal to zero, variances σ2c and σ2m′ and covariance σc,m. The eij are assumed to be independent of the random effects. Modeling the Effect of Serial Marketing. To simulate serial marketing, the BW data for each of the 10 growfinishing units were truncated by modeling current typical marketing procedures (Schinckel et al., 2003). Twice weekly, Monday and Friday, semi-trailers were marketed when 170 pigs were >120 kg of BW. At each marketing day, the heaviest pigs were marketed. When the fifth semi-trailer was filled with pigs >120 kg of BW, the remaining 150 pigs were also marketed to empty the facility. After marketing the first semi-trailer, weekly pig BW measurements were included in the analyses. The remaining weekly pig BW data were assigned to percentile groups based on the percentage of pigs remaining. With N percentage of the pigs remaining, the pig data were ranked and then divided into N equal-sized groups and assigned to percentile groups 1 to N. The biweekly and subsequent weekly truncated data were analyzed with the same random nonlinear model as the complete biweekly BW data. Evaluation of the Four BW Variables. Four variables were evaluated by the univariate procedure of SAS. The first variable was the traditional single BW measurement taken biweekly for each pig from 70 to 196 d of age. The second variable was the actual mean BW for each percentile at each age. The third variable was the mean value of each percentile predicted from the mixed model nonlinear function using the complete biweekly BW data. The fourth variable was the mean value of each percentile predicted from the mixed model nonlinear function using the truncated BW data. The relationship of the serial BW data for the four variables was evalu-
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ated by regression analyses (Proc REG; SAS). The values of each of the four variables later in the finish pe-
Schinckel et al.
riod (112, 140, 168, and 196 d of age) were regressed on the earlier (70 or 112 d) values of the same variable.
The equations included the linear and quadratic effects of the prior BW data.
TABLE 1. Statistical parameters for BW data of individual pigs, actual percentile means, and percentile means predicted from either complete or truncated data setsa. Quantile Item 70-d BW, kg Individual data Actual percentile means Predicted percentile means—complete data Predicted percentile means—truncated data 84-d BW, kg Individual data Actual percentile means Predicted percentile means—complete data Predicted percentile means—truncated data 98-d BW, kg Individual data Actual percentile means Predicted percentile means—complete data Predicted percentile means—truncated data 112-d BW, kg Individual data Actual percentile means Predicted percentile means—complete data Predicted percentile means—truncated data 126-d BW, kg Individual data Actual percentile means Predicted percentile means—complete data Predicted percentile means—truncated data 140-d BW, kg Individual data Actual percentile means Predicted percentile means—complete data Predicted percentile means—truncated data 154-d BW, kg Individual data Actual percentile means Predicted percentile means—complete data Predicted percentile means—truncated data 168-d BW, kg Individual data Actual percentile means Predicted percentile means—complete data Predicted percentile means—truncated data 182-d BW, kg Individual data Actual percentile means Predicted percentile means—complete data 196-d BW, kg Individual data Actual percentile means Predicted percentile means—complete data
Mean
SD
Skewness
90%
10%
37.17 37.17 37.20 37.25
3.15 3.16 2.93 2.98
0.026 0.028 0.025 0.096
41.2 41.2 40.8 41.1
33.2 33.2 33.4 33.5
49.04 49.04 48.99 49.00
4.09 4.11 3.85 3.91
0.072 0.070 0.021 0.076
54.2 54.2 53.8 54.0
43.8 43.8 44.0 44.1
61.38 61.37 61.38 61.35
4.78 4.81 4.81 4.85
0.066 0.069 0.017 0.055
67.4 67.4 67.4 67.5
55.2 55.2 55.2 55.3
74.10 74.10 74.06 74.01
5.64 5.66 5.77 5.79
0.01 0.001 0.012 0.031
81.3 81.3 81.2 81.3
67.0 67.0 66.7 66.7
86.76 86.76 86.76 86.71
6.54 6.57 6.71 6.69
0.001 0.005 0.007 0.006
94.9 95.0 95.1 95.1
78.4 78.4 78.2 78.2
99.10 99.11 99.22 99.22
7.47 7.51 7.61 7.54
0.0190 0.0270 0.0020 −0.020
108.3 108.3 108.6 108.5
89.7 89.6 89.5 89.6
111.40 111.40 111.27 111.35
8.24 8.28 8.45 8.33
−0.00 −0.00 −0.00 −0.05
121.7 121.7 121.7 121.5
100.9 100.7 100.4 100.6
122.81 122.81 122.73 122.94
9.07 9.11 9.22 9.03
0.02 0.02 −0.00 −0.01
133.9 133.9 134.1 133.8
111.1 111.1 110.9 111.2
133.52 133.52 133.50
10.04 10.09 9.93
−0.05 −0.06 −0.02
145.9 145.9 145.8
120.4 120.4 120.7
144.44 143.44 144.48
10.65 10.71 10.54
−0.04 −0.04 −0.02
156.8 156.7 156.5
129.6 129.5 129.9 continued
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Evaluation of Pig Growth
TABLE 1. (continued) Statistical parameters for BW data of individual pigs, actual percentile means, and percentile means predicted from either complete or truncated data setsa. Quantile Item
Mean
SD
Skewness
90%
10%
153.49 153.37 153.37 153.21
9.86 10.27 10.27 9.90
0.63 0.56 0.56 0.53
166.0 166.5 166.5 166.5
142.0 141.5 141.5 141.5
165.83 165.61 165.67 165.60
11.44 11.60 11.61 11.38
0.73 0.60 0.61 0.58
181.1 180.6 180.6 180.5
153.0 152.7 152.2 152.3
Days to 110 kg
Days to 120 kg
a The individual BW data are for a single BW for each individual pig. The actual percentile mean BW data are the calculated percentile means for the random multiple BW measurements taken each day. The predicted percentile mean BW data are the percentile means predicted by fitting the percentile data 0% a mixed model nonlinear function to either the complete or truncated data set. Skewness and percentile quantiles as calculated by Proc Univariate (SAS Inst., Inc., Cary, NC).
Evaluation of the Growth of Subpopulations of Pigs. The growth rate of subpopulations of pigs can be substantially different (Schinckel et al., 2004). Precise stochastic models require that the mean growth of subpopulations of pigs with different overall BW growth rates be accurately predicted. The fitting of the BW percentile mean should predict the actual growth of the subpopulations sorted by overall postweaning BW growth rate. Four BW variables were evaluated: 1) the actual BW data for individual pigs, 2) the actual percentile mean BW data, 3) the predicted BW data for each percentile using the complete biweekly data set, and 4) the predicted BW data for each percentile using the truncated data set. The data were sorted into five 20-percentile groups based on the predicted age for each pig or percentile to achieve 120 kg of BW. The mean ADG for each 20-percentile group was plotted for each variable relative to either BW or days of age.
Results and Discussion Simulation Results. The simulation model produced an average of
5.407 observations per pig/d with a SD of 1.23. The number of daily BW measurements ranged from one to nine. The marketing protocol resulted in identical marketing dates for all 10 grow-finish facilities. Full truckloads containing 170 pigs each were marketed at 155, 162, 166, 169, and 176 d of age. The truncated data set included weekly BW data with 1000, 830, 490, and 320 pigs at 154, 161, 168, and 175 d of age, respectively. The mean values and summary statistics were similar for the simulated individual pig BW and the mean percentile values of the multiple daily BW (Table 1). The results indicate that the percentile means closely approximate the overall distribution, including the mean, variance, and skewness of the data from individual pigs. The serial marketing of pigs may bias the mean of the percentile means at subsequent weigh days. Pigs were marketed when one individual pig BW measurement was above the target market BW of 120 kg and the pig was one of the 170 heaviest pigs. The fitting of the BW data to the percentile means and use of the percentile values as the random effect assumes that the individual pig is assigned to its correct percentile rank.
The serial marketing of pigs did produce a small bias on the mean BW of the remaining pigs, with respect to the mean of the BW of the same percentiles for the complete data set. With a complete data set, the 83% of pigs with the least BW at 161 d of age averaged 114.56 kg. When the heaviest pigs were marketed based on a single BW on d 155, the remaining 83% of the pigs weighed 114.65 kg at 161 d of age. This is due to the fact that the heaviest 17% of the actual BW observations in the complete data set have a greater mean than the actual BW of the upper 17% of the pigs based on a single BW taken 6 d prior. Some pigs are marketed on d 155 with a single BW in the upper 17% of the overall single BW, and this produces BW measurements that are less than the 17th percentile 6 d later. The mean of the actual lesser 49% of the complete BW observations collected on d 168 is 115.43 kg. The mean of the remaining observations after marketing the greater 51% of the pigs (three 170-pig groups) was 115.71 kg. At 175 d of age, the lesser 32% of the actual BW measurements averaged 117.56 kg while the mean of the observations of the remaining 32% of the pigs was 117.86 kg.
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TABLE 2. Parameter estimates for the fitting of the mean precentile BW data to the Bridges functiona. C 210.3 212.6 209.7 212.5 212.0 212.8 212.5 212.8 212.9 211.1
M′
A
var(c)
varm′
cov(c,m′)
var(e)
AICb
−9.096 −9.098 −9.118 −9.083 −9.097 −9.089 −9.098 −9.091 −9.105 −9.101
1.745 1.744 1.752 1.740 1.745 1.742 1.744 1.741 1.745 1.745
171.9 88.7 191.7 113.3 173.3 58.6 175.2 73.6 163.5 56.5
0.000405 0.000540 0.000296 0.000082 0.000390 0.000194 0.000386 0.000092 0.000601 0.000067
0.261 0.212 0.217 0.0843 0.258 0.0969 0.244 0.082 0.304 0.0607
0.0528 0.0575 0.0649 0.0843 0.0572 0.0417 0.06770 0.0640 0.0469 0.0574
842.8 948.2 1065.9 997.1 910.7 729.8 1090.8 1087.3 763.9 1053.5
The mixed effects model with C and M′ as random effects is (C+ ci) (1 − exp (−exp (M′ + m′i) tA)) + 1.4 + eij, where eij is normal with mean 0 and variance σ2e and ci and m′i are random effects with mean 0, and variances σ2c and σ2m′, with covariance c with m′ σc,m′. b AIC = Akaike’s Information Criteria. a
Random Effects Nonlinear Growth Function Parameters. The parameter estimates produced by fitting the random effects Bridges function to the complete biweekly percentile mean and the truncated percentile mean data for each of 10 simulated barns are presented in Table 2. The values of the fixed parameters (C, M′, and A) were similar for the ten 1000-head grow-finisher barns. The mean values of 211.9 for C and −9.097 for M′ were slightly less in absolute value than the mean simulated pig BW parameter values of 216.3 and −9.124, respectively. The values of the variance of c, variance of m′i, and covariance of ci and m′i differed substantially among the ten 1000-head populations of pigs. It is possible that alternative values of the variance-covariance of the random effects (ci and m′i) may result in similar variation in the predicted percentile means at each age. Variation in the Actual and Predicted BW. The summary statistics for the four BW variables are presented for one 1000-head population of pigs in Table 1. The predicted percentile parameters are similar to the individual pig BW and actual percentile mean parameters. In this data set, the magnitude of skewness is small
for all four BW variables. The magnitude of skewness for the predicted percentile means was slightly different from the actual BW data. The values of the 10 and 90 percentile quantiles of the four variables—the actual BW, percentile mean and predicted percentile means (complete biweekly and
truncated)—were within 0.2 to 0.4 kg of each other. The magnitude of skewness, in most cases caused by a greater number of slower-growing pigs than expected, is important in the evaluation of the optimal marketing strategy and barn close-out time. The magnitude of skewness increases as the health status of the pigs decreases (Schinckel and Craig, 2002). Further research should be conducted with populations of pigs with a greater magnitude of skewness for BW. The means and SD of the predicted BW percentile means for the ten 1000-head populations are presented in Table 3. The predicted mean BW and days to 110 or 120 kg BW were similar for the analyses of the 10 complete biweekly or truncated data sets. The predicted 154- and 182-d BW were 0.1 and 0.2 kg greater for the truncated data set analyses than for the complete biweekly analyses. The mean predicted ages to achieve 110and 120-kg BW were 0.2 d less for the truncated data set analyses vs the complete data set analyses. The SD of the predicted percentile BW means increased with age. The
TABLE 3. Mean and standard deviations of the predicted percentile means for BW produced by fitting random regression models to ten 1000-head populations of pigsa. Predicted mean
Predicted SD
Item
Mean
SD
Mean
SD
70-d BW, kg 98-d BW, kg 126-d BW, kg 154-d BW, kg 182-d BW, kg Days to 110 kg Days to 120 kg Truncated data set 70-d BW, kg 90-d BW, kg 126-d BW, kg 154-d BW, kg 182-d BW, kg Days to 110 kg Days to 120 kg
37.2 61.5 86.9 111.5 133.9 153.1 165.2
0.11 0.18 0.26 0.32 0.37 0.41 0.46
2.91 4.80 6.71 8.45 9.94 10.15 11.53
0.08 0.12 0.15 0.17 0.18 0.26 0.32
37.3 61.5 86.9 111.6 134.1 152.9 165.0
0.11 0.19 0.26 0.31 0.35 0.37 0.41
3.00 4.87 6.71 8.33 9.64 9.98 11.37
0.06 0.10 0.14 0.18 0.23 0.26 0.29
a
The SD is the SD of the ten 1000-head populations (n = 10).
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Evaluation of Pig Growth
TABLE 4. Regression of actual or predicted BW on prior actual or predicted BW. Item
Prior BW, kg
b0
b1
b2
RSDa, kg
R2
Derivative1
0.639 0.646 0.614 0.566 0.855 0.835 0.791
1.44 1.87 2.24 2.52 1.20 1.45 1.66
Simulated actual pig liveweight on prior liveweights (n = 1000) 112-d 140-d 168-d 196-d 140-d 168-d 196-d
BW BW BW BW BW BW BW
70-d BW 70-d BW 70-d BW 70-d BW 112-d BW 112-d BW 112-d BW
20.72 29.73 39.82 6.75 10.54 15.43 20.52
1.437** 1.870** 2.235** 4.865** 1.196** 1.449** 1.66**
NS NS NS 0.0315** NS NS NS
3.43 4.40 5.63 7.04 2.81 3.68 4.87
Actual percentile mean BW on prior actual percentile mean BW (n = 100) 112-d 140-d 168-d 196-d 140-d 168-d 168-d 176-d
BW BW BW BW BW BW BW BW
70-d BW 70-d BW 70-d BW 70-d BW 112-d BW 112-d BW 112-d BW 112-d BW
4.35 10.85 15.71 1.66 0.88 3.63 3.63 −7.13
1.963** 2.374** 2.881** 4.247** 1.325** 1.608** 1.608** 2.174**
−0.00232* NS NS −0.0116** NS NS NS −0.00192**
0.15 0.24 0.21 0.33 0.22 0.24 0.24 0.29
0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999
1.79 2.37 2.88 3.39 1.33 1.61 1.61 1.89
Predicted percentile mean BW on prior predicted percentile mean BW predicted from complete data (n = 100) 112-d 140-d 168-d 196-d 140-d 163-d 176-d
BW BW BW BW BW BW BW
70-d BW 70-d BW 70-d BW 70-d BW 112-d BW 112-d BW 112-d BW
−1.511 −2.52 −3.37 −3.95 −0.56 −1.03 −1.32
2.086** 2.866** 3.623** 7.319** 1.377** 1.745** 2.085**
−0.00148** −0.0349* −0.00625** −0.00951** −0.00040** −0.0010** −0.00174**
0.004 0.008 0.016 0.024 0.004 0.009 0.018
0.999 0.999 0.999 0.999 0.999 0.999 0.999
1.98 2.61 3.16 3.61 1.32 1.60 1.83
Predicted percentile mean BW on prior predicted percentile mean BW predicted from truncated data (n = 100) 112-d 140-d 168-d 140-d 168-d
BW BW BW BW BW
70-d BW 70-d BW 70-d BW 112-d BW 112-d BW
−7.97 −17.90 −31.2 −7.95 −19.83
2.46** 0.377** 5.26** 1.595** 2.30**
−0.00698** −0.0166** −0.0300 −0.00198** −0.00502**
0.13 0.31 0.57 0.14 0.37
0.999 0.998 0.996 0.999 0.998
1.94 2.53 3.93 1.30 1.56
a
RSD = Residual SD. The change in BW at the subsequent age per unit change in the prior BW at the mean value of the prior age. *P<0.10. **P<0.01. b
predicted SD were similar for the 10 populations. The coefficient of variation of the 1000-pig populations for the predicted percentile BW means for age to 110 or 120 kg of BW was under 2.8%. Thus, it can be concluded that alternative bivariate normal distributions of c and m′ can produce similar variation in the predicted percentile BW mean and predicted ages to achieve a specific target BW.
The predicted SD of the percentile means from 126 to 182 d of age were slightly less for the truncated data set analyses than for the complete data set analyses. The SD of the predicted ages to achieve 110 or 120 kg of BW were also less for the truncated analyses than for the complete data set analyses. Relationships Among the Serial BW Measurements. The correlations among the serial individual
pig BW ranged from 0.74 to 0.97. The correlations between the later sequential BW are greater (r = 0.94 to 0.97) than the correlations between the early sequential BW (r = 0.76 to 0.89). These correlations are affected by the extent that pigs have different-shaped BW growth curves and by the residual error variance of each single BW measurement (Craig and Schinckel, 2001; Schinckel and Craig, 2002).
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Figure 1. The mean ADG (kg/d) of the 20% of pigs with the least days to achieve 120 kg of BW at each BW for four variables. The four variables are the actual individual pig data (AC), the actual percentile data (PE), the predicted percentile data (PP) predicted by fitting a random effects model to a complete biweekly BW data set, and the predicted percentile predicted from a data set truncated (PT) to reflect common marketing procedures.
Figure 3. The mean ADG (kg/d) of the 20% of pigs with the greatest days to achieve 120 kg of BW at each BW for four variables. The four variables are the actual individual pig data (AC), the actual percentile data (PE), the predicted percentile data (PP) predicted by fitting a random effects model to a complete biweekly BW data set, and the predicted percentile predicted from a data set truncated (PT) to reflect common marketing procedures.
Figure 4. The mean ADG (kg/d) of the 20% of pigs with the least days to achieve 120 kg of BW at each day of age for four variables. The four variables are the actual individual pig data (AC), the actual percentile data (PE), the predicted percentile data (PP) predicted by fitting a random effects model to a complete biweekly BW data set, and the predicted percentile predicted from a data set truncated (PT) to reflect common marketing procedures.
The correlations among the actual percentile means and predicted percentile means are >0.999. The corre-
lations among the actual or predicted percentile means at the sequential ages averaged 0.9998. The regression of the actual or predicted BW on prior actual or predicted BW are shown in Table 4. The regression of later individual pig BW on prior individual pig BW had R2 ranging from 0.64 to 0.86. Only one equation, the regression of individual pig 196-d BW on 70-d BW, had a significant quadratic regression coefficient. The derivative of later pig BW on prior pig BW increased as the difference in age between the serial BW increased, which indicates that the individual pig BW spread apart as age increases. The R2 of either the actual or predicted percentile means (complete and truncated data sets) were >0.996. The RSD values were greater for the truncated equation data set than for the complete data set. Three of the regression equations of later actual percentile means on early actual percentile means had significant quadratic regression coefficients. All of the
regression equations of later predicted BW percentile means on earlier predicted BW percentile means
Figure 2. The mean ADG (kg/d) of the 20% of pigs with the average days to achieve 120 kg of BW at each day of age for four variables. The four variables are the actual individual pig data (AC), the actual percentile data (PE), the predicted percentile data (PP) predicted by fitting a random effects model to a complete biweekly BW data set, and the predicted percentile predicted from a data set truncated (PT) to reflect common marketing procedures.
Figure 5. The mean ADG (kg/d) of the 20% of pigs with the average days to achieve 120 kg of BW at each BW for four variables. The four variables are the actual individual pig data (AC), the actual percentile data (PE), the predicted percentile data (PP) predicted by fitting a random effects model to a complete biweekly BW data set, and the predicted percentile predicted from a data set truncated (PT) to reflect common marketing.
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Evaluation of Pig Growth
Figure 6. The mean ADG (kg/d) of the 20% of pigs with the greatest days to achieve 120 kg of BW at each day of age for four variables. The four variables are the actual individual pig data (AC), the actual percentile data (PE), the predicted percentile data (PP) predicted by fitting a random effects model to a complete biweekly BW data set, and the predicted percentile predicted from a data set truncated (PT) to reflect common marketing procedures.
had significant quadratic relationships. Although statistically significant, the addition of the quadratic coefficient increased the R2 of each equation by ≤0.001. The derivative of the later BW percentile means on early BW percentile means are greater than the derivatives of the actual pig data, which was due to the fact that the individual pigs have different-shaped growth curves, as indicated by the variation in the pig m′ values. Evaluation of Subpopulation Mean Growth Curves. The fitting of the mean percentile data to random effects nonlinear functions should predict similar BW growth curves for subpopulations of pigs with above average, average, and below average growth rates. The mean BW growth rates are presented in Figures 1 to 6 for the 20percentile groups with the least (Figures 1 and 4), average (Figures 2 and 5), and greatest (Figures 3 and 6) number of days to achieve 120 kg. The actual BW, actual percentile mean, and predicted percentile mean data produced similar
BW growth curves relative to either age (Figures 1 to 3) or BW (Figures 4 to 6). The ADG curves of the four variables were most similar for the pigs with least days to 120 kg of BW. The ADG curves were slightly different for the four variables for the pigs with the greatest days to achieve 120 kg of BW. The use of the truncated data was expected to produce small biases in the prediction of the actual BW growth from 100 to 130 kg of BW. This bias would be expected to be greater for the pigs with the greatest days to 120 kg, as the effect of serial marketing on the observed vs actual unbiased percentile means is greatest for this group of pigs. This is due to the fact that the marketing of pigs based on single BW measurement increases the subsequent means of the remaining BW percentile means. The predicted ADG for the truncated percentile data were 0.01 to 0.02 kg/d greater than the ADG predicted for the other three variables for the slowest growing pigs (greatest days to 120 kg of BW) from 100 to 130 kg of BW.
Discussion The method of fitting the daily percentile data from an AST to a mixed model nonlinear function did reproduce the overall population mean BW at each age. The mean and variance of the actual days to achieve 110 and 120 kg of BW were predicted by the percentile analyses. The method of percentile mean analyses presented in this paper could be used to forecast the number and BW of pigs to be marketed. Also, the optimal age to initiate the feeding of Paylean威 for the current group of pigs could be predicted. One assumption made was that the number of BW measurements taken per pig was independent of the pig’s BW growth rates. Pigs responding to a disease challenge or other stressors would likely be less
active and consume fewer meals per day than healthy, nonstressed pigs. Further research needs to be conducted with commercial pigs that are exposed to disease and environmental stressors. The ability of this method to reproduce the magnitude of skewness observed in commercial pigs also needs further evaluation.
Implications Pig BW data collected by AST without individual identification can be used to model pig BW growth. Fitting the percentile mean data with random effects nonlinear models can provide parameters that describe the magnitude of variation in BW at each age and predicted age to reach specific target BW.
Acknowledgments The authors acknowledge the helpful comments of Bruce Schmeiser, Department of Industrial Engineering, Purdue University.
Literature Cited Boland, M. A., P. V. Preckel, and A. P. Schinckel. 1993. Optimal slaughter weights under alternative price systems. J. Agric. Appl. Econ. 25:148. Bridges, T. C., U. W. Turner, E. M. Smith, T. S. Stahly, and O. J. Loewer. 1986. A mathematical procedure for estimating animal growth and body composition. Trans. ASAE 29:1342. Craig, B. A., and A. P. Schinckel. 2001. Nonlinear mixed effects model for swine growth. Prof. Anim. Sci. 17:256. King, R. H. 1999. A review—Nutritional constraints to pig performance and pig variability. In Manipulating Pig Production VII. P. D. Cranwell (Ed.). p 245. Aust. Pig Sci. Assoc., Werribee, Victoria, Australia. Le Dividich, J. 1999. A review-Neonatal and weaner pig: Management to reduce
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variation. In Manipulating Pig Production VII. P. D. Cranwell (Ed.). p 135. Aust. Pig Sci. Assoc., Werribee, Victoria, Australia. Li, N. 2003. Economic analysis of optimal production and marketing management strategies for swine production and operations with Paylean. Ph.D. thesis. Purdue Univ., West Lafayette, IN. Patrick, G. F., C. A. Hart, and C. Overend. 1993. Marketing concerns in all-in/all-out
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production. In 1993 Swine Day Rep. Purdue University, West Lafayette, IN.
fects models of swine growth. Prof. Anim. Sci. 18:219.
Ramaekers, P. J. L. 1996. Control of individual growth in group-housed pigs using feeding stations. Ph.D Thesis, Dep. Anim. Nutr., Wageningen Agricultural Univ., Wageningen, The Netherlands.
Schinckel, A. P., N. Li, P. V. Preckel, M. E. Einstien, and D. Miller. 2003. Development of a stochastic pig compositional growth model. Prof. Anim. Sci. 19:255.
Schinckel, A. P., and B. A. Craig. 2002. Evaluation of alternative nonlinear mixed ef-
Schinckel, A. P., J. Ferrel, M. E. Einstien, S. M. Pearce, and R. D. Boyd. 2004. Analysis of pig growth from birth to sixty days of age. Prof. Anim. Sci. 20:79.
Evaluation of a Method to Analyze Pig Live Weight Data from Animal 1
Sorting Technologies
A. P. SCHINCKEL*,2, PAS, M. E. EINSTEIN*, and D. MILLER† *Department of Animal Sciences and †Department of Agricultural Economics, Purdue University, West Lafayette, IN 47907
Abstract A method to analyze pig BW data collected by an animal sorting technology scale without individual pig identification was evaluated. Data for ten 1000pig grow-finish barns were simulated by a stochastic model. The BW at each age was modeled as a predicted BW plus a daily residual error (mean = 0; SD = 1.4 kg) and a within-day residual error (mean = 0; SD = 0.98 kg). The number of times each pig was weighed was simulated to vary among pigs and to vary daily for each pig. The number of daily BW measurements taken per pig had an overall mean of 5.40 and SD of 1.23. Two types of data sets were simulated. A complete data set had biweekly data from 70 to 196 d of age. A truncated data set was simulated to reflect typical serial marketing of pigs and included biweekly data from 70 to 154 d of age and weekly truncated data from 161 to 175 d of age. The percentile means of the BW data were calculated and assigned a percentile identification of 1 to 100. The percentile means were fit to a mixed model nonlinear function (Bridges) with two random effects predicted
1
Purdue Agriculture Research Program No. 17412. 2 To whom correspondence should be addressed: [email protected]
for each percentile. The fitting of either the complete or truncated data sets reproduced the mean and variance of BW at each age and predicted age to achieve 120 kg of BW. The serial marketing of pigs may produce small biases in the prediction of the actual percentile means. The fitting of the mean percentile data can be used to model the underlying mean and variation of BW growth. (Key Words: Mixed Effects Model, Nonlinear Growth Functions, Swine Growth.)
Introduction Variability in the growth rates of pigs is important to the economic costs and returns of both the pork producer and processor (Patrick et al., 1993; King, 1999). Pork processors have the objective to market lean pork products that are uniform in BW and composition (Boland et al., 1993). The optimization of pork production systems, including the evaluation of alternative management and marketing strategies, requires knowledge of the between-pig variation in BW and carcass composition (King, 1999; Le Dividich, 1999). Recently, mixed model nonlinear analysis software has been made available, which accounts for the underlying variancecovariance structure of serial BW data
(Craig and Schinckel, 2001; Schinckel and Craig, 2002) and has led to the development of a stochastic pig growth model (Schinckel et al., 2003). Recently, scales have been developed that can automatically weigh individual pigs. Pigs are trained to individually enter and walk through an electronic scale and to subsequently exit into a pen with a bank of feeders. Producers can monitor the distribution of BW data and set a sort BW for marketing. Pigs above the sort BW are released into a market pen. These animal sorting technologies (AST) reduce the amount of labor required to sort pigs for marketing and reduce the discounts caused by over- and underweight carcasses. The AST also can increase returns when used to target the optimal Paylean威 (Elanco, Greenfield, IN) use and marketing strategy (Li, 2003). These electronic scales can collect the BW data over any specific period of time. Pigs may be weighed several times per day. However, without individual pig identification, conventional pig random effects models cannot be fit to the BW data, and, subsequently, the BW growth of individual pigs cannot be modeled. Alternative data analyses must be considered to predict the mean and variation of the BW values. The objectives of this study were 1) to develop and evaluate an alternative method of analyzing the BW
Evaluation of Pig Growth
data collected by an AST system and 2) to evaluate the impact of the serial marketing of pigs on the predicted BW growth rates and predicted days to achieve a specific market BW.
Materials and Methods Data from a Purdue University research trial were used as the example data set. High lean gain gilts were reared via all-in all-out procedures (Schinckel and Craig, 2002). A total of 96 gilts were weighed and measured via real-time ultrasound at 49, 70, 104, 132, and 153 d of age. The 42 slowest-growing gilts had an additional BW measurement at 174 d of age. The BW data were fitted to alternate mixed nonlinear models using the nonlinear mixed (NLMIXED) procedure of SAS威 (SAS Institute, Cary, NC; Schinckel and Craig, 2002). The best model of the Bridges function (Bridges et al., 1986), based on residual standard deviation (RSD) and Akaike’s Information Criteria values, was BWit = (C + ci)(1 − exp (− exp (M′ + m′i) tA)) + birth BW + eit, where C, M′, and A are fixed population mean parameters, ci and m′i are random effects for pig i, t is days of age, birth BW is a constant (1.4 kg), and eit is the residual error. The estimated values for C, M, and A were 216.27, −9.124, and 1.755 with SE of 11.5, 0.077, and 0.028, respectively (Schinckel and Craig, 2002). The equation had an R2 of 0.998 and a RSD of 1.70 kg. The NLMIXED procedure estimated a value of ci and m′i for each individual pig. By using these values, the predicted age required to reach a specific target BW can be calculated. Predicted days of age at 110 and 120 kg of BW were used as a measure of overall growth rate. The ci values had a SD of 20.75. The m′i values had a SD of 0.0968. The ci and m′i values also exhibited a negative correlation (r = −0.658; P<0.001). Simulation of the Variation in BW Growth. A set of 1000 ci and m′i values were sampled from a large sam-
ple of ci and m′i values with the same bivariate normal distribution as the observed values. These values, when used in the nonlinear BW function, reproduce a population of pigs with a distribution of individual live growth curves. The BW at each specific age is the predicted BW (BWit) plus two residual error terms, a daily residual error (mean = 0; SD = 1.4 kg) and a within-day residual error (mean = 0; SD = 0.098 kg; Ramaekers, 1996). Based on previous data, the number of meals consumed varies among pigs and varies daily for individual pigs. The number of times each pig was weighed was modeled by the equation Nit = µ + pi + pit, where µ is the mean (5.4), pi is the random effect for the variation between pigs during their postweaning growth (mean = 0; SD = 1.0), and pit is the normally distributed random effect (mean = 0; SD = 0.70) for the variation among days for each individual pig. The value of Nit was rounded to the nearest whole number. This procedure simulated BW data for 1000 individual pigs with a distribution of live growth curves and a varying number of times weighed per day. The process was repeated to simulate data for ten 1000-head grow-finishers. To evaluate the use of AST, these BW data were considered to be measurements for unidentified, random pigs. Daily BW data, biweekly from 70 to 196 d of age and weekly from 154 to 175 d of age, were sorted into percentile groups. The mean of each percentile group was calculated, and the percentile rank (1 to 100) was assigned to the mean value. The percentile means for the 10 biweekly BW from each of the ten 1000-head grow-finishers were fitted to the mixed model nonlinear Bridges function using the nonlinear mixed (NLMIXED) procedure of SAS. The function had the form MBWit = (C + ci){1 − exp [−exp (M′ + m′i) tA]} + birth BW + eit, where MBWit is the mean BW of percentile i at t days of age; C, M′, and A are fixed population mean parameters; ci and m′i are
51
random effects for percentile I; t is days of age; birth BW is a constant (1.4 kg); and eit is the residual error. The random effects ci and m′i are assumed to be multivariate normal with means equal to zero, variances σ2c and σ2m′ and covariance σc,m. The eij are assumed to be independent of the random effects. Modeling the Effect of Serial Marketing. To simulate serial marketing, the BW data for each of the 10 growfinishing units were truncated by modeling current typical marketing procedures (Schinckel et al., 2003). Twice weekly, Monday and Friday, semi-trailers were marketed when 170 pigs were >120 kg of BW. At each marketing day, the heaviest pigs were marketed. When the fifth semi-trailer was filled with pigs >120 kg of BW, the remaining 150 pigs were also marketed to empty the facility. After marketing the first semi-trailer, weekly pig BW measurements were included in the analyses. The remaining weekly pig BW data were assigned to percentile groups based on the percentage of pigs remaining. With N percentage of the pigs remaining, the pig data were ranked and then divided into N equal-sized groups and assigned to percentile groups 1 to N. The biweekly and subsequent weekly truncated data were analyzed with the same random nonlinear model as the complete biweekly BW data. Evaluation of the Four BW Variables. Four variables were evaluated by the univariate procedure of SAS. The first variable was the traditional single BW measurement taken biweekly for each pig from 70 to 196 d of age. The second variable was the actual mean BW for each percentile at each age. The third variable was the mean value of each percentile predicted from the mixed model nonlinear function using the complete biweekly BW data. The fourth variable was the mean value of each percentile predicted from the mixed model nonlinear function using the truncated BW data. The relationship of the serial BW data for the four variables was evalu-
52
ated by regression analyses (Proc REG; SAS). The values of each of the four variables later in the finish pe-
Schinckel et al.
riod (112, 140, 168, and 196 d of age) were regressed on the earlier (70 or 112 d) values of the same variable.
The equations included the linear and quadratic effects of the prior BW data.
TABLE 1. Statistical parameters for BW data of individual pigs, actual percentile means, and percentile means predicted from either complete or truncated data setsa. Quantile Item 70-d BW, kg Individual data Actual percentile means Predicted percentile means—complete data Predicted percentile means—truncated data 84-d BW, kg Individual data Actual percentile means Predicted percentile means—complete data Predicted percentile means—truncated data 98-d BW, kg Individual data Actual percentile means Predicted percentile means—complete data Predicted percentile means—truncated data 112-d BW, kg Individual data Actual percentile means Predicted percentile means—complete data Predicted percentile means—truncated data 126-d BW, kg Individual data Actual percentile means Predicted percentile means—complete data Predicted percentile means—truncated data 140-d BW, kg Individual data Actual percentile means Predicted percentile means—complete data Predicted percentile means—truncated data 154-d BW, kg Individual data Actual percentile means Predicted percentile means—complete data Predicted percentile means—truncated data 168-d BW, kg Individual data Actual percentile means Predicted percentile means—complete data Predicted percentile means—truncated data 182-d BW, kg Individual data Actual percentile means Predicted percentile means—complete data 196-d BW, kg Individual data Actual percentile means Predicted percentile means—complete data
Mean
SD
Skewness
90%
10%
37.17 37.17 37.20 37.25
3.15 3.16 2.93 2.98
0.026 0.028 0.025 0.096
41.2 41.2 40.8 41.1
33.2 33.2 33.4 33.5
49.04 49.04 48.99 49.00
4.09 4.11 3.85 3.91
0.072 0.070 0.021 0.076
54.2 54.2 53.8 54.0
43.8 43.8 44.0 44.1
61.38 61.37 61.38 61.35
4.78 4.81 4.81 4.85
0.066 0.069 0.017 0.055
67.4 67.4 67.4 67.5
55.2 55.2 55.2 55.3
74.10 74.10 74.06 74.01
5.64 5.66 5.77 5.79
0.01 0.001 0.012 0.031
81.3 81.3 81.2 81.3
67.0 67.0 66.7 66.7
86.76 86.76 86.76 86.71
6.54 6.57 6.71 6.69
0.001 0.005 0.007 0.006
94.9 95.0 95.1 95.1
78.4 78.4 78.2 78.2
99.10 99.11 99.22 99.22
7.47 7.51 7.61 7.54
0.0190 0.0270 0.0020 −0.020
108.3 108.3 108.6 108.5
89.7 89.6 89.5 89.6
111.40 111.40 111.27 111.35
8.24 8.28 8.45 8.33
−0.00 −0.00 −0.00 −0.05
121.7 121.7 121.7 121.5
100.9 100.7 100.4 100.6
122.81 122.81 122.73 122.94
9.07 9.11 9.22 9.03
0.02 0.02 −0.00 −0.01
133.9 133.9 134.1 133.8
111.1 111.1 110.9 111.2
133.52 133.52 133.50
10.04 10.09 9.93
−0.05 −0.06 −0.02
145.9 145.9 145.8
120.4 120.4 120.7
144.44 143.44 144.48
10.65 10.71 10.54
−0.04 −0.04 −0.02
156.8 156.7 156.5
129.6 129.5 129.9 continued
53
Evaluation of Pig Growth
TABLE 1. (continued) Statistical parameters for BW data of individual pigs, actual percentile means, and percentile means predicted from either complete or truncated data setsa. Quantile Item
Mean
SD
Skewness
90%
10%
153.49 153.37 153.37 153.21
9.86 10.27 10.27 9.90
0.63 0.56 0.56 0.53
166.0 166.5 166.5 166.5
142.0 141.5 141.5 141.5
165.83 165.61 165.67 165.60
11.44 11.60 11.61 11.38
0.73 0.60 0.61 0.58
181.1 180.6 180.6 180.5
153.0 152.7 152.2 152.3
Days to 110 kg
Days to 120 kg
a The individual BW data are for a single BW for each individual pig. The actual percentile mean BW data are the calculated percentile means for the random multiple BW measurements taken each day. The predicted percentile mean BW data are the percentile means predicted by fitting the percentile data 0% a mixed model nonlinear function to either the complete or truncated data set. Skewness and percentile quantiles as calculated by Proc Univariate (SAS Inst., Inc., Cary, NC).
Evaluation of the Growth of Subpopulations of Pigs. The growth rate of subpopulations of pigs can be substantially different (Schinckel et al., 2004). Precise stochastic models require that the mean growth of subpopulations of pigs with different overall BW growth rates be accurately predicted. The fitting of the BW percentile mean should predict the actual growth of the subpopulations sorted by overall postweaning BW growth rate. Four BW variables were evaluated: 1) the actual BW data for individual pigs, 2) the actual percentile mean BW data, 3) the predicted BW data for each percentile using the complete biweekly data set, and 4) the predicted BW data for each percentile using the truncated data set. The data were sorted into five 20-percentile groups based on the predicted age for each pig or percentile to achieve 120 kg of BW. The mean ADG for each 20-percentile group was plotted for each variable relative to either BW or days of age.
Results and Discussion Simulation Results. The simulation model produced an average of
5.407 observations per pig/d with a SD of 1.23. The number of daily BW measurements ranged from one to nine. The marketing protocol resulted in identical marketing dates for all 10 grow-finish facilities. Full truckloads containing 170 pigs each were marketed at 155, 162, 166, 169, and 176 d of age. The truncated data set included weekly BW data with 1000, 830, 490, and 320 pigs at 154, 161, 168, and 175 d of age, respectively. The mean values and summary statistics were similar for the simulated individual pig BW and the mean percentile values of the multiple daily BW (Table 1). The results indicate that the percentile means closely approximate the overall distribution, including the mean, variance, and skewness of the data from individual pigs. The serial marketing of pigs may bias the mean of the percentile means at subsequent weigh days. Pigs were marketed when one individual pig BW measurement was above the target market BW of 120 kg and the pig was one of the 170 heaviest pigs. The fitting of the BW data to the percentile means and use of the percentile values as the random effect assumes that the individual pig is assigned to its correct percentile rank.
The serial marketing of pigs did produce a small bias on the mean BW of the remaining pigs, with respect to the mean of the BW of the same percentiles for the complete data set. With a complete data set, the 83% of pigs with the least BW at 161 d of age averaged 114.56 kg. When the heaviest pigs were marketed based on a single BW on d 155, the remaining 83% of the pigs weighed 114.65 kg at 161 d of age. This is due to the fact that the heaviest 17% of the actual BW observations in the complete data set have a greater mean than the actual BW of the upper 17% of the pigs based on a single BW taken 6 d prior. Some pigs are marketed on d 155 with a single BW in the upper 17% of the overall single BW, and this produces BW measurements that are less than the 17th percentile 6 d later. The mean of the actual lesser 49% of the complete BW observations collected on d 168 is 115.43 kg. The mean of the remaining observations after marketing the greater 51% of the pigs (three 170-pig groups) was 115.71 kg. At 175 d of age, the lesser 32% of the actual BW measurements averaged 117.56 kg while the mean of the observations of the remaining 32% of the pigs was 117.86 kg.
54
Schinckel et al.
TABLE 2. Parameter estimates for the fitting of the mean precentile BW data to the Bridges functiona. C 210.3 212.6 209.7 212.5 212.0 212.8 212.5 212.8 212.9 211.1
M′
A
var(c)
varm′
cov(c,m′)
var(e)
AICb
−9.096 −9.098 −9.118 −9.083 −9.097 −9.089 −9.098 −9.091 −9.105 −9.101
1.745 1.744 1.752 1.740 1.745 1.742 1.744 1.741 1.745 1.745
171.9 88.7 191.7 113.3 173.3 58.6 175.2 73.6 163.5 56.5
0.000405 0.000540 0.000296 0.000082 0.000390 0.000194 0.000386 0.000092 0.000601 0.000067
0.261 0.212 0.217 0.0843 0.258 0.0969 0.244 0.082 0.304 0.0607
0.0528 0.0575 0.0649 0.0843 0.0572 0.0417 0.06770 0.0640 0.0469 0.0574
842.8 948.2 1065.9 997.1 910.7 729.8 1090.8 1087.3 763.9 1053.5
The mixed effects model with C and M′ as random effects is (C+ ci) (1 − exp (−exp (M′ + m′i) tA)) + 1.4 + eij, where eij is normal with mean 0 and variance σ2e and ci and m′i are random effects with mean 0, and variances σ2c and σ2m′, with covariance c with m′ σc,m′. b AIC = Akaike’s Information Criteria. a
Random Effects Nonlinear Growth Function Parameters. The parameter estimates produced by fitting the random effects Bridges function to the complete biweekly percentile mean and the truncated percentile mean data for each of 10 simulated barns are presented in Table 2. The values of the fixed parameters (C, M′, and A) were similar for the ten 1000-head grow-finisher barns. The mean values of 211.9 for C and −9.097 for M′ were slightly less in absolute value than the mean simulated pig BW parameter values of 216.3 and −9.124, respectively. The values of the variance of c, variance of m′i, and covariance of ci and m′i differed substantially among the ten 1000-head populations of pigs. It is possible that alternative values of the variance-covariance of the random effects (ci and m′i) may result in similar variation in the predicted percentile means at each age. Variation in the Actual and Predicted BW. The summary statistics for the four BW variables are presented for one 1000-head population of pigs in Table 1. The predicted percentile parameters are similar to the individual pig BW and actual percentile mean parameters. In this data set, the magnitude of skewness is small
for all four BW variables. The magnitude of skewness for the predicted percentile means was slightly different from the actual BW data. The values of the 10 and 90 percentile quantiles of the four variables—the actual BW, percentile mean and predicted percentile means (complete biweekly and
truncated)—were within 0.2 to 0.4 kg of each other. The magnitude of skewness, in most cases caused by a greater number of slower-growing pigs than expected, is important in the evaluation of the optimal marketing strategy and barn close-out time. The magnitude of skewness increases as the health status of the pigs decreases (Schinckel and Craig, 2002). Further research should be conducted with populations of pigs with a greater magnitude of skewness for BW. The means and SD of the predicted BW percentile means for the ten 1000-head populations are presented in Table 3. The predicted mean BW and days to 110 or 120 kg BW were similar for the analyses of the 10 complete biweekly or truncated data sets. The predicted 154- and 182-d BW were 0.1 and 0.2 kg greater for the truncated data set analyses than for the complete biweekly analyses. The mean predicted ages to achieve 110and 120-kg BW were 0.2 d less for the truncated data set analyses vs the complete data set analyses. The SD of the predicted percentile BW means increased with age. The
TABLE 3. Mean and standard deviations of the predicted percentile means for BW produced by fitting random regression models to ten 1000-head populations of pigsa. Predicted mean
Predicted SD
Item
Mean
SD
Mean
SD
70-d BW, kg 98-d BW, kg 126-d BW, kg 154-d BW, kg 182-d BW, kg Days to 110 kg Days to 120 kg Truncated data set 70-d BW, kg 90-d BW, kg 126-d BW, kg 154-d BW, kg 182-d BW, kg Days to 110 kg Days to 120 kg
37.2 61.5 86.9 111.5 133.9 153.1 165.2
0.11 0.18 0.26 0.32 0.37 0.41 0.46
2.91 4.80 6.71 8.45 9.94 10.15 11.53
0.08 0.12 0.15 0.17 0.18 0.26 0.32
37.3 61.5 86.9 111.6 134.1 152.9 165.0
0.11 0.19 0.26 0.31 0.35 0.37 0.41
3.00 4.87 6.71 8.33 9.64 9.98 11.37
0.06 0.10 0.14 0.18 0.23 0.26 0.29
a
The SD is the SD of the ten 1000-head populations (n = 10).
55
Evaluation of Pig Growth
TABLE 4. Regression of actual or predicted BW on prior actual or predicted BW. Item
Prior BW, kg
b0
b1
b2
RSDa, kg
R2
Derivative1
0.639 0.646 0.614 0.566 0.855 0.835 0.791
1.44 1.87 2.24 2.52 1.20 1.45 1.66
Simulated actual pig liveweight on prior liveweights (n = 1000) 112-d 140-d 168-d 196-d 140-d 168-d 196-d
BW BW BW BW BW BW BW
70-d BW 70-d BW 70-d BW 70-d BW 112-d BW 112-d BW 112-d BW
20.72 29.73 39.82 6.75 10.54 15.43 20.52
1.437** 1.870** 2.235** 4.865** 1.196** 1.449** 1.66**
NS NS NS 0.0315** NS NS NS
3.43 4.40 5.63 7.04 2.81 3.68 4.87
Actual percentile mean BW on prior actual percentile mean BW (n = 100) 112-d 140-d 168-d 196-d 140-d 168-d 168-d 176-d
BW BW BW BW BW BW BW BW
70-d BW 70-d BW 70-d BW 70-d BW 112-d BW 112-d BW 112-d BW 112-d BW
4.35 10.85 15.71 1.66 0.88 3.63 3.63 −7.13
1.963** 2.374** 2.881** 4.247** 1.325** 1.608** 1.608** 2.174**
−0.00232* NS NS −0.0116** NS NS NS −0.00192**
0.15 0.24 0.21 0.33 0.22 0.24 0.24 0.29
0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999
1.79 2.37 2.88 3.39 1.33 1.61 1.61 1.89
Predicted percentile mean BW on prior predicted percentile mean BW predicted from complete data (n = 100) 112-d 140-d 168-d 196-d 140-d 163-d 176-d
BW BW BW BW BW BW BW
70-d BW 70-d BW 70-d BW 70-d BW 112-d BW 112-d BW 112-d BW
−1.511 −2.52 −3.37 −3.95 −0.56 −1.03 −1.32
2.086** 2.866** 3.623** 7.319** 1.377** 1.745** 2.085**
−0.00148** −0.0349* −0.00625** −0.00951** −0.00040** −0.0010** −0.00174**
0.004 0.008 0.016 0.024 0.004 0.009 0.018
0.999 0.999 0.999 0.999 0.999 0.999 0.999
1.98 2.61 3.16 3.61 1.32 1.60 1.83
Predicted percentile mean BW on prior predicted percentile mean BW predicted from truncated data (n = 100) 112-d 140-d 168-d 140-d 168-d
BW BW BW BW BW
70-d BW 70-d BW 70-d BW 112-d BW 112-d BW
−7.97 −17.90 −31.2 −7.95 −19.83
2.46** 0.377** 5.26** 1.595** 2.30**
−0.00698** −0.0166** −0.0300 −0.00198** −0.00502**
0.13 0.31 0.57 0.14 0.37
0.999 0.998 0.996 0.999 0.998
1.94 2.53 3.93 1.30 1.56
a
RSD = Residual SD. The change in BW at the subsequent age per unit change in the prior BW at the mean value of the prior age. *P<0.10. **P<0.01. b
predicted SD were similar for the 10 populations. The coefficient of variation of the 1000-pig populations for the predicted percentile BW means for age to 110 or 120 kg of BW was under 2.8%. Thus, it can be concluded that alternative bivariate normal distributions of c and m′ can produce similar variation in the predicted percentile BW mean and predicted ages to achieve a specific target BW.
The predicted SD of the percentile means from 126 to 182 d of age were slightly less for the truncated data set analyses than for the complete data set analyses. The SD of the predicted ages to achieve 110 or 120 kg of BW were also less for the truncated analyses than for the complete data set analyses. Relationships Among the Serial BW Measurements. The correlations among the serial individual
pig BW ranged from 0.74 to 0.97. The correlations between the later sequential BW are greater (r = 0.94 to 0.97) than the correlations between the early sequential BW (r = 0.76 to 0.89). These correlations are affected by the extent that pigs have different-shaped BW growth curves and by the residual error variance of each single BW measurement (Craig and Schinckel, 2001; Schinckel and Craig, 2002).
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Figure 1. The mean ADG (kg/d) of the 20% of pigs with the least days to achieve 120 kg of BW at each BW for four variables. The four variables are the actual individual pig data (AC), the actual percentile data (PE), the predicted percentile data (PP) predicted by fitting a random effects model to a complete biweekly BW data set, and the predicted percentile predicted from a data set truncated (PT) to reflect common marketing procedures.
Figure 3. The mean ADG (kg/d) of the 20% of pigs with the greatest days to achieve 120 kg of BW at each BW for four variables. The four variables are the actual individual pig data (AC), the actual percentile data (PE), the predicted percentile data (PP) predicted by fitting a random effects model to a complete biweekly BW data set, and the predicted percentile predicted from a data set truncated (PT) to reflect common marketing procedures.
Figure 4. The mean ADG (kg/d) of the 20% of pigs with the least days to achieve 120 kg of BW at each day of age for four variables. The four variables are the actual individual pig data (AC), the actual percentile data (PE), the predicted percentile data (PP) predicted by fitting a random effects model to a complete biweekly BW data set, and the predicted percentile predicted from a data set truncated (PT) to reflect common marketing procedures.
The correlations among the actual percentile means and predicted percentile means are >0.999. The corre-
lations among the actual or predicted percentile means at the sequential ages averaged 0.9998. The regression of the actual or predicted BW on prior actual or predicted BW are shown in Table 4. The regression of later individual pig BW on prior individual pig BW had R2 ranging from 0.64 to 0.86. Only one equation, the regression of individual pig 196-d BW on 70-d BW, had a significant quadratic regression coefficient. The derivative of later pig BW on prior pig BW increased as the difference in age between the serial BW increased, which indicates that the individual pig BW spread apart as age increases. The R2 of either the actual or predicted percentile means (complete and truncated data sets) were >0.996. The RSD values were greater for the truncated equation data set than for the complete data set. Three of the regression equations of later actual percentile means on early actual percentile means had significant quadratic regression coefficients. All of the
regression equations of later predicted BW percentile means on earlier predicted BW percentile means
Figure 2. The mean ADG (kg/d) of the 20% of pigs with the average days to achieve 120 kg of BW at each day of age for four variables. The four variables are the actual individual pig data (AC), the actual percentile data (PE), the predicted percentile data (PP) predicted by fitting a random effects model to a complete biweekly BW data set, and the predicted percentile predicted from a data set truncated (PT) to reflect common marketing procedures.
Figure 5. The mean ADG (kg/d) of the 20% of pigs with the average days to achieve 120 kg of BW at each BW for four variables. The four variables are the actual individual pig data (AC), the actual percentile data (PE), the predicted percentile data (PP) predicted by fitting a random effects model to a complete biweekly BW data set, and the predicted percentile predicted from a data set truncated (PT) to reflect common marketing.
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Evaluation of Pig Growth
Figure 6. The mean ADG (kg/d) of the 20% of pigs with the greatest days to achieve 120 kg of BW at each day of age for four variables. The four variables are the actual individual pig data (AC), the actual percentile data (PE), the predicted percentile data (PP) predicted by fitting a random effects model to a complete biweekly BW data set, and the predicted percentile predicted from a data set truncated (PT) to reflect common marketing procedures.
had significant quadratic relationships. Although statistically significant, the addition of the quadratic coefficient increased the R2 of each equation by ≤0.001. The derivative of the later BW percentile means on early BW percentile means are greater than the derivatives of the actual pig data, which was due to the fact that the individual pigs have different-shaped growth curves, as indicated by the variation in the pig m′ values. Evaluation of Subpopulation Mean Growth Curves. The fitting of the mean percentile data to random effects nonlinear functions should predict similar BW growth curves for subpopulations of pigs with above average, average, and below average growth rates. The mean BW growth rates are presented in Figures 1 to 6 for the 20percentile groups with the least (Figures 1 and 4), average (Figures 2 and 5), and greatest (Figures 3 and 6) number of days to achieve 120 kg. The actual BW, actual percentile mean, and predicted percentile mean data produced similar
BW growth curves relative to either age (Figures 1 to 3) or BW (Figures 4 to 6). The ADG curves of the four variables were most similar for the pigs with least days to 120 kg of BW. The ADG curves were slightly different for the four variables for the pigs with the greatest days to achieve 120 kg of BW. The use of the truncated data was expected to produce small biases in the prediction of the actual BW growth from 100 to 130 kg of BW. This bias would be expected to be greater for the pigs with the greatest days to 120 kg, as the effect of serial marketing on the observed vs actual unbiased percentile means is greatest for this group of pigs. This is due to the fact that the marketing of pigs based on single BW measurement increases the subsequent means of the remaining BW percentile means. The predicted ADG for the truncated percentile data were 0.01 to 0.02 kg/d greater than the ADG predicted for the other three variables for the slowest growing pigs (greatest days to 120 kg of BW) from 100 to 130 kg of BW.
Discussion The method of fitting the daily percentile data from an AST to a mixed model nonlinear function did reproduce the overall population mean BW at each age. The mean and variance of the actual days to achieve 110 and 120 kg of BW were predicted by the percentile analyses. The method of percentile mean analyses presented in this paper could be used to forecast the number and BW of pigs to be marketed. Also, the optimal age to initiate the feeding of Paylean威 for the current group of pigs could be predicted. One assumption made was that the number of BW measurements taken per pig was independent of the pig’s BW growth rates. Pigs responding to a disease challenge or other stressors would likely be less
active and consume fewer meals per day than healthy, nonstressed pigs. Further research needs to be conducted with commercial pigs that are exposed to disease and environmental stressors. The ability of this method to reproduce the magnitude of skewness observed in commercial pigs also needs further evaluation.
Implications Pig BW data collected by AST without individual identification can be used to model pig BW growth. Fitting the percentile mean data with random effects nonlinear models can provide parameters that describe the magnitude of variation in BW at each age and predicted age to reach specific target BW.
Acknowledgments The authors acknowledge the helpful comments of Bruce Schmeiser, Department of Industrial Engineering, Purdue University.
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