Purdue University 2002 Swine Research Report

Development of a Stochastic Pig Compositional Growth Model

A. P. Schinckel1, N. Li2, M. E. Einstein1, and D. Miller2
Departments of 1Animal Sciences and 2Agricultural Economics

Introduction

Several deterministic swine growth models have been developed which can be used to optimize the nutrition and management of the average pig within a population of pigs. Stochastic models incorporate the variation between pigs by modeling the compositional and live weight growth of numerous individual pigs. The objective of this research was to develop a simple stochastic compositional pig growth model.

Materials and Methods

Data from a Purdue University research trial was used as the example data set. High lean gain gilts were reared via all-in all-out procedures. Serial live weight and real time ultrasound measurements were taken at 21-day intervals starting at 49 days of age. Empty body protein and lipid mass were predicted from the live weight and serial ultrasound measurements.

The liveweight data were fit to alternate mixed nonlinear models. The best model based on residual standard deviation (RSD) and Akaikes Information Criteria (AIC) statistics was WTit = (C + ci) (1 exp (-exp (M' + m'i) tA) + BW, where WTit is the weight of the ith pig at t days of age; C, M', and A are fixed population mean parameters; ci and m'i are random effects for the ith pig; t is days of age and BW is birth weight (3.1 lb). The means and variances of the ci and m'i values and covariance between the ci and m'i values were calculated. Equations were developed from a set of ci and m'i values sampled from a large sample of ci and m'i values with the same distribution as the observed values. These values, when used in the nonlinear live weight function, reproduce a population of pigs with a distribution of individual live growth curves.

To produce this data, the live weight of a pig at each specific age is the predicted live weight (WTit) plus a residual error term (eit). The residual error term is a random effect produced by multiplying the RSD of the original equation by a value sampled from standard normal distribution (mean = 0, variance = 1).

Using the original live weight data, the predicted empty body protein (MTPRO) mass was fitted to live weight. Several mixed nonlinear functions were evaluated. The best fit was MTPRO = C ((LW)) + cpi ((LW))D + eij: where LW is live weight, (LW) = (1 (exp(b0 + b1 LW + b2 LW2)), C and D are fixed effects, cpi is a random effect for the ith pig, and eij is the residual error of the ith pig at the ith live weight. The value of D describes the relative magnitude of the between pig standard deviation relative to the mean MTPRO at a specific live weight. The value of D was 1.853, indicating that the predicted between pig coefficient of variation increased as live weight increased. In other words, the variation in MTPRO percentage increased as live weight increased.

The mean and variance of cpi was calculated. The relationship of cpi, with live weight growth was evaluated via regression analysis. The best equation to predict cpi was a function of predicted age at 242 lb (D242) and D2422 with an R2 of 0.0596. The distribution and relationship of cpi to the live weight function was cpi = cpi-hat + b1 x Z, where cpi-hat is the value of cpi predicted from the D242, D2422 equation, Z is a random variable with a standard normal distribution, and b1 is a coefficient calculated to produce cpi with the same total variance as the original cpi values. The MTPRO mass at a specific weight is cpi-hat + RSD x Z, where the RSD is the residual standard deviation of the original equation and Z is a random variable with a standard normal distribution. Utilizing these relationships and a program that produces a distribution of the three predicted random effects (ci and m'i for live weight; cpi for protein to live weight function), a distribution of pigs can be produced to reflect the true variation in predicted compositional growth.

Several functions from a daily compositional growth model were utilized to predict daily lipid accretion and metabolizable energy intake (ME, Mcal): Total body lean mass (TBLEAN) = 6.8 (MTPRO).867, empty body weight (live weight minus gut fill) = 0.93 x on-farm live weight, and total body fat tissue mass (TBFAT) = empty body weight TBLEAN. Also TBFAT = a (empty body lipid mass)b where a and b are sex-population specific parameters. Thus, empty body lipid mass = (TBFAT/a)1/b. Daily ME intake (Mcal/day) is a function of maintenance plus the energy cost of protein and lipid accretion: MEI, Mcal/day = 0.255 (LW, kg).60 + (8.84 protein accretion, kg/d) + (11.4 lipid accretion, kg/d)

Prediction equations were developed for several common carcass backfat and muscle measurements. The predicted value of each carcass measurement was a function of carcass weight, fat-free lean or total carcass fat mass, sex, and lean of fat percentage plus Z * RSD, where Z is a value sampled from a standard normal distribution and RSD is the residual standard deviation of the prediction equation.

Results

The means, standard deviations and correlations of the serial live weights are shown in Table 1. The standard deviation in live weight increases with age and the serial correlation of serial live weights at the younger ages (49 to 70 days and 70 to 104 days) is lower than the correlations of the serial live weights after 153 days of age. The predicted standard deviation in carcass weight, fat-free lean mass, total carcass fat tissue mass, and all carcass measurements increase as the age at marketing increases (Table 2).

The stochastic model predicts a live weight growth curve for each individual pig. Also, each pig has an individual compositional growth curve including a predicted daily carcass fat-free lean and carcass fat tissue gain. For this reason, the stochastic model can be used to predict the live weight and carcass composition of groups of barrows and gilts marketed at different ages. The marketing strategy that maximizes the daily return for the grow-finish facility above daily feed costs can be identified. Stochastic models can be used to develop optimal sorting and marketing strategies and to evaluate the costs and returns of specific management decisions that effect variation.

Implications

This stochastic model can be used to develop marketing and Paylean use strategies that target specific mean and distribution of carcass composition end points. This stochastic model is a tool in which to refine vertically coordinated pork production systems.

Table 1. Predicted means, standard deviation and correlations of serial live weights

     

Correlations

Age

Mean, lb

SD

70

104

132

153

174

49

49.0

5.51

0.78

0.76

0.73

0.69

0.67

70

85.2

7.67

 

0.87

0.86

0.83

0.81

104

153.1

12.01

   

0.94

0.93

0.91

132

210.9

15.94

     

0.96

0.96

153

252.4

19.05

       

0.98

174

290.8

21.69

         

 

Table 2. Mean and standard deviations for live weight and carcass measurements at alternative marketing ages

Age

146 days

160 days

174 days

 

Mean

SD

Mean

SD

Mean

SD

Live weight, lb

238.9

18.1

265.6

19.8

290.6

21.7

Hot carcass wt, lb

179.4

15.1

202.0

16.7

223.4

18.3

Fat-free lean, lb

94.0

8.1

103.1

8.8

111.3

9.7

Total carcass fat, lb

54.4

8.5

62.4

10.4

70.8

12.1

Fat depth, 10th rib

0.82

0.11

0.88

0.13

0.94

0.15

10th Rib loin muscle area, in2

6.34

0.43

6.70

0.47

7.24

0.53

Optical probe fat depth, in

0.81

0.10

0.84

0.11

0.89

0.13

Optical probe muscle depth, in

2.06

0.12

2.13

0.12

2.20

0.13

Midline backfat last rib, in

0.93

0.16

1.00

0.17

1.06

0.18


Index of 2002 Purdue Swine Research Articles