Evaluation of Different Mixed Model Nonlinear Functions on Pigs Fed Low-Nutrient Excretion Diets1

Professional Animal Scientist, Oct 2006 by Schinckel, A P, Pence, S, Einstein, M E, Hinson, R, Et al

Abstract

Three nonlinear growth functions were evaluated on barrows (n=108) and gilts (n=105) fed diets designed to reduce nitrogen and phosphorous excretion. The pigs were weighed at birth and at approximate 14-d intervals from 62 to 147 d of age and then weekly to 190 d of age. Mixed models including pig specific random effects were evaluated for the Bridges, Weibull, and generalized Michaelis-Menten (GMM) functions. Two pig specific random effects were included in each function-one for predicted mature BW and one variable associated with the age at which maximum ADG was achieved. Alternative analyses were completed in which a random effect for a third parameter was predicted as a linear function of the random effect for mature BW. The alternative analyses resulted in improved likelihood statistics and smaller standard errors for the between-pig variance in mature BW. The 3 functions provided similar likelihood statistics, residual standard deviations, predicted BW, and predicted mean age (140 d for barrows and 134 d of age for gilts) and mean BW (83 kg for barrows and 73 kg for gilts) at which maximum ADG was achieved. The Weibull and Bridges functions predicted that 3 barrows and 6 gilts had mature BW of less than 130 kg. The GMM function allowed for more gradual growth to 50% greater mature BW than the Weibull and Bridges functions. The GMM equation allows for nonsymmetric sigmoidal growth and in some cases may provide a better fit to the BW data of pigs.

Key words: mixed effects model, nonlinear growth functions, pig 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). Mixed model nonlinear analysis software has been made available that accounts for the underlying variance-covariance 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) that can be used to develop optimal marketing strategies. Pigs reared under commercial conditions have lesser ADG than pigs reared under more ideal highhealth conditions (Hoick et al., 1998; Schinckel et al., 2002). Pigs reared under commercial conditions have greater variation in BW than pigs reared under more ideal health conditions and have substantially greater variation in age required to achieve target market BW (Schinckel and Craig, 2002). The ongoing implementation of nutrient management regulations has increased the use of swine diets that reduce the excretion of N and P. The objective of this study was to evaluate the use of alternative mixed model analyses to parameterize and model the BW growth of pigs reared under commercial conditions and fed diets formulated to reduce P and N excretion.

Materials and Methods

The 216 pigs, 108 barrows, and 108 gilts used in the trial were farrowed at the Purdue University research farm and weighed at birth. The pigs were produced by mating Hampshire-Duroc sires to Yorkshire-Landrace females. The pigs were transferred to an environmentally-controlled grow-finish facility that had been completely emptied and cleaned. Pigs were phase-fed a series of diets formulated to reduce daily nutrient excretion of N and P and included synthetic amino acids and phytase. Pigs were allotted based on BW into pens of 4 gilts or 4 barrows with 1.1 m^sup 2^ per pig. The pigs started test with a mean age of 64.2 d (SD = 1.8) and a mean BW of 21.65 kg (SD = 3.2 kg). The first grower diet was fed from 1 to 4 wk. The first low-nutrient excretion diet contained 15.4% CP, 1.05% Lys, 0.60% Ca, 0.34% total P, 0.23% available P, 0.075% phytase premix (600 PU/g), and 3.39 Meal ME. The second grower diet, fed from 5 to 8 wk, contained 0.95% Lys, 13.7% CP, 0.32% total P, 0.21% available P, 0.075% phytase premix, and 3.43 Meal ME/kg. The first finisher diet, fed from 9 to 12 wk, contained 12.7% CP, 0.85% Lys, 0.50% Ca, 0.31% total P, 0.21% available P, 0.075% phytase premix, and 3.48 Meal ME/kg. The second finisher diet was a conventional corn-soybean meal diet, which contained 11.5% CP, 0.60% Lys, 0.50% Ca, 0.40% total P, 0.16% available P, and 0.05% phytase premix, was fed from 13 to 18 wk.

Pigs were weighed at approximately 14-d intervals for 12 wk and then weekly for an additional 6 wk (Table 1). The protocol for this trial was approved by the Purdue University Animal Care and Use Committee.

In this function, any combination of C, M', or WF could be considered random. For example, the model with all 3 random effects can be expressed as WT^sub i,t^ = (WF wf^sub i^){1 - exp [-exp(M' m'^sub i^) t^sup (C c^sub i^^]} e^sub i,t^. where wf^sub i^, m^sub i^ and c^sub i^ would be each pig's random effects assumed to be multivariate normal with mean σ^sub c^^sup 2^ and variances σ^sub wf^^sup 2^, σ^sub m'^^sup 2^, and σ^sub c^^sup 2^, respectively. Additionally, the random effects of each pig may be correlated (Schinckel and Craig, 2002). The e^sub i,t^ are independent, normal with mean O and variance σ^sup 2^^sub e^ and assumed independent of the random effects.