Romero L F, Zuidhof M J, Renema R A, Robinson F E, Naeima A
Agricultural, Food and Nutritional Science, University of Alberta, Edmonton, Alberta, Canada, T6G 2P5.
Poult Sci. 2009 Jun;88(6):1310-20. doi: 10.3382/ps.2008-00102.
This study developed mathematical models to overcome limitations of linear models of energy partitioning in hens. The fit of 1 linear and 2 nonlinear models of ME intake (MEI) were compared, using empirical data of 288 caged broiler breeder hens from 20 to 60 wk of age. Pullets were individually caged at 16 wk and assigned to 1 of 4 feed allocation groups. Three groups had feed allocated on a group basis with divergent target BW: standard (STD), HIGH (STD x 1.1), and LOW (STD x 0.9). The fourth group had individual-based feed allocation (IND) and followed the STD BW target. The linear model expressed MEI as a function of BW(0.75), ADG, egg mass (EM), and temperature. Nonlinear mixed models employed a normally distributed term associated with hen metabolic BW, and exponential terms of ADG and EM, or Cobb-Douglas form interactions between terms. Fit was evaluated with the Bayesian information criterion and systematic bias was analyzed through linear regressions of observed versus expected values. The linear model estimated energy partitioned to maintenance and retention in the range of reported values in the literature. However, this model had the poorest fit (R(2) = 0.64) and exhibited a slope bias of 0.91 (i.e., MEI was overestimated at low values and underestimated at high values). The first nonlinear mixed model indicated that MEI partitioned to ADG was a factor of ADG(1.15), whereas the ME partitioned to EM was a factor of EM(1.12). This model had improved fit (R(2) = 0.71) relative to the linear model. The second nonlinear mixed model indicated that the energy requirement for ADG increased by 0.60% and the EM energy requirement decreased by 2.07% for each 1% increment in BW. This model further improved fit (R(2) = 0.75). Nonlinear mixed models reduced estimation bias by accounting for individual variation in maintenance energy expenditure. These nonlinear mixed models may be used to analyze energy partitioning in animals, to develop prediction equations of MEI, to evaluate individual efficiency for maintenance, and to assess diets regarding the slope of bias in coefficients of maintenance energy requirements.
本研究开发了数学模型，以克服母鸡能量分配线性模型的局限性。使用288只20至60周龄笼养肉种鸡的经验数据，比较了1个线性模型和2个非线性模型对代谢能摄入量（MEI）的拟合情况。小母鸡在16周龄时单独笼养，并分配到4个饲料分配组中的1组。三组按组分配饲料，目标体重不同：标准组（STD）、高组（STD×1.1）和低组（STD×0.9）。第四组采用个体饲料分配（IND），并遵循标准体重目标。线性模型将MEI表示为体重（0.75）、平均日增重（ADG）、蛋重（EM）和温度的函数。非线性混合模型采用与母鸡代谢体重相关的正态分布项，以及ADG和EM的指数项，或各项之间的柯布-道格拉斯形式相互作用。用贝叶斯信息准则评估拟合情况，并通过观察值与预期值的线性回归分析系统偏差。线性模型估计分配到维持和留存的能量在文献报道值范围内。然而，该模型的拟合度最差（R² = 0.64），斜率偏差为0.91（即，MEI在低值时被高估，在高值时被低估）。第一个非线性混合模型表明，分配到ADG的MEI是ADG（1.15）的一个因子，而分配到EM的ME是EM（1.12）的一个因子。相对于线性模型，该模型的拟合度有所提高（R² = 0.71）。第二个非线性混合模型表明，体重每增加1%，ADG的能量需求增加0.60%，EM的能量需求减少2.07%。该模型进一步提高了拟合度（R² = 0.75）。非线性混合模型通过考虑维持能量消耗的个体差异降低了估计偏差。这些非线性混合模型可用于分析动物的能量分配，开发MEI的预测方程，评估个体维持效率，以及评估关于维持能量需求系数偏差斜率的日粮。
