Nonlinear mixed models to study metabolizable energy utilization in broiler breeder hens

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 BW0.75, 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 EM1.12. 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.