Growth models describe body weight (BW) changes over time, allowing information from longitudinal measurements to be combined into a few parameters with biological interpretation. Nonlinear mixed models (NLMM) allow for the inclusion of random factors. Random factors can account for a relatively large subset of the total variance explained by bird-specific measurement correlation. The objectives of the current study were 1) to evaluate different nonlinear mixed models with and without inclusion of random coefficients to account for knowable individual sources of variation using birds from 2 heritage chicken lines: New Hampshire (NH) and Brown Leghorn (BL); 2) to obtain estimated values for random coefficients of growth parameters including growth rate and mature BW; 3) to investigate the effect of minor feed restriction on production efficiency.
A total of 32 birds (16 mixed sex birds from each strain) were raised to 17 wk of age. After 12 wk, half were continued on ad libitum (AL) feed intake, and half were pair-fed, using a precision feeding system; they were given 95% of the AL intake of a paired bird closest in BW. Residual feed intake (RFI) of birds, as an indicator of production efficiency, was increased in pair-fed BL birds as a result of minor feed restriction. Growth data of the birds were fit to a mixed Gompertz model with a variety of different bird-specific random coefficients. The model had the form: BW=Wm×exp−exp−b(t−tinf); where Wm was the mature BW, b was the rate of maturing, t was age (d), tinf was the inflection point (d). This fixed-effects model was compared with NLMM using model evaluation criteria to evaluate relative model suitability. Random coefficients, Wmu ~ N(0,VWm) and bu ~ N(0,Vb), were tested separately and together and their differences, for strains, sex, and feeding treatments, were reported as different where P ≤ 0.05.
Inclusion of random effects accounted for bird-specific variation in Wm and b resulted in reduced bias (systemic error) in prediction of individual BW through increasing the homogeneity of residual variation. Residual feed intake (RFI) of birds, as an indicator of production efficiency, was increased in pair-fed Brown Leghorn birds (BL) as a result of minor feed restriction. The RFI was decreased with age for all groups, that is, the birds became more efficient as age advanced. Growth data of the birds were fit to a mixed Gompertz model with a variety of different bird-specific random coefficients. The model with both random coefficients was determined to be the most parsimonious model, based on an assessment of serial correlation of the residuals. NLMM coefficients allow stochastic prediction of the mean age and its variation that birds need to achieve a certain BW, allowing for unique new decision support modeling applications; these could be used in stochastic modeling to evaluate the economic impact of management decisions.
In this study, a nonlinear mixed-effects growth model was developed for growth data of NH and BL birds. The growth model with 2 random parameters for Wm and b was found to be the most parsimonious model based on fit statistics, and further analysis showed that it reduced autocorrelation bias in longitudinal growth data. The mixed-effects model provided an estimation of random coefficients for growth parameters of different subsets of the population. Mature BW (Wm) and rate of maturing (b) could be used in genetic selection programs. These random coefficients could be used as a tool in different scenarios of poultry production system such as stochastic prediction of BW of individuals at any age to better match nutrient supply to nutrient requirements, and to predict and evaluate the economic impact of management decisions on designing target growth curves, breeding programs, and nutritional management decisions.
Growth models describe body weight (BW) changes over time, allowing information from longitudinal measurements to be combined into a few parameters with biological interpretation. Nonlinear mixed models (NLMM) allow for the inclusion of random factors. Random factors can account for a relatively large subset of the total variance explained by bird-specific measurement correlation. The aim of this study was to evaluate different NLMM using birds from 2 heritage chicken lines; New Hampshire (NH) and Brown Leghorn (BL). A total of 32 birds (16 mixed sex birds from each strain) were raised to 17 wk of age. After 12 wk, half were continued on ad libitum (AL) feed intake, and half were pair-fed, using a precision feeding system; they were given 95% of the AL intake of a paired bird closest in BW. Residual feed intake (RFI) of birds, as an indicator of production efficiency, was increased in pair-fed BL birds as a result of minor feed restriction. Growth data of the birds were fit to a mixed Gompertz model with a variety of different bird-specific random coefficients. The model had the form: BW=Wm×exp−exp−b(t−tinf); where Wm was the mature BW, b was the rate of maturing, t was age (d), tinf was the inflection point (d). This fixed-effects model was compared with NLMM using model evaluation criteria to evaluate relative model suitability. Random coefficients, Wmu ∼ N(0,VWm) and bu ∼ N(0,Vb), were tested separately and together and their differences, for strains, sex, and feeding treatments, were reported as different where P ≤ 0.05. The model with both random coefficients was determined to be the most parsimonious model, based on an assessment of serial correlation of the residuals. NLMM coefficients allow stochastic prediction of the mean age and its variation that birds need to achieve a certain BW, allowing for unique new decision support modeling applications; these could be used in stochastic modeling to evaluate the economic impact of management decisions.
