Improving a nonlinear Gompertz growth model using bird-specific random coefficients in two heritage chicken lines

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: B W = W m × e x p − e x p − b ( t − t i n f ) ; 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.