Evaluation of alternative nonlinear mixed effects models of duck growth

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Abstract
Two nonlinear growth functions were evaluated on 6 groups of 32 ducks. Ducks were randomly assigned to 1 of 6 dietary treatments and weighed weekly from 1 to 43 d of age. The Weibull function had the form: BW(it) = A - (A - B) exp - [(C - 1)/C] (t/IP)**C, where BW(it) is the BW of the ith duck at age t in days and A, B, C, and IP are fixed parameters. The variable A represents mature BW and the variable IP is the age (inflection point) at which maximum average daily gain is achieved. The addition of a single random effect to the Weibull growth function (ip), in which the age to reach the BW at the overall population inflection point of each duck varies, provided a substantially better fit than any other alternative fixed or mixed models. Overall, the Weibull function under-predicted the d-1 BW (46.7 vs. 55.1 g, P < 0.05) and over-predicted the d-8 BW (233.6 vs. 211.7 g, P < 0.05). The predicted BW from d 15 to 43 was very close to the actual mean BW at each age. This model predicts that the between-duck variance in BW increases with age and that the CV increases from 1 to 8 d of age, reaches a plateau from 15 to 22 d of age, and then slowly declines. This mixed effects model predicts the mean age and approximate variation in age that ducks require to reach a specific BW, and is easily adaptable to stochastic modeling.

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