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A multilevel nonlinear mixed-effects approach to model growth in pigs

A. B. Strathe^*, A. Danfær^*, H. Sørensen and E. Kebreab

^* Section of Nutrition, Department of Basic Animal and Veterinary Sciences, Faculty of Life Sciences, University of Copenhagen, DK-1870, Frederiksberg, Denmark , Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen Ø, Denmark Department of Animal Science, University of California, Davis 95616

ekebreab{at}ucdavis.edu

Abstract

Growth functions have been used to predict market weight of pigs and maximize return over feed costs. This study was undertaken to compare 4 growth functions and methods of analyzing data, particularly 1 that considers nonlinear repeated measures. Data were collected from an experiment with 40 pigs maintained from birth to maturity and their weight measured weekly or biweekly up to 1,007 d. Gompertz, Logistic, Bridges and Lopez functions were fitted to the data and compared using information criteria. For each function, a multilevel nonlinear mixed effects model was employed because it allowed for estimation of all growth profiles simultaneously and different sources of variation (i.e., gender, pig and litter effects) were incorporated directly into the parameters. Furthermore, variance in-homogeneity and within-pig correlation were introduced to the functions. Inclusion of a variance of power function and a continuous autoregressive process of first order rendered a substantially improved fit to data for all 4 growth functions. The Lopez function provided the best fit to the data set and was used for characterizing mean growth curves for the 3 genders (barrows, boars and gilts). It was estimated that the maximum growth rate occurs at 117, 134 and 96 kg BW for barrows, boars and gilts, respectively. Hence, the gilts reached their maximum growth rate at earlier stage in life compared to boars. Mature size of pigs varied systematically with gender and it was estimated to be 466, 537 and 382 kg BW for the barrows, boars and gilts, respectively. These estimates are significantly affected by the duration of the experimental period and it is recommended that future studies looking at estimating the mature size in animals are conducted long enough so that the BW visually stabilizes. Furthermore, studies should consider adding continuous autoregressive process when analyzing nonlinear mixed models with repeated measures.

Key Words: growth • multilevel mixed effect model • sigmoidal functions