Use of structured antedependence models for the genetic analysis of growth curves.

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Abstract
Growth curve analysis is an important issue for many agricultural and laboratory species, for both phenotypic and genetic studies. The aim of this paper is to present the use of a novel statistical approach, namely the structured antedependence (SAD) models, to deal with this issue. The basic idea of these models is that an observation at time t can be explained by the previous observations. These models are especially appropriate to deal with cumulative traits such as growth, as BW at age t clearly depends on BW measures at ages (t –1), (t –2), etc. These models were applied on an INRA experimental Charolais herd data set. The data comprised BW records for 560 cows born over an 11-yr period (from 1988 to 1998) from 60 sires and 369 dams. The proposed SAD models were compared with the well-known random regression (RR) models that are already widely used in various areas of longitudinal data analysis. It was found that the SAD models fit the growth process better with far fewer parameters than the RR models (9 instead of 16 covariance parameters for the phenotypic analysis, and 14 instead of 21 for the genetic analysis). Despite this smaller number of covariance parameters, the likelihood value was found to be much higher with the SAD vs. the RR models, with a difference of 262.9 for the phenotypic analysis with a quartic polynomial for the RR and 751.5 for the genetic analysis with a cubic polynomial for both the genetic and environmental parts of the RR model. The SAD models also proved to be better able to interpolate missing values. Heritability, genetic, and environmental correlation coefficients were estimated for weights from birth to adulthood. The structured antedependence models proved, in this study, to be very appropriate to model growth data in a parsimonious and flexible way.