Random regression models for analyses of longitudinal data in animal breeding

Animal breeding is concerned with the genetic improvement of farmed livestock. A central task is the estimation of genetic parameters or, equivalently, variance components, required to design selection programmes and in identification of genetically superior animals. Statistical techniques used rely heavily on linear, mixed models. Whilst some traits of interest are measured only once per animal, others are recorded repeatedly and may change, gradually and continually, as time progresses. Typical examples are test day records for dairy cows, with milk production at the beginning and end of lactation having quite different means and variances but high genetic correlations, and growth of meat-producing animals. Recently, so-called random regression (RR) models have become popular for the analysis of such data, as they allow complete ‘growth curves’ to be fitted within the linear, mixed model framework, correctly modelling changes in mean and dispersion with time, and are suitable for large scale applications. This paper reviews the use of RR models in analyses of data from livestock improvement schemes, concentrating on variance component estimation.