Breeding value accuracy estimates for growth traits using random regression and multi-trait models in Nelore cattle

Comparison between multiple-trait and random regression models for genetic evaluation of weight traits in Australian meat sheep

Random regression (RR) models are recommended as an alternative to multiple-trait (MT) models for better capturing the variance-covariance structure over a trajectory and hence more accurate genetic evaluation of traits that are repeatedly measured and genetically change gradually over time. However, a limited number of studies have been done to empirically compare RR over a MT model to determine how much extra benefit could be achieved from one method over another. We compared the prediction accuracy of RR and MT models for growth traits of Australian meat sheep measured from 60 to 525 d, using 102,579 weight records from 24,872 animals. Variance components and estimated breeding values (EBVs) estimated at specific ages were compared and validated with forward prediction. The accuracy of EBVs obtained from the MT model was 0.58, 0.51, 0.54, and 0.56 for weaning, postweaning, yearling, and hogget weight stages, respectively. RR model produced accuracy estimates of 0.56, 0.51, 0.54, and 0.54 for equivalent weight stages. Regression of adjusted phenotype on EBVs was very similar between the MT and the RR models (P > 0.05). Although the RR model did not significantly increase the accuracy of predicting future progeny performance, there are other benefits of the model such as no limit to the number of records per animal, estimation of EBVs for early and late growth, no need for age correction. Therefore, RR can be considered a more flexible method for the genetic evaluation of Australian sheep for early and late growth, and no need for age correction.

Invited review: Advances and applications of random regression models: From quantitative genetics to genomics

An important goal in animal breeding is to improve longitudinal traits; that is, traits recorded multiple times during an individual's lifetime or physiological cycle. Longitudinal traits were first genetically evaluated based on accumulated phenotypic expression, phenotypic expression at specific time points, or repeatability models. Until now, the genetic evaluation of longitudinal traits has mainly focused on using random regression models (RRM). Random regression models enable fitting random genetic and environmental effects over time, which results in higher accuracy of estimated breeding values compared with other statistical approaches. In addition, RRM provide insights about temporal variation of biological processes and the physiological implications underlying the studied traits. Despite the fact that genomic information has substantially contributed to increase the rates of genetic progress for a variety of economically important traits in several livestock species, less attention has been given to longitudinal traits in recent years. However, including genomic information to evaluate longitudinal traits using RRM is a feasible alternative to yield more accurate selection and culling decisions, because selection of young animals may be based on the complete pattern of the production curve with higher accuracy compared with the use of traditional parent average (i.e., without genomic information). Moreover, RRM can be used to estimate SNP effects over time in genome-wide association studies. Thus, by analyzing marker associations over time, regions with higher effects at specific points in time are more likely to be identified. Despite the advances in applications of RRM in genetic evaluations, more research is needed to successfully combine RRM and genomic information. Future research should provide a better understanding of the temporal variation of biological processes and their physiological implications underlying the longitudinal traits.

Genetic structured antedependence and random regression models applied to the longitudinal feed conversion ratio in growing Large White pigs

The objective of the present study was to compare a random regression model, usually used in genetic analyses of longitudinal data, with the structured antedependence (SAD) model to study the longitudinal feed conversion ratio (FCR) in growing Large White pigs and to propose criteria for animal selection when used for genetic evaluation. The study was based on data from 11,790 weekly FCR measures collected on 1,186 Large White male growing pigs. Random regression (RR) using orthogonal polynomial Legendre and SAD models was used to estimate genetic parameters and predict FCR-based EBV for each of the 10 wk of the test. The results demonstrated that the best SAD model (1 order of antedependence of degree 2 and a polynomial of degree 2 for the innovation variance for the genetic and permanent environmental effects, i.e., 12 parameters) provided a better fit for the data than RR with a quadratic function for the genetic and permanent environmental effects (13 parameters), with Bayesian information criteria values of -10,060 and -9,838, respectively. Heritabilities with the SAD model were higher than those of RR over the first 7 wk of the test. Genetic correlations between weeks were higher than 0.68 for short intervals between weeks and decreased to 0.08 for the SAD model and -0.39 for RR for the longest intervals. These differences in genetic parameters showed that, contrary to the RR approach, the SAD model does not suffer from border effect problems and can handle genetic correlations that tend to 0. Summarized breeding values were proposed for each approach as linear combinations of the individual weekly EBV weighted by the coefficients of the first or second eigenvector computed from the genetic covariance matrix of the additive genetic effects. These summarized breeding values isolated EBV trajectories over time, capturing either the average general value or the slope of the trajectory. Finally, applying the SAD model over a reduced period of time suggested that similar selection choices would result from the use of the records from the first 8 wk of the test. To conclude, the SAD model performed well for the genetic evaluation of longitudinal phenotypes.