Scope for a random regression model in genetic evaluation of beef cattle for growth

doi:10.1016/S0301-6226(03)00142-8

Livestock Production Science

Volume 86, Issues 1–3, March 2004, Pages 69-83

https://doi.org/10.1016/S0301-6226(03)00142-8 Get rights and content

Abstract

Potential improvement in accuracy of genetic evaluation of beef cattle for growth from replacing the current multi-trait (MT) model comprising birth, weaning, yearling and final weights as separate traits, with a random regression (RR) model analysis is examined by simulation. Maintaining the original data and pedigree structure for three beef cattle data sets, data were simulated assuming a cubic regression on polynomials of age for direct and maternal, genetic and permanent environmental effects and heterogeneous measurement error variances. Ages at weighing from birth to 730 days were considered. Data set I represented records from an experimental herd with monthly weighing of animals. Data sets II and III were field data, selecting a subset of herds in which at least 50% of animals had four or more weights recorded and records for all herds for a small breed, respectively. Simulated records were analysed fitting a MT model and RR models. Field data sets were expanded by adding a fictitious weight approximately 3 months after the original records. Accuracy of genetic evaluation was calculated as correlation between true and estimated values for each analysis. For the same subset of data, accuracies from a RR analysis were consistently higher than for a MT analysis, due to more appropriate modelling of variances and genetic parameters. Using all records available, RR accuracies for breeding value estimates for 200, 400 and 600 days in data set I were 0.023–0.034 or 4.3–5.9% higher than for MT. Corresponding gains were 3.1–3.6% for data set II and 1.5–1.7% for data set III. Expanding the field data sets by 100%, increased RR accuracies by 0.027–0.038 over those from MT analyses. While small in absolute terms, this was equivalent to a proportional increase of 5.7–8.3%. Results showed that substantial benefits could be obtained from the implementation of a RR model, if additional weight records were collected.

Introduction

Random regression (RR) models have become a popular choice for modelling of traits, which are measured repeatedly per individual, but change gradually and continually with time. Growth of animals is a typical example for such traits, and the ‘infinite-dimensional’ model, where covariances are modelled as functions of polynomials of age has been first been presented in this context (Kirkpatrick et al., 1990).

Applications in genetic evaluation schemes so far, however, have been limited to the analysis of test-day records for dairy cattle. Genetic merit for growth of meat producing animals is generally assessed treating records taken at different ages, or ranges of ages, as different traits. breedplan, the Australian genetic evaluation scheme for beef cattle (Johnston et al., 1999), for instance, distinguishes between birth, weaning, yearling, final and mature cow weights as separate traits, allowing ranges in age at recording of 200 days or more for weaning, yearling and final weights with some pre-adjustment for differences in age at recording. A RR model appears an obvious and preferable alternative, which would not only remove current limits on the number of records per animal which can be utilised and eliminate the need for age correction, but also provide estimates of genetic merit for any age at recording.

The current ‘standard’ multi-trait (MT) analysis employed in breedplan has been shown to model changes in growth over time quite well, and has facilitated considerable genetic improvement in growth of beef cattle (Farquharson et al., 2002). Whilst the RR model is clearly conceptually highly appealing, it is not certain how much can be gained by its adoption. There has been concern that use of a RR model might increase computational requirements over those of a MT model, as incidence and coefficient matrices are denser and the number of effects to be estimated might be increased. Nobre et al. (2002) reported that a RR model fitting a cubic regression on age at recording for all random effects required less memory and substantially less time than a MT analysis, assigning weights from birth to 2 years of age to eight separate traits.

Simple selection index calculations suggest that the gain in accuracy of genetic evaluation due to inclusion of additional records is small for animals, which have birth, weaning, yearling and final weight recorded. However, in most breeds under performance recording, the average number of records per animal is only about two. Moreover, such calculations ignore the fact that analyses are carried out within contemporary groups, which tend to be small, and the complex utilisation of information from a range of relatives in an animal model, mixed model analysis. Theoretical values can be obtained from the inverse of the coefficient matrix in the mixed model equation or an approximation thereof, but can be inappropriate in individual cases.

This paper presents a simulation study, attempting to quantify the potential increase in accuracy of genetic evaluation for beef cattle due to implementation of a RR model.

Section snippets

Simulation

Data were simulated assuming a RR model for three beef cattle data sets, maintaining the original data and pedigree structure while replacing the original observations by simulated values. Simulations assumed a cubic regression on Legendre polynomials of age at recording for direct genetic, maternal genetic, direct permanent environmental and maternal permanent environmental effects, and heterogeneous measurement error variances. Changes in the latter with age were modelled as a step function

Expected gain in accuracy

Phenotypic variances and genetic parameters resulting from the population values assumed for covariances between RR coefficients are given in Table 2 for ages in 100 day intervals. Values were estimates obtained for Hereford data (Meyer, 2002), resulting in direct heritabilities for weaning weight somewhat lower and the proportion of variance due to maternal permanent environmental effects (not shown) substantially higher than in most other breeds. Whilst genetic correlations assumed between

Discussion

Results show that there is substantial scope for a RR model to yield more accurate estimates of genetic merit for growth than the four trait, multivariate models. As with any simulation study, results are highly dependent on the assumptions made, both for the genetic parameters and variances, and the data and pedigree structure. The latter is clearly demonstrated by differences in results for the three data sets examined.

The RR model achieves somewhat higher accuracies than the MT model for

Conclusions

Accuracy of genetic evaluation for growth of beef cattle can be improved by replacing a four-trait model with a RR model. Benefits for the current data structure in commercial beef herds would arise mainly from more appropriate modelling of variances and genetic parameters and the elimination of age adjustments. However, if more records per animal were collected, considerable additional gains due to increased amounts of information utilised could be achieved.

Acknowledgements

This work was supported by grant BFGEN.002 of Meat and Livestock Australia Ltd (MLA).

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¹: AGBU is a joint venture of NSW Agriculture and the University of New England.

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