Genet. Sel. Evol. 38 (2006) 45-64
DOI: 10.1051/gse:200502

A bivariate quantitative genetic model for a linear Gaussian trait and a survival trait

Lars Holm Damgaard^{a, b} and Inge Riis Korsgaard<sup>b

a</sup>  Department of Large Animal Sciences, Royal Veterinary and Agricultural University, Grønnegårdsvej 2, 1870 Frederiksberg C, Denmark
^b  Department of Genetics and Biotechnology, Danish Institute of Agricultural Sciences, P.O. Box 50, 8830 Tjele, Denmark

(Received 20 April 2005; accepted 16 September 2005 ; published online 21 December 2005)

Abstract - With the increasing use of survival models in animal breeding to address the genetic aspects of mainly longevity of livestock but also disease traits, the need for methods to infer genetic correlations and to do multivariate evaluations of survival traits and other types of traits has become increasingly important. In this study we derived and implemented a bivariate quantitative genetic model for a linear Gaussian and a survival trait that are genetically and environmentally correlated. For the survival trait, we considered the Weibull log-normal animal frailty model. A Bayesian approach using Gibbs sampling was adopted. Model parameters were inferred from their marginal posterior distributions. The required fully conditional posterior distributions were derived and issues on implementation are discussed. The two Weibull baseline parameters were updated jointly using a Metropolis-Hasting step. The remaining model parameters with non-normalized fully conditional distributions were updated univariately using adaptive rejection sampling. Simulation results showed that the estimated marginal posterior distributions covered well and placed high density to the true parameter values used in the simulation of data. In conclusion, the proposed method allows inferring additive genetic and environmental correlations, and doing multivariate genetic evaluation of a linear Gaussian trait and a survival trait.

Key words: survival / Gaussian / bivariate / genetic / Bayesian

Correspondence and reprints: lars.damgaard@agrsci.dk

© INRA, EDP Sciences 2005