A bivariate quantitative genetic model for a threshold trait and a survival traitLars Holm Damgaarda, b and Inge Riis Korsgaardb
a Department of Animal Science and Animal Health, 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 16 November 2005; accepted 2 June 2006; published online 28 November 2006)
Abstract - Many of the functional traits considered in animal breeding can be analyzed as threshold traits or survival traits with examples including disease traits, conformation scores, calving difficulty and longevity. In this paper we derive and implement a bivariate quantitative genetic model for a threshold character 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 in which model parameters were augmented with unobserved liabilities associated with the threshold trait. The fully conditional posterior distributions associated with parameters of the threshold trait reduced to well known distributions. For the survival trait the two baseline Weibull parameters were updated jointly by a Metropolis-Hastings step. The remaining model parameters with non-normalized fully conditional distributions were updated univariately using adaptive rejection sampling. The Gibbs sampler was tested in a simulation study and illustrated in a joint analysis of calving difficulty and longevity of dairy cattle. The simulation study showed that the estimated marginal posterior distributions covered well and placed high density to the true values used in the simulation of data. The data analysis of calving difficulty and longevity showed that genetic variation exists for both traits. The additive genetic correlation was moderately favorable with marginal posterior mean equal to 0.37 and 95% central posterior credibility interval ranging between 0.11 and 0.61. Therefore, this study suggests that selection for improving one of the two traits will be beneficial for the other trait as well.
Key words: bivariate genetic model / survival trait / ordered categorical trait / Bayesian analysis
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