Bayesian analysis of twinning and ovulation rates using a multiple-trait threshold model and Gibbs sampling.

The Multiple-Trait Gibbs Sampler for Animal Models programs were extended to allow analysis of ordered categorical data using a Bayesian threshold model. The algorithm is based on data augmentation, where a value on the unobserved underlying normally distributed variable (liability) is generated in each round of iteration for each categorical observation. The programs allow analysis of several continuous and ordered categorical traits. Categorical traits can have any number of response levels. Models can be different for each trait. The programs were used to analyze twinning and ovulation rates from a herd of cattle selected for twinning rate at the U.S. Meat Animal Research Center. Data included number of calves born at each parturition for the lifetime of a cow and number of eggs ovulated for several estrous cycles before first breeding as heifers. A total of 6,411 calvings was recorded for 2,087 cows with 83.2% single and 16.8% multiple births. A total of 19,849 ovulations was recorded for 2,332 heifers with 85.2% single and 14.8% multiple ovulations. Mean posterior estimates of heritability and fraction of variance accounted for by permanent environmental effects (PE) were .128 and .103 for twinning rate and .168 and .079 for ovulation rate. Mean posterior estimate of genetic correlation was .808, and correlation of PE effects was .517. Use of a threshold model could allow for more rapid genetic improvement of the twinning herd through improved identification and selection of genetically superior animals because of higher heritability on the underlying scale.