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Title: BAYESIAN ANALYSIS OF TWINNING AND OVULATION RATES USING A MULTIPLE-TRAIT THRESHOLD MODEL AND GIBBS SAMPLING

Author
item Van Tassell, Curtis - Curt
item Van Vleck, Lloyd
item Gregory, Keith

Submitted to: Journal of Animal Science
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 1/16/1998
Publication Date: N/A
Citation: N/A

Interpretive Summary: Gibbs sampling is a relatively new method for statistical analysis in animal genetics. Results necessary for implementation of Gibbs sampling for combined analysis of categorical and continuous data were derived. Programs previously available for analysis of continuous data using Gibbs sampling (Multiple-Trait Gibbs Sampler for Animal Models) were extended based on these results. The extended programs are available to researchers through the internet. 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. Results for models with and without genetic groups were compared. Estimates of heritability and fraction of variance accounted for by permanent environmental effects for models including (excluding) genetic groups were .128 and .103 (.169 and .078) for twinning and .168 and .079 (.190 and .065) for ovulation. Estimates of genetic correlation for models with (without) genetic groups was .808 (.786), and correlation of permanent environmental effects was .517 (.440). These results are the first ever obtained for multiple-trait categorical data analyzed with the appropriate threshold model, which results in more accurate genetic parameters and no need to use approximations when estimating genetic values. Genetic progress for the twinning herd will be improved using this more correct model because breeders will be better able to identify and select genetically superior animals.

Technical Abstract: 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: a value on the unobserved underlying normally distributed variable (liability) is generated in each iteration round for each categorical observation. The programs allow analysis of several continuous and ordered categorical traits with any number of response levels. The programs allow any number of fixed and random effects for categorical or continuous traits. Models can be different for each trait. Twinning and ovulation rates were analyzed for 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 a cow's lifetime and number of eggs ovulated for several estrous cycles before first breeding as heifers. A total of 6411 calvings was recorded for 2087 cows with 83.2% single and 16.8% multiple births; 19,849 ovulations were recorded for 2332 heifers with 85.2% single and 14.8% multiple ovulations. Results for models with and without genetic groups were compared. Mean posterior estimates of heritability and variance fraction accounted for by permanent environmental effects (PE) for models with (without) genetic groups were .128 and .103 (.169 and .078) for twinning and .168 and .079 (.190 and .065) for ovulation. Mean posterior estimate of genetic correlation for models with (without) genetic groups was .808 (.786); correlation of PE effects was .517 (.440). Use of a threshold model could allow 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.