Genetic analyses of reproductive discrete traits in sheep using linear and nonlinear models

In sheep production, reproductive and fitness traits such as fertility, prolificacy and lamb survival are major factors influencing profitability. These traits present a discrete phenotypic expression. Statistical methods for estimation of genetic parameters for these traits taking into consideration their discrete nature have been proposed. In this study, linear and nonlinear models were used to estimate genetic parameters for reproductive and fitness traits, and the performance of these models was compared in terms of goodness of fit and predictive ability. Data from the Rambouillet flock at the University of Illinois-Urbana, and the Finnsheep flock at the Roman L. Hruska U.S. Meat Animal Research Center, Clay Center were utilized in this study.Fertility, litter size and ovulation rate were analyzed with linear and nonlinear sire, animal and ewe models. Nonlinear models included the threshold model for categorical data (fertility, survival), and Poisson and Negative Binomial models for count data (litter size, ovulation rate). Poisson and Negative Binomial models yielded non interpretable results due to problems with variance component estimation. Threshold sire models yielded heritability and repeatability estimates that were larger than those obtained with linear sire models. The greater the number of categories of response for a trait, the smaller the difference between estimates of genetic parameters obtained from different models. Animal models resulted in higher heritability and repeatability estimates than sire models.In terms of goodness of fit, nonlinear models did not show any significant advantage relative to linear models. Linear and threshold models yielded similar results, and both outperformed Poisson and Negative Binomial models for goodness of fit. Relative to predictive ability, differences between linear and nonlinear models were almost negligible. When permanent environmental effects were included in the models, measures of goodness of fit and predictive ability improved.Analyses of survival data from birth to weaning with linear and threshold models revealed that maternal effects were an important source of variation. Maternal effects were more important in the more prolific Finnsheep breed than in the less prolific Rambouillet breed. The high coefficient of variation, the positive correlation between direct and maternal effects and the greater magnitude of the heritabilities found with threshold models indicated that genetic improvement of lamb survival through selection is possible.Approximate and exact posterior distributions of parameters of a logistic model for survival were constructed using an asymptotic normal approximation and Monte Carlo integration with importance sampling, respectively. The asymptotic normal approximation yielded satisfactory results and is expected to be appropriate for inferences about fixed effects for the sample sizes frequently encountered in experimental animal breeding.