This work presents a model for the joint analysis of a binomial and a Gaussian trait using a recursive parametrization that leads to a computationally efficient implementation. The model is illustrated in an analysis of mortality and litter size in two breeds of Danish pigs, Landrace and Yorkshire. Available evidence suggests that mortality of piglets increased partly as a result of successful selection for total number of piglets born. In recent years there has been a need to decrease the incidence of mortality in pig-breeding programs. We report estimates of genetic variation at the level of the logit of the probability of mortality and quantify how it is affected by the size of the litter. Several models for mortality are considered and the best fits are obtained by postulating linear and cubic relationships between the logit of the probability of mortality and litter size, for Landrace and Yorkshire, respectively. An interpretation of how the presence of genetic variation affects the probability of mortality in the population is provided and we discuss and quantify the prospects of selecting for reduced mortality, without affecting litter size.
Keywords: Bayesian analysis; litter size; mortality; recursive model.