Product versus additive model for studying artificial insemination results in several livestock populations

Two models can be used for studying binary results of AI. The additive threshold model proposes an underlying variable as summing the environmental and genetic effects from the 2 individuals involved in the mating, and the product threshold model assumes that the conditional probability of AI success is the product of the probabilities of success of 2 unobserved binary phenotypes (one is the male fertility; the other is the female fertility). The purpose of this paper is to compare the predictive ability of the product and the additive threshold models for studying AI results and to compare results obtained with the 2 models in 3 different species: cattle, sheep, and rabbits. Results showed that the predictive ability of the product model is similar to the additive model in sheep and rabbits but worst in cattle (percentage of wrong prediction = 42, 27, and 35% in the additive model; 43, 28, and 47% in the product model in sheep, rabbits, and cattle, respectively). Even when the 2 models have similar performance, they differed in their EBV (for instance, Pearson correlation between EBV predicted with the 2 models = 0.46 in sheep for male fertility). The product model can determine which sex is responsible for an AI failure. In sheep, the female was the responsible in 94% of the cases and male in 2% of them; in rabbits, the female was the responsible in 54% of the cases and the male in 39% of them. Different estimates of probabilities for male and female fertility success obtained with the product model in the 3 species suggest that male and female fertilities behave differently depending on the species and the uniqueness of the data sets. Although product model seems to provide additional information in the fertility process, further research is needed to understand the worst performance of the product model in cattle.