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A Bayesian analysis with a threshold model was performed for fertility defined as a binary trait (1 = successful mating, 0 = unsuccessful mating) in two populations of rabbits of different reproductive potential and different genetic origin: Line P selected for litter size and Line C selected for growth rate. There were 20,793 records of natural mating (86.2% successful) in Line C between 1983 and 2003, and 17,548 records (80.5% successful) in Line P, between 1992 and 2003. Data related to 5,388 and 3,848 females and 1,021 and 685 males in Lines C and P, respectively. The pedigree included 6,409 and 4,533 individuals in Lines C and P, respectively. The binary response was modeled under a probit approach. The model for the latent variable included male and female additive genetic effects, male and female permanent environmental effects, and the year-season and physiological status of the female …