Different ways to model biological relationships between fertility and pH of the semen in rabbits

This work aimed to study the relationship between pH of the semen and fertility (Fert, defined as the success or failure of conception), which is of special interest because pH of the semen can be considered a global marker of the expression of some seminal quality traits. Different methods used to model the relationship between Fert and pH are presented here: 1) ignoring genetic and environmental correlations and including pH either as a covariate or as a cross-classified effect on fertility, 2) a bivariate mixed model, and 3) recursive bivariate mixed models. A total of 653 pH records and 6,365 Fert records after AI were used. Crossbreed does from 2 maternal lines were artificially inseminated with buck semen from a paternal line in a commercial environment. A negative, and almost linear, effect of pH on Fert was detected. The posterior median of pH and Fert heritabilities, and the highest posterior density interval at 95% (in parentheses) were approximately 0.18 (0.05, 0.29) and approximately 0.10 (0.02, 0.20) across all the models, respectively. Genetic correlations between traits were negative, but the highest posterior density interval at 95% included zero [i.e., -0.31 (-0.91, 0.33) in the bivariate mixed model and -0.17 (-0.99, 0.48) and -0.44 (-0.99, 0.10) in the recursive bivariate mixed models including pH as a covariate or as a cross-classified effect, respectively]. All models predicted Fert data reasonably well (i.e., 76 and 62% correct predictions for success and failure, respectively). No differences in the prediction of the EBV for male fertility were encountered between models, showing a good concordance in the animals ranked by their EBV (the correlation between EBV in all models was close to 1). Thus, no differences in results were obtained considering, or not considering, genetic and environmental correlations between pH and Fert and assuming, or not assuming, recursiveness between each trait. This is because the magnitude of the effect of pH on Fert was not large enough; therefore, the same results were obtained even though the models were of different complexity.