A multivariate gametic model for the analysis of purebred and crossbred data. An example between two populations of Iberian pigs

Crossbreeding plays a pivotal role within pig breeding programmes, aiming to maximize heterosis and improve reproductive traits in crossbred maternal lines. Nevertheless, there is evidence indicating that the performance of reciprocal crosses between two genetic lines might exhibit variability. These variations in performance can be attributed to differences in the correlations between gametic effects, acting as either sire or dam, within purebred and crossbred populations. To address this issue, we propose a multivariate gametic model that incorporates up to four correlated gametic effects for each parental population. The model is employed on a data set comprising litter size data (total number of piglets born—TNB- and number of piglets born alive—NBA-) derived from a reciprocal cross involving two Iberian pig populations: Entrepelado and Retinto. The data set comprises 6933 records from 1564 purebred Entrepelado (EE) sows, 4995 records from 1015 Entrepelado × Retinto (ER) crosses, 2977 records from 756 Retinto × Entrepelado (RE) crosses and 7497 records from 1577 purebred Retinto (RR) sows. The data set is further supplemented by a pedigree encompassing 6007 individual-sire-dam entries. The statistical model also included the order of parity (with six levels), the breed of the service sire (five levels) and the herd-year-season effects (141 levels). Additionally, the model integrates random dominant and permanent environmental sow effects. The analysis employed a Bayesian approach, and the results revealed all the posterior estimates of the gametic correlations to be positive. The range of the posterior mean estimates of the correlations varied across different gametic effects and traits, with a range between 0.04 (gametic correlation between the paternal effects for purebred and the maternal for crossbred in Retinto) and 0.53 (gametic correlation between the paternal effects for purebred and the paternal for crossbred in Entrepelado). Furthermore, the posterior mean variance estimates of the maternal gametic effects were consistently surpassed those for paternal effects within all four populations. The results suggest the possible influence of imprinting effects on the genetic control of litter size, and underscore the importance of incorporating crossbred data into the breeding value predictions for purebred individuals.