A cross-specific multiplicative binomial recursive model for the analysis of perinatal mortality in a diallel cross among three varieties of Iberian pig

Abstract

Perinatal piglet mortality is an important factor in pig production from economic and animal welfare perspectives; however, the statistical analysis of mortality is difficult because of its categorical nature. Recent studies have suggested that a binomial model for the survival of each specific piglet with a logit approach is appropriate and that recursive relationships between traits are useful for taking into account non-genetic relationships with other traits. In this study, the recursive binomial model is expanded in two directions: (1) the recursive phenotypic dependence among traits is allowed to vary among groups of individuals or crosses, and (2) the binomial distribution is replaced by the multiplicative binomial distribution to account for over or underdispersion. In this study, five recursive multiplicative binomial models were used to obtain estimates of the Dickerson crossbreeding parameters in a diallel cross among three varieties of Iberian pigs [Entrepelado (EE), Torbiscal (TT), and Retinto (RR)]. Records (10,255) from 2110 sows were distributed as follows: EE (433 records, 100 sows), ER (2336, 527), ET (942, 177), RE (806, 196), RR (870, 175), RT (2450, 488), TE (193, 36), TR (1993, 359), and TT (232, 68). Average litter size [Total Number Born (TNB)] and number of stillborns (SB) were 8.46 ± 2.27 and 0.25 ± 0.72, respectively. The overdispersion was evident with all models. The model with the best fit included a linear recursive relationship between TNB and the logit of [Formula: see text] of the multiplicative binomial distribution, and it implies that piglet mortality increases with litter size. Estimates of direct effects showed small differences among populations. The analysis of maternal effects indicated that the dams whose mothers were EE had a larger SB, while dams with RR mothers reduced the probability of born dead. The posterior estimates of heterosis suggested a reduction in SB when the sow is crosbred. The multiplicative binomial distribution provides a useful alternative to the binomial distribution when there is overdispersion in the data. Recursive models can be used for modeling non-genetic relationships between traits, even if the phenotypic dependency between traits varies among environments or groups of individuals. Piglet perinatal mortality increased with TNB and is reduced by maternal heterosis.

Figure 1

Probability density of the multiplicative binomial distribution for the probability of the Bernoulli events of 0.50 (a) and 0.25 (b) with values of the θ parameter of 0.90, 1.00, and 1.10.

Figure 2

Posterior mean (and Highest Posterior Density at 95%) estimates of the deviation of the cross effects (EE—Entrepelado, ER—Entrepelado-Retinto-, ET—Entrepelado-Torbiscal-, RE—Retinto-Entrepelado-, RR—Retinto, RT—Retinto-Torbiscal-, TE—Torbiscal-Entrepelado-, TR—Torbiscal-Retinto and TT—Torbiscal) with respect to their average (a) and of the direct line (L_E, L_R, and L_T), maternal (M_E, M_R and M_T), and heterosis (H_ER, H_ET, H_RT) effects of the Dickerson model (b) for total number born (TNB) under model II.

Figure 3

Posterior mean (and highest posterior density at 95%) estimates of the deviation of the cross effects (EE—Entrepelado, ER—Entrepelado-Retinto-, ET—Entrepelado-Torbiscal-, RE—Retinto-Entrepelado-, RR—Retinto, RT—Retinto-Torbiscal-, TE—Torbiscal-Entrepelado-, TR—Torbiscal-Retinto and TT—Torbiscal) with respect to their average (a) and of the direct line (L_E, L_R, and L_T), maternal (M_E, M_R and M_T), and heterosis (H_ER, H_ET, H_RT) effects of the Dickerson model (b) for the logit of the Φ parameter of the multiplicative binomial distribution under model II.