Title:
Comparison of linear, skewed-linear, and proportional hazard models for the analysis of lambing interval in Ripollesa ewes.

Abstract:
Lambing interval is a relevant reproductive indicator for sheep populations under continuous mating systems, although there is a shortage of selection programs accounting for this trait in the sheep industry. Both the historical assumption of small genetic background and its unorthodox distribution pattern have limited its implementation as a breeding objective. In this manuscript, statistical performances of 3 alternative parametrizations [i.e., symmetric Gaussian mixed linear (GML) model, skew-Gaussian mixed linear (SGML) model, and piecewise Weibull proportional hazard (PWPH) model] have been compared to elucidate the preferred methodology to handle lambing interval data. More specifically, flock-by-flock analyses were performed on 31,986 lambing interval records (257.3 ± 0.2 d) from 6 purebred Ripollesa flocks. Model performances were compared in terms of deviance information criterion (DIC) and Bayes factor (BF). For all flocks, PWPH models were clearly preferred; they generated a reduction of 1,900 or more DIC units and provided BF estimates larger than 100 (i.e., PWPH models against linear models). These differences were reduced when comparing PWPH models with different number of change points for the baseline hazard function. In 4 flocks, only 2 change points were required to minimize the DIC, whereas 4 and 6 change points were needed for the 2 remaining flocks. These differences demonstrated a remarkable degree of heterogeneity across sheep flocks that must be properly accounted for in genetic evaluation models to avoid statistical biases and suboptimal genetic trends. Within this context, all 6 Ripollesa flocks revealed substantial genetic background for lambing interval with heritabilities ranging between 0.13 and 0.19. This study provides the first evidence of the suitability of PWPH models for lambing interval analysis, clearly discarding previous parametrizations focused on mixed linear models.