Comparison between linear and proportional hazard models for the analysis of age at first lambing in the Ripollesa breed

Abstract

Age at first lambing (AFL) plays a key role on the reproductive performance of sheep flocks, although there are no genetic selection programs accounting for this trait in the sheep industry. This could be due to the non-Gaussian distribution pattern of AFL data, which must be properly accounted for by the analytical model. In this manuscript, two different parameterizations were implemented to analyze AFL in the Ripollesa sheep breed, that is, the skew-Gaussian mixed linear model (sGML) and the piecewise Weibull proportional hazards model (PWPH). Data were available from 10 235 ewes born between 1972 and 2013 in 14 purebred Ripollesa flocks located in the north-east region of Spain. On average, ewes gave their first lambing short after their first year and a half of life (590.9 days), and within-flock averages ranged between 523.4 days and 696.6 days. Model fit was compared using the deviance information criterion (DIC; the smaller the DIC statistic, the better the model fit). Model sGML was clearly penalized (DIC = 200 059), whereas model PWPH provided smaller estimates and reached the minimum DIC when one cut point was added to the initial Weibull model (DIC = 132 545). The pure Weibull baseline and parameterizations with two or more cut points were discarded due to larger DIC estimates (>134 200). The only systematic effect influencing AFL was the season of birth, where summer-and fall-born ewes showed a remarkable shortening of their AFL, whereas neither birth type nor birth weight had a relevant impact on this reproductive trait. On the other hand, heritability on the original scale derived from model PWPH was high, with a model estimate place at 0.114 and its highest posterior density region ranging from 0.079 and 0.143. As conclusion, Gaussian-related mixed linear models should be avoided when analyzing AFL, whereas model PWPH must be viewed as better alternative with superior goodness of fit; moreover, the additive genetic background underlying this reproductive trait supports its inclusion into current genetic selection programs given its economic importance.

Genetic Parameters and Genetic Trends for Reproductive Traits of Santa Ines Sheep Kept in Extensive Environments in Brazil

“…In the present study was observed notorious phenotypic and permanent environment variation for all traits analyzed, which consequently affects the magnitude of the additive genetic component. Estimated ℎ 2 of AFL trait was 0.13 ± 0.10, which is in accordance to the findings of Casellas [16] in Ripollese sheep, using Bayesian inference (Piecewise Weibull Proportional Hazards models). Also, in a study by Ono [18], considering data from the same population studied in this research, but without including a permanent environment effect, obtained a moderate heritability (0.24 ± 0.05), also by a Bayesian approach.…”

“…Numerous studies on the estimation of genetic parameters for "local" breeds of sheep were performed considering reproductive traits related to prolificacy: litter size at birth, litter size at weaned, total litter weight at birth, total litter weight at weaned [6][7][8][9][10][11][12][13]; survivability at weaning age [14,15]; and for the age at first lambing [16].…”

Technical note: PaGELL v.1.5: A flexible parametric program for the Bayesian analysis of longevity data within the context of animal breeding

“…Survival analysis by proportional hazard models (Cox, 1972) must be viewed as an emerging statistical tool in the animal science framework with remarkable applications to several domestic species (Ducrocq et al, 1988a(Ducrocq et al, ,b, 2000Sánchez et al, 2006;Fernàndez de Sevilla et al, 2008) and economically relevant traits (Schneider et al, 2005;Zavadilová and Štípková, 2013;Casellas, 2016). The weight of functional characters such as survival or longevity in selection indexes has increased during recent decades (Serenius et al, 2006;Forabosco et al, 2009), given their close relation with culling costs (Stott, 1994;Horn et al, 2012) and society's concern for the well-being of domestic animals (Camm and Bowles, 2000).…”