Genetic variation of lactation curves in dairy sheep: quadratic function versus Wood’s model

Abstract

Daily milk yield records (1752) of 451 first-lactation ewes in four flocks from Nebraska and Wisconsin were analyzed. Most ewes did not have test-day records prior to day 30, and milk yield was recorded more frequently in the second half of lactation. Objectives were to investigate genetic variation of features of lactation curves using a quadratic function (Q), and to compare this with non-linear Wood’s model (W). A three-stage Bayesian hierarchical model was used. At stage 1 of Q, the function y= a+ bt+ ct 2+ e represented within-ewe variation, where t is time. The stage 2 model described variation in a, b and c between ewes. It had a linear structure with flock-year, age at lambing, type of lambing, length of suckling period and percentage of East Friesian origin genes as fixed effects, and additive genetic effects as random. Stage 3 had prior distributions for all unknowns. A chain of 70,000 iterations (burn-in=12,000) was generated using Gibbs sampling. Posterior means of the residual variance were 0.0234 kg 2 for Q and 0.042 kg 2 for W. Heritabilities of a, b and c in Q were 0.23, 0.15 and 0.17, respectively. Genetic correlations between parameters in Q ranged between −0.51 and −0.36. Q had an R 2=0.92, higher than the 0.74 found for W. The log-Bayes factor for Q relative to W was 11.64, strongly favoring the quadratic model. Using three residual standard deviations as cut-off, the percentages of outliers were 0.2 and 0.4% for the Q and W models, respectively. Both models fitted well, but Q failed to predict total milk yield accurately. Although model W is more appealing than Q, because its parameters have a mechanistic interpretation, it was not well supported by the data.