To allow easy comparison with other studies, herd-year variances and permanent environmental variances were not included in the phenotypic variance but are provided in Additional file 1: Tables S1 and S2.
The repeatability of a trait was calculated as the sum of the additive and permanent environmental variance divided by the phenotypic variance.
Estimates of maternal permanent environmental variance as a proportion of phenotypic variance were 0.19, 0.08 and 0.09 for BW, WW and ADG, respectively.
Moreover, and represent prior values for the maternal permanent environmental variance and the white-noise error variance, respectively.
Finally, it remains to specify the full conditional posterior distribution of the maternal permanent environmental variance.
The permanent environmental variance also increased slightly between July and October (Fig. 6, green lines).
σ h 2 and σ p 2 are the herd and maternal permanent environmental variances.
For comparison with other reports, heritability was also estimated using a repeatability model in which the genetic and permanent environmental variances were assumed to be constant over ages.
As in models of phenotypic covariances, residual variances for singly measured traits (AFR and L) were fixed to zero, allowing estimation of the covariance between residual and nongenetic permanent environment variances of single- and repeated-measures traits, respectively.
A "plausible" prior assuming weak genetic control (additive genetic variance, permanent environmental variance and residual variance accounting for 0.2, 0.1 and 0.7) was used with the smallest possible degree of belief parameter (n = 1).
It should be noted to allow for identifiability, mod(3) (and, for the same reason, mod(4) to mod(7)) considered no litter effect for observations on single-reared lambs; i.e. σ l 1 2 = 0. Mod(4) assumed that both the maternal permanent effect and residual variance depended on the number of lambs reared.
