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1 Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, N-1432 Ås, Norway
2 GENO Breeding and AI Association, N-1432 Ås, Norway
3 Department of Dairy Science, University of Wisconsin, Madison 53706
Corresponding author: I. M. Andersen-Ranberg; e-mail: ina.ranberg{at}umb.no.
A bivariate threshold-linear (TL) and a bivariate linear-linear (LL) model were assessed for the genetic analysis of 56-d nonreturn (NR56) and interval from calving to first insemination (CFI) in first-lactation Norwegian Red (former Norwegian Dairy Cattle) (NRF). Three different datasets were used to infer genetic parameters and to predict transmitting abilities for NRF sires. Mean progeny group sizes were 147.8, 102.7, and 56.5 daughters, and the corresponding number of sires were 746, 743, and 742 in the 3 datasets. Otherwise, the structures of the 3 datasets were similar. When the TL model was used, heritability of liability to NR56 was 2.8% in the 2 larger datasets and 3.8% in the smallest dataset. In the LL model, the heritability of NR56 in the largest dataset and in the 2 smaller datasets was 1.2 and 0.9%, respectively. For CFI, the heritability was similar in TL and LL models, ranging from 2.4 to 2.7%. The small heritability of the 2 reproductive traits implies that most of the variation is environmental and that large progeny groups are required to get accurate sire PTA. The point estimates of the genetic correlation between NR56 and CFI were near zero in both models. The 2 bivariate models were compared in terms of predictive ability using logistic regression and a 
2 statistic based on differences between observed and predicted outcomes for NR56 in a separate dataset. Comparison was also with respect to ranking of sires and correlations between sire posterior means (TL model) and PTA (LL model). We found very small differences in ability to predict NR56 between the 2 bivariate models, regardless of the dataset used. Correlations between sire posterior means (TL) and sire PTA (LL) and rank correlations between sire evaluations were all >0.98 in the 3 datasets. At present, the LL model is preferred for sire evaluations of NR56 and CFI in NRF. This is because the LL model is less computationally demanding and more robust with respect to the structure of the data than TL.
Key Words: female fertility • genetic parameter • model comparison • bivariate threshold model
Abbreviation key: CFI = interval from calving to first insemination, LL = linear-linear, MCMC = Markov chain Monte Carlo, NR56 = 56-d nonreturn rate, NRF = Norwegian Red, TL = threshold-linear.
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