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* Institute of Animal Breeding and Genetics, University of Göttingen, 37075 Göttingen, Germany
Department of Animal and Poultry Science, University of Guelph, Guelph, Canada N1G 2W1
Department of Animal Sciences, University of Wisconsin, Madison 53076
Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, N-1432 Ås, Norway
1 Corresponding author: skoenig2{at}gwdg.de
Relationships between claw disorders and test-day milk yield recorded in 2005 on 5,360 Holstein cows, kept on 11 large-scale dairy farms in eastern Germany, were analyzed in a Bayesian framework with standard linear and threshold models and recursive linear and threshold models. Four different claw disorders, digital dermatitis (DD), sole ulcer (SU), wall disorder (WD), and interdigital hyperplasia (IH), were scored as binary traits within 200 d after calving and analyzed separately. Incidences of disorders were 13.7% for DD, 16.5% for SU, 9.8% for WD, and 6.7% for IH. Heritabilities of disorders were greater when applying threshold or recursive threshold models than with linear or linear recursive models. Posterior means of genetic correlations between test-day milk production and claw disorders ranged from 0.17 to 0.44, suggesting that breeding strategies focusing on increased milk yield will increase incidences of disorders as a correlated response. A progressive path of lagged relationships was postulated for recursive models describing first the influence of test-day milk yield (MY1) on claw disorders and second, the effect of the disorder on milk production level at the following test day (MY2). In recursive models, structural coefficients describe recursive relationships at the phenotypic level. The structural coefficient 
21 was the gradient of disease (trait 2) with respect to MY1 (trait 1) for a model with a recursive effect of trait 1 on trait 2. The increase of disease incidence of the 4 different disorders per 1-kg increase of MY1 ranged from 21=0.006 to 21= 0.024 on the visible scale when applying recursive linear models, and from 21= 0.003 to 21= 0.016 on the underlying liability scale for recursive threshold models. The rate of change in MY2 (trait 3) with respect to the previous claw disorder is given by 32 for a model with a recursive effect from trait 2 to trait 3. Structural coefficients 32 ranged from –0.12 to –0.68 predicting that a 1-unit increase in the incidence of any disorder reduces milk yield at the following test day by up to 0.67 kg. Rank correlations between sire posterior means for the same claw disorders among different models were >0.84, but some changes in rank of sires in distinct top-10 lists were observed. Structural equation models are of increasing importance in genetic evaluations, and this study showed the possible application of recursive systems, even for categorical data.
Key Words: claw disorder • milk yield • recursive threshold model • Bayesian method
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