The objective of the present study was to assess the predictive ability of subsets of single nucleotide polymorphism (SNP) markers for development of low-cost, low-density genotyping assays in dairy cattle. Dense SNP genotypes of 4,703 Holstein bulls were provided by the USDA Agricultural Research Service. A subset of 3,305 bulls born from 1952 to 1998 was used to fit various models (training set), and a subset of 1,398 bulls born from 1999 to 2002 was used to evaluate their predictive ability (testing set). After editing, data included genotypes for 32,518 SNP and August 2003 and April 2008 predicted transmitting abilities (PTA) for lifetime net merit (LNM$), the latter resulting from progeny testing. The Bayesian least absolute shrinkage and selection operator method was used to regress August 2003 PTA on marker covariates in the training set to arrive at estimates of marker effects and direct genomic PTA. The coefficient of determination (R(2)) from regressing the April 2008 progeny test PTA of bulls in the testing set on their August 2003 direct genomic PTA was 0.375. Subsets of 300, 500, 750, 1,000, 1,250, 1,500, and 2,000 SNP were created by choosing equally spaced and highly ranked SNP, with the latter based on the absolute value of their estimated effects obtained from the training set. The SNP effects were re-estimated from the training set for each subset of SNP, and the 2008 progeny test PTA of bulls in the testing set were regressed on corresponding direct genomic PTA. The R(2) values for subsets of 300, 500, 750, 1,000, 1,250, 1,500, and 2,000 SNP with largest effects (evenly spaced SNP) were 0.184 (0.064), 0.236 (0.111), 0.269 (0.190), 0.289 (0.179), 0.307 (0.228), 0.313 (0.268), and 0.322 (0.291), respectively. These results indicate that a low-density assay comprising selected SNP could be a cost-effective alternative for selection decisions and that significant gains in predictive ability may be achieved by increasing the number of SNP allocated to such an assay from 300 or fewer to 1,000 or more.

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 lambda21 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 lambda21 = 0.006 to lambda21 = 0.024 on the visible scale when applying recursive linear models, and from lambda21 = 0.003 to lambda21 = 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 lambda32 for a model with a recursive effect from trait 2 to trait 3. Structural coefficients lambda32 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.

Predictive ability of models for litter size in swine on the basis of different sources of genetic information was investigated. Data represented average litter size on 2598, 1604 and 1897 60K genotyped sows from two purebred and one crossbred line, respectively. The average correlation (r) between observed and predicted phenotypes in a 10-fold cross-validation was used to assess predictive ability. Models were: pedigree-based mixed-effects model (PED), Bayesian ridge regression (BRR), Bayesian LASSO (BL), genomic BLUP (GBLUP), reproducing kernel Hilbert spaces regression (RKHS), Bayesian regularized neural networks (BRNN) and radial basis function neural networks (RBFNN). BRR and BL used the marker matrix or its principal component scores matrix (UD) as covariates; RKHS employed a Gaussian kernel with additive codes for markers whereas neural networks employed the additive genomic relationship matrix (G) or UD as inputs. The non-parametric models (RKHS, BRNN, RNFNN) gave similar predictions to the parametric counterparts (average r ranged from 0.15 to 0.23); most of the genome-based models outperformed PED (r 5 0.16). Predictive abilities of linear models and RKHS were similar over lines, but BRNN varied markedly, giving the best prediction (r 5 0.31) when G was used in crossbreds, but the worst (r 5 0.02) when the G matrix was used in one of the purebred lines. The r values for RBFNN ranged from 0.16 to 0.23. Predictive ability was better in crossbreds (0.26) than in purebreds (0.15 to 0.22). This may be related to family structure in the purebred lines.

Health and fertility are complex traits, and the phenotype for one trait may affect the phenotype of one or more other traits. For instance, disease in early lactation may impair a cow's ability to show estrus and to conceive after insemination. The objectives of the present study were to explore phenotypic and genetic relationships among health and fertility traits in Norwegian Red cows using a recursive effects model, which allows disentangling causal effects of phenotypes from the genetic and environmental correlations among traits. Records of interval from calving to first insemination (CFI), nonreturn rate within 56 d after first insemination (NR56), clinical mastitis (CM), ketosis (KET), and retained placenta from 55,568 first-lactation daughters of 1,577 Norwegian Red sires were analyzed. Trivariate recursive Gaussian-threshold models were used to analyze the 2 fertility traits (CFI and NR56) together with 1 disease trait in each analysis. The estimated structural coefficients of the recursive models imply that presence of KET or retained placenta lengthened CFI, whereas causal effects from CM to fertility were negligible. Recursive effects of disease on NR56, and of CFI on NR56, were all close to zero. Genetic correlations between health and fertility traits were low or moderate. The strongest genetic correlation was between KET and CFI (0.29), whereas genetic correlations between CM and NR56 and between CFI and NR56 were nil. In general, selection against disease is expected to slightly improve fertility (shorter CFI and higher NR56) as a correlated response and vice versa. The present results suggest that the use of structural-equation models, such as the one used here, may enhance our understanding of complex relationships among traits.

Paratuberculosis (Johne's disease) is an infectious enteric disease in dairy cattle and other species that causes substantial economic loss worldwide. In this study, two recursive Gaussian-threshold models were employed in order to infer the effects of Johne's disease on milk yield, fat yield, and protein yield while simultaneously estimating genetic parameters (i.e. heritability and genetic correlation) in an Israeli Holstein population. Disease diagnosis was based on ELISA serum antibody tests. Data were available for 4694 daughters of 361 sires; 3.5% were positive; and 1.6% were suspect for the disease test. Disease status was coded either as a binary character (negative vs. positive) or as an ordered categorical trait (negative, suspect, and positive) in the two recursive models and as a binary trait in a linear model. Among sires with ≥ 50 daughters, predicted probability of Mycobacterium avium ssp. paratuberculosis (MAP) infection in future daughters ranged from <1% to 16.5%. Heritability estimates for Johne's disease were near 0.15, confirming a genetic contribution to disease susceptibility. Genetic correlation estimates for Johne's disease with the three yield traits were 0.15-0.22. Residual correlations for Johne's disease with the yield traits were between -0.01 and -0.10. For the linear regression model, yield losses associated with a positive disease diagnosis during 305 days of lactation were 300 kg milk and around 10 kg for fat and protein. Yield loss estimates from the recursive models were 25-50% less than linear model estimates. Recursive modeling has theoretical advantages over linear models for these phenotypes, but the estimated genetic parameters in this study did not differ significantly between the two types of models.