Prediction of fatty acid composition using milk spectral data and its associations with various mid-infrared spectral regions in Michigan Holsteins.

Fatty acid composition in milk is not only reflective of nutritional quality but also potentially predictive of other attributes (e. g. including the cow's energy balance and its relative output of methane emissions). Furthermore, a higher ratio of long-chain to short-chain fatty acids or mean carbon number has been associated with negative energy balance in dairy cows, whereas enhanced nutritional properties have been generally associated with higher levels of unsaturation. We set out to directly compare Bayesian regression strategies with partial least squares for the prediction of various milk fatty acids using Fourier-transform infrared spectrum data on 777 milk samples taken from 579 cows on 4 Michigan dairy herds between 5 and 90 d in milk. We also set out to identify those spectral regions that might be associated with fatty acids and whether carbon number or level of unsaturation might contribute to the strength of these associations. These associations were based on adaptively clustered windows of wavenumbers to mitigate the distorting effects of severe multicollinearity on marginal associations involving individual wavenumbers. In general, Bayesian regression methods, particularly the variable selection method BayesB, outperformed partial least squares regression for cross-validation prediction accuracy for both individual fatty acids and fatty acid groups. Strong signals for wavenumber associations using BayesB were well distributed throughout the mid-infrared spectrum, particularly between 910 and 3,998 cm-1. Carbon number appeared to be linearly related to strength of wavenumber associations for 38 moderately to highly predicted fatty acids within the spectral regions of 2,286 to 2,376 and 2,984 to 3,100 cm-1, whereas nonlinear associations were determined within 1,141 to 1,205; 1,570 to 1,630; and 1,727 to 1,768 cm-1. However, no such associations were detected with level of unsaturation. Spectral regions where there were significant relationships between strength of association and carbon number may be useful targets for inferring the relative proportion of long-chain to short-chain fatty acids, and hence energy balance.

Association between days open and milk spectral data in dairy cows.

Data on 19,489 Brown Swiss cows reared in northeastern Italy were used to associate absorbances of individual wavenumbers within the mid-infrared range with days open (DO). Different postcalving days in milk (DIM) intervals were studied to determine the most informative milk sampling periods for predicting DO. Milk samples were analyzed using a MilkoScan (Foss Electric, Hillerød, Denmark) Fourier-transform infrared (FTIR) spectrometer for 1,060 wavenumbers (wn) ranging from 5,011 to 925 cm-1. To determine DO, we considered an insemination to lead to conception when there was no return of heat (i.e., no successive insemination) and the cow had a subsequent calving date whereby gestation length was required to be within ±30 d of 290 d. Only milk records within the first 90 DIM were considered. Associations were inferred by (1) fitting linear regression models between the DO and each individual wavenumber or milk component, and (2) fitting a Bayesian regression model that included the complete FTIR spectral data. The effects of including systematic effects (parity number, year-season, herd) in the model on these associations were also studied. These analyses were performed for the complete data (5-90 DIM) and for data stratified by DIM period (5 to 30, 31 to 60, and 61 to 90 DIM). Overall, regions of wavenumbers of the milk FTIR spectra that were associated with DO included wn 2,973 to 2,830 cm-1 [related to fat-B (C-H stretch)], wn 2,217 to 1,769 cm-1 [related to fat-A (C = O stretch)], wn 1,546 cm-1 (related to protein), wn 1,465 cm-1 (related to urea and fat), wn 1,399 to 1,245 cm-1 (related to acetone), and wn 1,110 cm-1 (related to lactose). Estimated effects depended on the DIM period, with milk samples drawn during DIM intervals 31 to 60 d and 61 to 90 d being most strongly associated with DO. These DIM intervals are also typically most associated with negative energy balance and peak lactation.

Genetic parameters for fertility traits assessed in herds divergent in milk energy output in Holstein-Friesian, Brown Swiss, and Simmental cattle.

In this study, we aimed to investigate differences in the genetics of fertility traits (heritability of traits and correlations between traits in divergent environments) in dairy cows of different production levels defined on the basis of the herd-average daily milk energy output (herd-dMEO). Data were obtained from Holstein-Friesian (n = 37,359 for fertility traits, 381,334 for dMEO), Brown Swiss (n = 79,638 for fertility traits, 665,697 for dMEO), and Simmental cows (n = 63,048 for fertility traits, 448,445 for dMEO) reared in northeastern Italy. Fertility traits under study were interval from calving to first service, interval from first service to conception, days open, calving interval, calving rate, and nonreturn rate at d 56. We classified herds into low and high productivity based on the herd-average dMEO (inferred using mixed effects models). We estimated genetic parameters using Bayesian bivariate animal models, where expressions of a phenotype in the low and high dMEO herds were taken as being different-albeit correlated-traits. Fertility traits were more favorable in Simmental than in Holstein-Friesian cows, whereas for all traits, Holstein-Friesian had the highest estimates of intraherd heritability [ranging from 0.021 (0.006-0.038) to 0.126 (0.10-0.15)] and Simmental the lowest [ranging from 0.008 (0.001-0.017) to 0.101 (0.08-0.12)]. The genetic correlations between fertility traits and dMEO were moderate and unfavorable, ranging, in absolute values, from 0.527 (0.37-0.68) to 0.619 (0.50-0.73) in Holstein-Friesian; from 0.339 (0.20-0.47) to 0.556 (0.45-0.66) in Brown Swiss; and from 0.340 (0.10-0.60) to 0.475 (0.33-0.61) in Simmental cattle. The only exception was the nonreturn rate at d 56, which had weak genetic correlations with dMEO in all 3 breeds. The herd correlations between fertility and dMEO tended to be modest and favorable and the residual correlations modest and variable. The heritability of fertility traits tended to be greater in the low dMEO than in the high dMEO herds in the case of the Holstein-Friesians, but not in the case of the Brown Swiss or Simmentals. The additive genetic correlations between fertility traits in the low and high dMEO herds were always lower than 1 [0.329 (-0.17 to 0.85) to 0.934 (0.86 to 0.99)] for all traits considered in all breeds. The correlation was particularly low for the threshold characters and the interval from first service to conception in Holstein-Friesian, suggesting that the relative performances of genotypes vary significantly between herds of different dMEO levels. Although there was large variability in the estimates, results might support making separate genetic evaluations of fertility in the different herd production groups. Our results also indicate that Simmental, a dual-purpose breed, has higher fertility and lower environmental sensitivity than Holstein-Friesian, with Brown Swiss being intermediate.

A landscape of the heritability of Fourier-transform infrared spectral wavelengths of milk samples by parity and lactation stage in Holstein cows.

Fourier-transform near- and mid-infrared (FTIR) milk spectral data are routinely collected in many countries worldwide. Establishing an optimal strategy to use spectral data in genetic evaluations requires knowledge of the heritabilities of individual FTIR wavelength absorbances. Previous FTIR heritability estimates have been based on relatively small sample sizes and have not considered the possibility that heritability may vary across parities and stages of the lactation. We used data from ∼370,000 test-day records of Canadian Holstein cows to produce a landscape of the heritability of FTIR spectra, 1,060 wavelengths in the near- and mid-infrared spectrum (5,011-925 cm-1), by parity and month of the lactation (mo 1 to 3 and mo 1 to 6, respectively). The 2 regions of the spectrum associated with absorption of electromagnetic energy by water molecules were estimated to have very high phenotypic variances, very low heritabilities, and very low proportion of variance explained by herd-year-season (HYS) subclasses. The near- or short-wavelength infrared (SWIR: 5,066-3,672 cm-1) region was also characterized by low heritability estimates, whereas the estimated proportion of the variance explained by HYS was high. The mid-wavelength infrared region (MWIR: 3,000-2,500 cm-1) and the transition between mid and long-wavelength infrared region (MWIR-LWIR: 1,500-925 cm-1) harbor several waves characterized by moderately high (≥0.4) heritabilities. Most of the high-heritability regions contained wavelengths that are reported to be associated with important milk metabolites and components. Interestingly, these 2 same regions tended to show more variability in heritabilities between parity and lactation stage. Second parity showed heritability patterns that were distinctly different from those of the first and third parities, whereas the first 2 mo of the lactation had clearly distinct heritability patterns compared with mo 3 to 6.

Genomic variance estimates: With or without disequilibrium covariances?

Whole-genome regression methods are often used for estimating genomic heritability: the proportion of phenotypic variance that can be explained by regression on marker genotypes. Recently, there has been an intensive debate on whether and how to account for the contribution of linkage disequilibrium (LD) to genomic variance. Here, we investigate two different methods for genomic variance estimation that differ in their ability to account for LD. By analysing flowering time in a data set on 1,057 fully sequenced Arabidopsis lines with strong evidence for diversifying selection, we observed a large contribution of covariances between quantitative trait loci (QTL) to the genomic variance. The classical estimate of genomic variance that ignores covariances underestimated the genomic variance in the data. The second method accounts for LD explicitly and leads to genomic variance estimates that when added to error variance estimates match the sample variance of phenotypes. This method also allows estimating the covariance between sets of markers when partitioning the genome into subunits. Large covariance estimates between the five Arabidopsis chromosomes indicated that the population structure in the data led to strong LD also between physically unlinked QTL. By consecutively removing population structure from the phenotypic variance using principal component analysis, we show how population structure affects the magnitude of LD contribution and the genomic variance estimates obtained with the two methods.

Genotype by environment (climate) interaction improves genomic prediction for production traits in US Holstein cattle.

Genotype by environment interaction (G × E) in dairy cattle productive traits has been shown to exist, but current genetic evaluation methods do not take this component into account. As several environmental descriptors (e.g., climate, farming system) are known to vary within the United States, not accounting for the G × E could lead to reranking of bulls and loss in genetic gain. Using test-day records on milk yield, somatic cell score, fat, and protein percentage from all over the United States, we computed within herd-year-season daughter yield deviations for 1,087 Holstein bulls and regressed them on genetic and environmental information to estimate variance components and to assess prediction accuracy. Genomic information was obtained from a 50k SNP marker panel. Environmental effect inputs included herd (160 levels), geographical region (7 levels), geographical location (2 variables), climate information (7 variables), and management conditions of the herds (16 total variables divided in 4 subgroups). For each set of environmental descriptors, environmental, genomic, and G × E components were sequentially fitted. Variance components estimates confirmed the presence of G × E on milk yield, with its effect being larger than main genetic effect and the environmental effect for some models. Conversely, G × E was moderate for somatic cell score and small for milk composition. Genotype by environment interaction, when included, partially eroded the genomic effect (as compared with the models where G × E was not included), suggesting that the genomic variance could at least in part be attributed to G × E not appropriately accounted for. Model predictive ability was assessed using 3 cross-validation schemes (new bulls, incomplete progeny test, and new environmental conditions), and performance was compared with a reference model including only the main genomic effect. In each scenario, at least 1 of the models including G × E was able to perform better than the reference model, although it was not possible to find the overall best-performing model that included the same set of environmental descriptors. In general, the methodology used is promising in accounting for G × E in genomic predictions, but challenges exist in identifying a unique set of covariates capable of describing the entire variety of environments.

Use of genotype × environment interaction model to accommodate genetic heterogeneity for residual feed intake, dry matter intake, net energy in milk, and metabolic body weight in dairy cattle.

Feed efficiency in dairy cattle has gained much attention recently. Due to the cost-prohibitive measurement of individual feed intakes, combining data from multiple countries is often necessary to ensure an adequate reference population. It may then be essential to model genetic heterogeneity when making inferences about feed efficiency or selecting efficient cattle using genomic information. In this study, we constructed a marker × environment interaction model that decomposed marker effects into main effects and interaction components that were specific to each environment. We compared environment-specific variance component estimates and prediction accuracies from the interaction model analyses, an across-environment analyses ignoring population stratification, and a within-environment analyses using an international feed efficiency data set. Phenotypes included residual feed intake, dry matter intake, net energy in milk, and metabolic body weight from 3,656 cows measured in 3 broadly defined environments: North America (NAM), the Netherlands (NLD), and Scotland (SAC). Genotypic data included 57,574 single nucleotide polymorphisms per animal. The interaction model gave the highest prediction accuracy for metabolic body weight, which had the largest estimated heritabilities ranging from 0.37 to 0.55. The within-environment model performed the best when predicting residual feed intake, which had the lowest estimated heritabilities ranging from 0.13 to 0.41. For traits (dry matter intake and net energy in milk) with intermediate estimated heritabilities (0.21 to 0.50 and 0.17 to 0.53, respectively), performance of the 3 models was comparable. Genomic correlations between environments also were computed using variance component estimates from the interaction model. Averaged across all traits, genomic correlations were highest between NAM and NLD, and lowest between NAM and SAC. In conclusion, the interaction model provided a novel way to evaluate traits measured in multiple environments in which genetic heterogeneity may exist. This model allowed estimation of environment-specific parameters and provided genomic predictions that approached or exceeded the accuracy of competing within- or across-environment models.

The 'heritability' of domestication and its functional partitioning in the pig.

We propose to estimate the proportion of variance explained by regression on genome-wide markers (or genomic heritability) when wild/domestic status is considered the phenotype of interest. This approach differs from the standard Fst in that it can accommodate genetic similarity between individuals in a general form. We apply this strategy to complete genome data from 47 wild and domestic pigs from Asia and Europe. When we partitioned the total genomic variance into components associated to subsets of single nucleotide polymorphisms (SNPs) defined in terms of their annotation, we found that potentially deleterious non-synonymous mutations (9566 SNPs) explained as much genetic variance as the whole set of 25 million SNPs. This suggests that domestication may have affected protein sequence to a larger extent than regulatory or other kinds of mutations. A pathway-guided analysis revealed ovarian steroidogenesis and leptin signaling as highly relevant in domestication. The genomic regression approach proposed in this study revealed molecular processes not apparent through typical differentiation statistics. We propose that at least some of these processes are likely new discoveries because domestication is a dynamic process of genetic selection, which may not be completely characterized by a static metric like Fst. Nevertheless, and despite some particularly influential mutation types or pathways, our analyses tend to rule out a simplistic genetic basis for the domestication process: neither a single pathway nor a unique set of SNPs can explain the process as a whole.

Bayesian regression models outperform partial least squares methods for predicting milk components and technological properties using infrared spectral data.

The aim of this study was to assess the performance of Bayesian models commonly used for genomic selection to predict "difficult-to-predict" dairy traits, such as milk fatty acid (FA) expressed as percentage of total fatty acids, and technological properties, such as fresh cheese yield and protein recovery, using Fourier-transform infrared (FTIR) spectral data. Our main hypothesis was that Bayesian models that can estimate shrinkage and perform variable selection may improve our ability to predict FA traits and technological traits above and beyond what can be achieved using the current calibration models (e.g., partial least squares, PLS). To this end, we assessed a series of Bayesian methods and compared their prediction performance with that of PLS. The comparison between models was done using the same sets of data (i.e., same samples, same variability, same spectral treatment) for each trait. Data consisted of 1,264 individual milk samples collected from Brown Swiss cows for which gas chromatographic FA composition, milk coagulation properties, and cheese-yield traits were available. For each sample, 2 spectra in the infrared region from 5,011 to 925 cm(-1) were available and averaged before data analysis. Three Bayesian models: Bayesian ridge regression (Bayes RR), Bayes A, and Bayes B, and 2 reference models: PLS and modified PLS (MPLS) procedures, were used to calibrate equations for each of the traits. The Bayesian models used were implemented in the R package BGLR (http://cran.r-project.org/web/packages/BGLR/index.html), whereas the PLS and MPLS were those implemented in the WinISI II software (Infrasoft International LLC, State College, PA). Prediction accuracy was estimated for each trait and model using 25 replicates of a training-testing validation procedure. Compared with PLS, which is currently the most widely used calibration method, MPLS and the 3 Bayesian methods showed significantly greater prediction accuracy. Accuracy increased in moving from calibration to external validation methods, and in moving from PLS and MPLS to Bayesian methods, particularly Bayes A and Bayes B. The maximum R(2) value of validation was obtained with Bayes B and Bayes A. For the FA, C10:0 (% of each FA on total FA basis) had the highest R(2) (0.75, achieved with Bayes A and Bayes B), and among the technological traits, fresh cheese yield R(2) of 0.82 (achieved with Bayes B). These 2 methods have proven to be useful instruments in shrinking and selecting very informative wavelengths and inferring the structure and functions of the analyzed traits. We conclude that Bayesian models are powerful tools for deriving calibration equations, and, importantly, these equations can be easily developed using existing open-source software. As part of our study, we provide scripts based on the open source R software BGLR, which can be used to train customized prediction equations for other traits or populations.

Obesity and mortality: are the risks declining? Evidence from multiple prospective studies in the United States.

We evaluated whether the obesity-associated years of life lost (YLL) have decreased over calendar time. We implemented a meta-analysis including only studies with two or more serial body mass index (BMI) assessments at different calendar years. For each BMI category (normal weight: BMI 18.5 to <25 [reference]; overweight: BMI 25 to <30; grade 1 obesity: BMI 30 to <35; and grade 2-3 obesity: BMI ≥ 35), we estimated the YLL change between 1970 and 1990. Because of low sample sizes for African-American, results are reported on Caucasian. Among men aged ≤60 years YLL for grade 1 obesity increased by 0.72 years (P < 0.001) and by 1.02 years (P = 0.01) for grade 2-3 obesity. For men aged >60, YLL for grade 1 obesity decreased by 1.02 years (P < 0.001) and increased by 0.63 years for grade 2-3 obesity (P = 0.63). Among women aged ≤60, YLL for grade 1 obesity decreased by 4.21 years (P < 0.001) and by 4.97 years (P < 0.001) for grade 2-3 obesity. In women aged >60, YLL for grade 1 obesity decreased by 3.98 years (P < 0.001) and by 2.64 years (P = 0.001) for grade 2-3 obesity. Grade 1 obesity's association with decreased longevity has reduced for older Caucasian men. For Caucasian women, there is evidence of a decline in the obesity YLL association across all ages.

Genome-enabled prediction of genetic values using radial basis function neural networks.

The availability of high density panels of molecular markers has prompted the adoption of genomic selection (GS) methods in animal and plant breeding. In GS, parametric, semi-parametric and non-parametric regressions models are used for predicting quantitative traits. This article shows how to use neural networks with radial basis functions (RBFs) for prediction with dense molecular markers. We illustrate the use of the linear Bayesian LASSO regression model and of two non-linear regression models, reproducing kernel Hilbert spaces (RKHS) regression and radial basis function neural networks (RBFNN) on simulated data and real maize lines genotyped with 55,000 markers and evaluated for several trait-environment combinations. The empirical results of this study indicated that the three models showed similar overall prediction accuracy, with a slight and consistent superiority of RKHS and RBFNN over the additive Bayesian LASSO model. Results from the simulated data indicate that RKHS and RBFNN models captured epistatic effects; however, adding non-signal (redundant) predictors (interaction between markers) can adversely affect the predictive accuracy of the non-linear regression models.

Assessment of Poisson, probit and linear models for genetic analysis of presence and number of black spots in Corriedale sheep.

Black skin spots are associated with pigmented fibres in wool, an important quality fault. Our objective was to assess alternative models for genetic analysis of presence (BINBS) and number (NUMBS) of black spots in Corriedale sheep. During 2002-08, 5624 records from 2839 animals in two flocks, aged 1 through 6 years, were taken at shearing. Four models were considered: linear and probit for BINBS and linear and Poisson for NUMBS. All models included flock-year and age as fixed effects and animal and permanent environmental as random effects. Models were fitted to the whole data set and were also compared based on their predictive ability in cross-validation. Estimates of heritability ranged from 0.154 to 0.230 for BINBS and 0.269 to 0.474 for NUMBS. For BINBS, the probit model fitted slightly better to the data than the linear model. Predictions of random effects from these models were highly correlated, and both models exhibited similar predictive ability. For NUMBS, the Poisson model, with a residual term to account for overdispersion, performed better than the linear model in goodness of fit and predictive ability. Predictions of random effects from the Poisson model were more strongly correlated with those from BINBS models than those from the linear model. Overall, the use of probit or linear models for BINBS and of a Poisson model with a residual for NUMBS seems a reasonable choice for genetic selection purposes in Corriedale sheep.

Predictive ability of subsets of single nucleotide polymorphisms with and without parent average in US Holsteins.

Genome-enabled prediction of breeding values using high-density panels (HDP) can be highly accurate, even for young sires. However, the cost of the assay may limit its use to elite animals only. Low-density panels (LDP) containing a subset of single nucleotide polymorphisms (SNP) may give reasonably accurate predictions and could be used cost-effectively with young males and females. This study evaluates strategies for selecting subsets of SNP for several traits, compares predictive ability of LDP with that of HDP, and assesses the benefits of including parent average (PA) as a predictor in models using LDP. Data consisting of progeny-test predicted transmitting ability (PTA) for net merit and 6 other traits of economic interest from 4,783 Holstein sires were evaluated using testing and training sets with regressions on their high-density genotypes and parent averages for net merit index. Additionally, SNP subsets of different sizes were selected using different strategies, including the "best" SNP based on the absolute values of their estimated effects from HDP models for either the trait itself or lifetime net merit, and evenly spaced (ES) SNP across the genome. Overall, HDP models had the best predictive ability, setting an upper bound for the predictive ability of LDP sets. Low-density panels targeting the SNP with strongest effects (for either a single trait or lifetime net merit) provided reasonably accurate predictions and generally outperformed predictions based on evenly spaced SNP. For example, evenly spaced sets would require at least 5,000 to 7,500 SNP to reach 95% of the predictive ability provided by HDP. On the other hand, this level of predictive ability can be achieved with sets of 2,000 SNP when SNP are selected based on magnitude of estimated effects for the trait. Accuracy of predictions based on LDP can be improved markedly by including parent average as a fixed effect in the model; for example, a set with the 1,000 best SNP using the parent average achieved the 95% of the accuracy of a HDP model.

Accuracy of direct genomic values derived from imputed single nucleotide polymorphism genotypes in Jersey cattle.

The objective of the present study was to evaluate the predictive ability of direct genomic values for economically important dairy traits when genotypes at some single nucleotide polymorphism (SNP) loci were imputed rather than measured directly. Genotypic data consisted of 42,552 SNP genotypes for each of 1,762 Jersey sires. Phenotypic data consisted of predicted transmitting abilities (PTA) for milk yield, protein percentage, and daughter pregnancy rate from May 2006 for 1,446 sires in the training set and from April 2009 for 316 sires in the testing set. The SNP effects were estimated using the Bayesian least absolute selection and shrinkage operator (LASSO) method with data of sires in the training set, and direct genomic values (DGV) for sires in the testing set were computed by multiplying these estimates by corresponding genotype dosages for sires in the testing set. The mean correlation across traits between DGV (before progeny testing) and PTA (after progeny testing) for sires in the testing set was 70.6% when all 42,552 SNP genotypes were used. When genotypes for 93.1, 96.6, 98.3, or 99.1% of loci were masked and subsequently imputed in the testing set, mean correlations across traits between DGV and PTA were 68.5, 64.8, 54.8, or 43.5%, respectively. When genotypes were also masked and imputed for a random 50% of sires in the training set, mean correlations across traits between DGV and PTA were 65.7, 63.2, 53.9, or 49.5%, respectively. Results of this study indicate that if a suitable reference population with high-density genotypes is available, a low-density chip comprising 3,000 equally spaced SNP may provide approximately 95% of the predictive ability observed with the BovineSNP50 Beadchip (Illumina Inc., San Diego, CA) in Jersey cattle. However, if fewer than 1,500 SNP are genotyped, the accuracy of DGV may be limited by errors in the imputed genotypes of selection candidates.

The relevance of purebred information for predicting genetic merit of survival at birth of crossbred piglets.

The objective of this study was to infer (co)variance components for piglet survival at birth in purebred and crossbred pigs. Data were from 13,643 (1,213 litters) crossbred and 30,919 (3,162 litters) purebred pigs, produced by mating the same 168 purebred boars to 460 Large White-derived crossbred females and 1,413 purebred sows, respectively. The outcome variable was piglet survival at birth as a binary trait. A Bayesian bivariate threshold model was implemented via Gibbs sampling. Flat priors were assigned to the effects of sex, parity of the dam, litter size, and year-month of birth. Gaussian priors were assigned to litter, dam, and sire effects. Marginal posterior means (SD) of the sire and dam variances for liability of piglet survival in purebred were 0.018 (0.008) and 0.077 (0.020), respectively. For crossbred, sire and dam variance estimates were 0.030 (0.018) and 0.120 (0.034), respectively. The posterior means (SD) of the heritability of liability of survival in purebred and crossbred and of the genetic correlation between these traits were 0.049 (0.023), 0.091 (0.054), and 0.248 (0.336), respectively. The greatest 95% confidence region (-0.406, 0.821) for the genetic correlation between purebred and crossbred liabilities of piglet survival included zero. Results suggest that the expected genetic progress for piglet survival in crossbreds when selection is based on purebred information may be nil.

Predictive ability of direct genomic values for lifetime net merit of Holstein sires using selected subsets of single nucleotide polymorphism markers.

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.

A dynamic linear model for genetic analysis of longitudinal traits.

A Bayesian model for quantitative genetic analysis of longitudinal traits is presented. It connects the model known as the Kalman filter (KF) with the standard mixed model of quantitative genetics. The KF model can be implemented easily in a Bayesian framework because, under standard prior assumptions, all fully conditional posterior distributions have closed forms. An analysis of beef cattle growth data including comparisons with a standard multivariate model was performed to assess applicability of the KF to animal breeding. Models were compared using the deviance information criterion and the Bayes factor. Models in which a KF acted on additive genetic and maternal effects were favored by the deviance information criterion, although KF did not describe residual (co)variance adequately. The Bayes factor did not provide conclusive evidence in favor of a specific model. Fitting KF to longitudinal traits provides estimates of genetic value for a whole range of time points, assuming that there are genetic differences through time between and within individuals. Different models embedding the KF in a mixed model were demonstrated to provide a more parsimonious (co)variance structure than a standard multitrait specification for the quantitative genetic analysis of longitudinal data.