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See detailShort communication: Alteration of priors for random effects in Gaussian linear mixed models
Vandenplas, Jérémie ULg; Christensen, Ole F.; Gengler, Nicolas ULg

in Journal of Dairy Science (2014), 97(9), 5880-5884

Linear mixed models, for which the prior multivariate normal distributions of random effects are assumed to have a mean equal to 0, are commonly used in animal breeding. However, some statistical analyses ... [more ▼]

Linear mixed models, for which the prior multivariate normal distributions of random effects are assumed to have a mean equal to 0, are commonly used in animal breeding. However, some statistical analyses (e.g., the consideration of a population under selection into a genomic scheme breeding, multiple-trait predictions of lactation yields, Bayesian approaches integrating external information into genetic evaluations) need to alter both the mean and (co)variance of the prior distributions and, to our knowledge, most software packages available in the animal breeding community do not permit such alterations. Therefore, the aim of this study was to propose a method to alter both the mean and (co)variance of the prior multivariate normal distributions of random effects of linear mixed models while using currently available software packages. The proposed method was tested on simulated examples with three different software packages available in animal breeding. The examples showed the possibility of the proposed method to alter both the mean and (co)variance of the prior distributions with currently available software packages through the use of an extended data file and a user supplied (co)variance matrix. [less ▲]

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See detailMicrobiota characterization of a protected designation of origin Belgian cheese: Herve cheese, using metagenomic analysis.
Delcenserie, Véronique ULg; Taminiau, Bernard ULg; Delhalle, Laurent ULg et al

in Journal of Dairy Science (2014), 97

Herve cheese is a Belgian soft cheese with a washed rind, and is made from raw or pasteurized milk. The specific microbiota of this cheese has never previously been fully explored and the use of raw or ... [more ▼]

Herve cheese is a Belgian soft cheese with a washed rind, and is made from raw or pasteurized milk. The specific microbiota of this cheese has never previously been fully explored and the use of raw or pasteurized milk in addition to starters is assumed to affect the microbiota of the rind and the heart. The aim of the study was to analyze the bacterial microbiota of Herve cheese using classical microbiology and a metagenomic approach based on 16S ribosomal DNA pyrosequencing. Using classical microbiology, the total counts of bacteria were comparable for the 11 samples of tested raw and pasteurized milk cheeses, reaching almost 8 log cfu/g. Using the metagenomic approach, 207 different phylotypes were identified. The rind of both the raw and pasteurized milk cheeses was found to be highly diversified. However, 96.3 and 97.9% of the total microbiota of the raw milk and pasteurized cheese rind, respectively, were composed of species present in both types of cheese, such as Corynebacterium casei, Psychrobacter spp., Lactococcus lactis ssp. cremoris, Staphylococcus equorum, Vagococcus salmoninarum, and other species present at levels below 5%. Brevibacterium linens were present at low levels (0.5 and 1.6%, respectively) on the rind of both the raw and the pasteurized milk cheeses, even though this bacterium had been inoculated during the manufacturing process. Interestingly, Psychroflexus casei, also described as giving a red smear to Raclettetype cheese, was identified in small proportions in the composition of the rind of both the raw and pasteurized milk cheeses (0.17 and 0.5%, respectively). In the heart of the cheeses, the common species of bacteria reached more than 99%. The main species identified were Lactococcus lactis ssp. cremoris, Psychrobacter spp., and Staphylococcus equorum ssp. equorum. Interestingly, 93 phylotypes were present only in the raw milk cheeses and 29 only in the pasteurized milk cheeses, showing the high diversity of the microbiota. Corynebacterium casei and Enterococcus faecalis were more prevalent in the raw milk cheeses, whereas Psychrobacter celer was present in the pasteurized milk cheeses. However, this specific microbiota represented a low proportion of the cheese microbiota. This study demonstrated that Herve cheese microbiota is rich and that pasteurized milk cheeses are microbiologically very close to raw milk cheeses, probably due to the similar manufacturing process. The characterization of the microbiota of this particular protected designation of origin cheese was useful in enabling us to gain a better knowledge of the bacteria responsible for the character of this cheese. [less ▲]

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See detailGenetic variance in micro-environmental sensitivity for milk and milk quality in Walloon Holstein cattle
Vandenplas, Jérémie ULg; Bastin, Catherine ULg; Gengler, Nicolas ULg et al

in Journal of Dairy Science (2013), 96

Animals that are robust to environmental changes are desirable in the current dairy industry. Genetic differences in micro-environmental sensitivity can be studied through heterogeneity of residual ... [more ▼]

Animals that are robust to environmental changes are desirable in the current dairy industry. Genetic differences in micro-environmental sensitivity can be studied through heterogeneity of residual variance between animals. However, residual variance between animals is usually assumed homogeneous in traditional genetic evaluations. The aim of this study was to investigate genetic heterogeneity of residual variance by estimating variance components in residual variance for milk yield, somatic cell score, contents in milk (g/dL) of two groups of milk fatty acids (i.e. saturated fatty acids and unsaturated fatty acids) and the content in milk of one individual fatty acid (i.e. the oleic acid, C18:1 cis-9), for first-parity Holstein cows in the Walloon Region of Belgium. A total of 146,027 test-day records from 26,887 cows in 747 herds were available. All cows had at least three records and had a known sire. These sires had at least 10 cows with records and each herd x test-day had at least five cows. The five traits were analyzed separately based on fixed lactation curve and random regression test-day models for the mean. Estimation of variance components was performed by running iteratively Expectation Maximization-Restricted Maximum Likelihood algorithm by the implementation of double hierarchical generalized linear models. Based on fixed lactation curve test-day mean models, heritability for residual variances ranged between 1.01*10-3 and 4.17*10-3 for all traits. The genetic standard deviation in residual variance (i.e. approximately the genetic coefficient of variation of residual variance) ranged between 0.12 and 0.17. Therefore, some genetic variance in micro-environmental sensitivity existed in the Walloon Holstein dairy cattle for the five studied traits. The standard deviations due to herd x test-day and permanent environment in residual variance ranged between 0.36 and 0.45 for herd x test-day effect and between 0.55 and 0.97 for permanent environmental effect. Therefore, non-genetic effects also contributed substantially to the micro-environmental sensitivity. Results also showed that the addition of random regressions to the mean model did not reduce heterogeneity in residual variance and that genetic heterogeneity of residual variance was not simply an effect of an incomplete mean model. [less ▲]

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See detailDirect use of MACE EBV in the Walloon single-step Bayesian genomic evaluation system
Vandenplas, Jérémie ULg; Colinet, Frédéric ULg; Faux, Pierre ULg et al

in Journal of Dairy Science (2013, July), 96(E-Supplement),

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See detailEvaluation of Heat Stress Effects on Production Traits and Somatic Cell Score of Holsteins in a Temperate Environment
Hammami, Hedi ULg; Bormann, Jeanne; M'Hamdi, Naceur et al

in Journal of Dairy Science (2013), 96(3), 1844-1855

This study was aimed to evaluate the degree of thermal stress exhibited by Holsteins under a continental temperate climate. Milk, fat, protein, and somatic cell count test-day records collected between ... [more ▼]

This study was aimed to evaluate the degree of thermal stress exhibited by Holsteins under a continental temperate climate. Milk, fat, protein, and somatic cell count test-day records collected between 2000 and 2011 from 23,963 cows in 604 herds were combined with meteorological data from 14 public weather stations in Luxembourg. Daily values of six different thermal indices (TI) weighted in term of temperature, relative humidity, solar radiation, and wind speed were calculated by averaging hourly TI over 24 hours. Heat stress thresholds were firstly identified by a broken-line regression model. Regression models were thereafter applied to quantify milk production losses due to heat stress. The tipping points at which milk and protein yields declined were effectively identified. For fat yield, no valid threshold was identified for any of the studied TI. Daily fat yields tended to decrease steadily with increasing values of TI. Daily somatic cell scores (SCS) pattern was marked by increased values at both lowest and highest TI ranges with a more pronounced reaction to cold stress for apparent temperature indices. Thresholds differed between TI and traits. For production traits, they ranged from 62 (TI1) to 80 (TI3) for temperature-humidity indices (THI) and from 16 (TI5) to 20 (TI6) for apparent temperature indices. Corresponding SCS thresholds were higher and ranged from 66 (TI1) to 82 (TI3) and from 20 (TI5) to 23 (TI6), respectively. The largest milk decline per unit of mild, moderate, and extreme heat stress levels of 0.164, 0.356, and 0.955 kg, respectively, was observed when using the conventional THI (TI1). The highest yearly milk, fat, and protein losses of 54, 5.7, and 4.2 kg respectively were detected by TI2, the THI index that is adjusted for wind speed and solar radiation. The latter index could be considered as the best indicator of heat stress to be used for forecast and herd management in a first step in temperate regions under anticipated climate changes. [less ▲]

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See detailGenetics of body energy status of Holstein cows predicted by mid-infrared spectrometry
Bastin, Catherine ULg; Berry, D.; Gengler, Nicolas ULg et al

in Journal of Dairy Science (2013), 96(E-Suppl. 1),

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See detailDevelopment of a genetic evaluation for body condition score for Canadian Holsteins
Loker, S.; Bastin, Catherine ULg; Miglior, F. et al

in Journal of Dairy Science (2013), 96

Valacta (Sainte-Anne-de-Bellevue, Québec, Canada) is the Canadian Dairy Herd Improvement organization responsible for milk recording in Québec and Atlantic provinces. Up to 14 first-lactation body ... [more ▼]

Valacta (Sainte-Anne-de-Bellevue, Québec, Canada) is the Canadian Dairy Herd Improvement organization responsible for milk recording in Québec and Atlantic provinces. Up to 14 first-lactation body condition score (BCS) records were collected per cow (average of 2.5 records per cow), allowing the trait to be described by a random regression animal model so that animals could be ranked by the shape of their BCS curve. However, Valacta’s BCS are available from Québec herds only and the long-term objective of this research is to develop a nationwide genetic evaluation of sires and cows for BCS. Alternatively, Holstein Canada (Brantford, Ontario, Canada) collects type trait records nationwide, primarily for first-lactation cows. Holstein Canada typically collects a single record per trait, so that selection for Holstein Canada BCS would be based on overall BCS level rather than the shape of the BCS curve. Several different methods of genetically evaluating Valacta’s BCS were investigated, including consideration of average BCS level across lactation, the amount of fluctuation in the BCS curve during lactation, and combinations of BCS level and BCS fluctuation. Sires with ≥25 daughters were compared (as opposed to comparing cows) because their BCS estimated breeding values (EBV) are based on more information, and so should be more reliable. Of the different methods of calculating Valacta BCS EBV, ranking bulls based on overall BCS level gave the best results in that their daughter phenotypic BCS curves showed limited loss in early lactation BCS and replenished condition by the end of lactation. Whereas Valacta’s BCS were analyzed using a random regression animal model, Holstein Canada only needs to collect 1 BCS record per cow at classification and the resulting BCS EBV was strongly correlated with Valacta’s BCS EBV. Furthermore, because Holstein Canada’s BCS are collected nationally and Valacta’s BCS are not, a national genetic evaluation for Holstein Canada’s BCS is more convenient. The results of this study do not eliminate the possibility of a genetic evaluation of BCS as a longitudinal trait, but indicate that other methods of calculating Valacta BCS EBV should be explored. Until that time, genetically evaluating Holstein Canada’s BCS is simple, easily implemented, and may be effective in altering the level and shape of the genetic BCS curve. [less ▲]

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See detailPotential of mid-infrared spectrum of milk to detect changes in the physiological status of dairy cows
Laine, Aurélie ULg; Goubau, Amaury; Hammami, Hedi ULg et al

in Journal of Dairy Science (2013)

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See detailGenetic parameters for methane emissions predicted from milk mid-infrared spectra in dairy cows
Kandel, Purna Bhadra ULg; Vanrobays, Marie-Laure ULg; Vanlierde, Amélie ULg et al

in Journal of Dairy Science (2013), 95(E-1), 388

Genetic selection of low methane (CH4) emitting animals is additive and permanent but the difficulties associated with individual CH4 measurement result in a paucity of records required to estimate ... [more ▼]

Genetic selection of low methane (CH4) emitting animals is additive and permanent but the difficulties associated with individual CH4 measurement result in a paucity of records required to estimate genetic variability of CH4 traits. Recently, it was shown that direct quantification of CH4 emissions by mid-infrared spectroscopy (MIR) from milk. The CH4 prediction equation was developed using 452 SF6 CH4 measurements with associated milk spectra and the calibration equation was developed using PLS regression. The obtained SD of predicted CH4 was 126.39 g/day with standard error of cross validation 68.68 g/day and a cross-validation coefficient of determination equal to 70%. The equation was applied on a total of 338,917 spectra obtained from milk samples collected between January 2007 and August 2012 during the Walloon milk recording for first parity Holstein cows. The prediction of MIR CH4 was 547 ± 111 g/d and MIR CH4 g/kg of fat and protein corrected milk (FPCM) was 23.66 ± 8.21.Multi-trait random regression test-day models were used to estimate the genetic variability of MIR predicted CH4 and milk production traits. The heritability, phenotypic and genetic correlations between MIR predicted CH4 traits and milk traits are presented in Table 1. Estimated heritability for CH4 g/day and CH4 g/kg of FPCM were lower than common production traits but would still be useful in breeding programs. While selection for cows emitting lower amounts of MIR predicted CH4 (g/d) would have little effect on milk production traits, selection on MIR predicted CH4 (g/kg of FPCM) would decrease FPCM, fat and protein yields. These genetic parameters of CH4 indicator traits might be entry point for selection that accounts mitigation of CH4 from dairy farming. Table 1. Heritability (diagonal), phenotypic (below the diagonal) and genetic (above the diagonal) correlations between MIR predicted CH4 and production traits Traits MIR CH4 (g/d) MIR CH4 ((g/kg of FPCM) FPCM Fat yield Protein yield MIR CH4 (g/d) 0.11 0.42 0.03 0.19 0.04 MIR CH4 (g/kg of FPCM)0.59 0.18 -0.83 -0.72 -0.77 FPCM -0.02 -0.65 0.20 0.95 0.91 Fat yield 0.01 -0.58 0.76 0.22 0.70 Protein yield -0.01 -0.61 0.78 0.69 0.20 [less ▲]

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See detailEffect of the milk recording time on the genetic parameters of milk production and mid-infrared milk components in Luxembourg dairy cattle
Arnould, Valérie ULg; Gengler, Nicolas ULg; Soyeurt, Hélène ULg

in Journal of Dairy Science (2012, July), 95

A particularity of the Luxembourg milk recording is the use of different schemes. Two principal schemes are applied: the scheme “S” applied on 69.1% of the total herds (n=712) and consisting in one ... [more ▼]

A particularity of the Luxembourg milk recording is the use of different schemes. Two principal schemes are applied: the scheme “S” applied on 69.1% of the total herds (n=712) and consisting in one proportionate sample of all daily milkings, and the scheme “T” (21.6% of the total herds) which consists in one sample of only one milking (morning or evening milking) (and alternating milking time from month to month). The problematic is that application of different schemes could influence the milk components (protein and fat yield) and the milk fat components (saturated and unsaturated groups of fatty acids) genetic parameters estimation and to prevent all comparisons between dairy population under different milk recording schemes. A total of 47,613 and 44,833 test-day records were obtained, respectively for schemes “S” and “T” from Holstein cows in first lactation in Luxembourg dairy herds. The used model included as fixed effects: herd x date of test, class of age, and month x year. Random effects were permanent environmental, additive genetics, and residual effects. The main objective of this work is to study the effect the choice of milk recording schemes (“S” or “T” schemes) on milk yield and milk components genetic parameters. A solution could be to add a fixed effect taking in account the milking time. The second objective is to study the effect of milking time (morning or evening) on genetic parameters estimated in the case of scheme “T”. According to the results, genetic parameters were statistically different between the schemes “S” and “T” for milk yield (P value < 0.0001). Further, the classifications of bulls according to their breeding values were very different when values were estimated on basis of scheme “S” or “T” (Spearman correlation value of 0.51 for milk yield for example). In conclusion, using several milk recording schemes do not allow any comparison of genetic parameters between dairy cattle’s. [less ▲]

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See detailRelationship between body condition score and health traits in first-lactation Canadian Holsteins.
Loker, S.; Miglior, F.; Koeck, A. et al

in Journal of Dairy Science (2012)

The objective of this research was to estimate daily genetic correlations between longitudinal body condition score (BCS) and health traits by using a random regression animal model in first-lactation ... [more ▼]

The objective of this research was to estimate daily genetic correlations between longitudinal body condition score (BCS) and health traits by using a random regression animal model in first-lactation Holsteins. The use of indicator traits may increase the rate of genetic progress for functional traits relative to direct selection for functional traits. Indicator traits of interest are those that are easier to record, can be measured early in life, and are strongly genetically correlated with the functional trait of interest. Several BCS records were available per cow, and only 1 record per health trait (1 = affected; 0 = not affected) was permitted per cow over the lactation. Two bivariate analyses were performed, the first between BCS and mastitis and the second between BCS and metabolic disease (displaced abomasum, milk fever, and ketosis). For the first analysis, 217 complete herds were analyzed, which included 28,394 BCS records for 10,715 cows and 6,816 mastitis records for 6,816 cows. For the second analysis, 350 complete herds were analyzed, which included 42,167 BCS records for 16,534 cows and 13,455 metabolic disease records for 13,455 cows. Estimation of variance components by a Bayesian approach via Gibbs sampling was performed using 400,000 samples after a burn-in of 150,000 samples. The average daily heritability (posterior standard deviation) of BCS was 0.260 (0.026) and the heritabilities of mastitis and metabolic disease were 0.020 (0.007) and 0.041 (0.012), respectively. Heritability estimates were similar to literature values. The average daily genetic correlation between BCS and mastitis was -0.730 (0.110). Cows with a low BCS during the lactation are more susceptible to mastitis, and mastitic cows are likely to have low BCS. Daily estimates of genetic correlations between BCS and mastitis were moderate to strong throughout the lactation, becoming stronger as the lactation progressed. The average daily genetic correlation between BCS and metabolic disease was -0.438 (0.125), and was consistent throughout the lactation. A lower BCS during the lactation is genetically associated with the occurrence of mastitis and metabolic disease. [less ▲]

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See detailBovine milk fat globule membrane affects virulence expression in Escherichia coli O157:H7
Tellez, Angela; Corredig, Milena; Guri, Anilda et al

in Journal of Dairy Science (2012)

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See detailGenetic and environmental relationships between body condition score and milk production traits in Canadian Holsteins.
Loker, S; Bastin, Catherine ULg; Miglior, F et al

in Journal of Dairy Science (2012), 95(1), 410-9

The objective of this research was to estimate genetic parameters of first-lactation body condition score (BCS), milk yield, fat percentage (Fat%), protein percentage (Prot%), somatic cell score (SCS ... [more ▼]

The objective of this research was to estimate genetic parameters of first-lactation body condition score (BCS), milk yield, fat percentage (Fat%), protein percentage (Prot%), somatic cell score (SCS), milk urea nitrogen (MUN), lactose percentage (Lact%), and fat to protein ratio (F:P) using multiple-trait random regression animal models. Changes in covariances between BCS and milk production traits on a daily basis have not been investigated before and could be useful for determining which BCS estimated breeding values (EBV) might be practical for selection in the future. Field staff from Valacta milk recording agency (Sainte-Anne-de-Bellevue, QC, Canada) collected BCS from Quebec herds several times per cow throughout the lactation. Average daily heritabilities and genetic correlations among the various traits were similar to literature values. On an average daily basis, BCS was genetically unfavorably correlated with milk yield (i.e., increased milk yield was associated with lower body condition). The unfavorable genetic correlation between BCS and milk yield became stronger as lactation progressed, but was equivalent to zero for the first month of lactation. Favorable genetic correlations were found between BCS with Prot%, SCS, and Lact% (i.e., greater BCS was associated with greater Prot%, lower SCS, and greater Lact%). These correlations were strongest in early lactation. On an average daily basis, BCS was not genetically correlated with Fat% or MUN, but was negatively correlated with F:P. Furthermore, BCS at 5 and 50 d in milk (DIM) had the most favorable genetic correlations with milk production traits over the lactation (at 5, 50, 150, and 250 DIM). Thus, early lactation BCS EBV shows potential for selection. Regardless, this study showed that the level of association BCS has with milk production traits is not constant over the lactation. Simultaneous selection for both BCS and milk production traits should be considered, mainly due to the unfavorable genetic correlation between BCS with milk yield. [less ▲]

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See detailGenetic correlations of days open with production traits and contents in milk of major fatty acids predicted by mid-infrared spectrometry.
Bastin, Catherine ULg; Berry, D. P.; Soyeurt, Hélène ULg et al

in Journal of Dairy Science (2012), 95(10), 6113-21

The objective of this study was to estimate the genetic relationships between days open (DO) and both milk production traits and fatty acid (FA) content in milk predicted by mid-infrared spectrometry. The ... [more ▼]

The objective of this study was to estimate the genetic relationships between days open (DO) and both milk production traits and fatty acid (FA) content in milk predicted by mid-infrared spectrometry. The edited data set included 143,332 FA and production test-day records and 29,792 DO records from 29,792 cows in 1,170 herds. (Co)variances were estimated using a series of 2-trait models that included a random regression for milk production and FA traits. In contrast to the genetic correlations with fat content, those between DO and FA content in milk changed considerably over the lactation. The genetic correlations with DO for unsaturated FA, monounsaturated FA, long-chain FA, C18:0, and C18:1 cis-9 were positive in early lactation but negative after 100 d in milk. For the other FA, genetic correlations with DO were negative across the whole lactation. At 5 d in milk, the genetic correlation between DO and C18:1 cis-9 was 0.39, whereas the genetic correlations between DO and C6:0 to C16:0 FA ranged from -0.37 to -0.23. These results substantiated the known relationship between fertility and energy balance status, explained by the release of long-chain FA in early lactation, from the mobilization of body fat reserves, and the consequent inhibition of de novo FA synthesis in the mammary gland. At 200 d in milk, the genetic correlations between DO and FA content ranged from -0.38 for C18:1 cis-9 to -0.03 for C6:0. This research indicates an opportunity to use FA content in milk as an indicator trait to supplement the prediction of genetic merit for fertility. [less ▲]

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See detailImputation of genotypes with low-density chips and its effect on reliability of direct genomic values in Dutch Holstein cattle.
Mulder, H. A.; Calus, M. P. L.; Druet, Tom ULg et al

in Journal of Dairy Science (2012), 95(2), 876-89

Genomic selection using 50,000 single nucleotide polymorphism (50k SNP) chips has been implemented in many dairy cattle breeding programs. Cheap, low-density chips make genotyping of a larger number of ... [more ▼]

Genomic selection using 50,000 single nucleotide polymorphism (50k SNP) chips has been implemented in many dairy cattle breeding programs. Cheap, low-density chips make genotyping of a larger number of animals cost effective. A commonly proposed strategy is to impute low-density genotypes up to 50,000 genotypes before predicting direct genomic values (DGV). The objectives of this study were to investigate the accuracy of imputation for animals genotyped with a low-density chip and to investigate the effect of imputation on reliability of DGV. Low-density chips contained 384, 3,000, or 6,000 SNP. The SNP were selected based either on the highest minor allele frequency in a bin or the middle SNP in a bin, and DAGPHASE, CHROMIBD, and multivariate BLUP were used for imputation. Genotypes of 9,378 animals were used, from which approximately 2,350 animals had deregressed proofs. Bayesian stochastic search variable selection was used for estimating SNP effects of the 50k chip. Imputation accuracies and imputation error rates were poor for low-density chips with 384 SNP. Imputation accuracies were higher with 3,000 and 6,000 SNP. Performance of DAGPHASE and CHROMIBD was very similar and much better than that of multivariate BLUP for both imputation accuracy and reliability of DGV. With 3,000 SNP and using CHROMIBD or DAGPHASE for imputation, 84 to 90% of the increase in DGV reliability using the 50k chip, compared with a pedigree index, was obtained. With multivariate BLUP, the increase in reliability was only 40%. With 384 SNP, the reliability of DGV was lower than for a pedigree index, whereas with 6,000 SNP, about 93% of the increase in reliability of DGV based on the 50k chip was obtained when using DAGPHASE for imputation. Using genotype probabilities to predict gene content increased imputation accuracy and the reliability of DGV and is therefore recommended for applications of imputation for genomic prediction. A deterministic equation was derived to predict accuracy of DGV based on imputation accuracy, which fitted closely with the observed relationship. The deterministic equation can be used to evaluate the effect of differences in imputation accuracy on accuracy and reliability of DGV. [less ▲]

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See detailUse of milk fatty acids to substitute for body condition score in breeding purposes
Bastin, Catherine ULg; Berry, D.P.; Soyeurt, Hélène ULg et al

in Journal of Dairy Science (2012), 95, Suppl. 2

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See detailA recursive algorithm for decomposition and creation of the inverse of the genomic relationship matrix
Faux, Pierre ULg; Gengler, Nicolas ULg; Misztal, Ignacy

in Journal of Dairy Science (2012), 95(10), 6093-6102

As the number of genotyped animals increases, some genomic prediction models have issues related to inversion of the genomic relationship and related matrices. We developed a recursive algorithm to ... [more ▼]

As the number of genotyped animals increases, some genomic prediction models have issues related to inversion of the genomic relationship and related matrices. We developed a recursive algorithm to approximate the inverses of those matrices. The algorithm converges after a few rounds of recursion, but additional work is needed to reduce computing costs further. [less ▲]

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