The relationships between early lactation energy status indicators and endocrine fertility traits in dairy cows.

The relationships between dairy cow milk-based energy status (ES) indicators and fertility traits were studied during periods 8 to 21, 22 to 35, 36 to 49, and 50 to 63 d in milk. Commencement of luteal activity (C-LA) and interval from calving to the first heat (CFH), based on frequent measurements of progesterone by the management tool Herd Navigator (DeLaval), were used as fertility traits. Energy status indicator traits were milk ß-hydroxybutyrate (BHB) concentration provided by Herd Navigator and milk fat:protein ratio, concentration of C18:1 cis-9, the ratio of fatty acids (FA) C18:1 cis-9 and C10:0 in test-day milk samples, and predicted plasma concentration of nonesterified fatty acids (NEFA) on test days. Plasma NEFA predictions were based either directly on milk mid-infrared spectra (MIR) or on milk fatty acids based on MIR spectra (NEFAmir and NEFAfa, respectively). The average (standard deviation) C-LA was 39.3 (±16.6) days, and the average CFH was 50.7 (±17.2) days. The correlations between fertility traits and ES indicators tended to be higher for multiparous (r < 0.28) than for primiparous (r < 0.16) cows. All correlations were lower in the last period than in the other periods. In period 1, correlations of C-LA with NEFAfa and BHB, respectively, were 0.15 and 0.14 for primiparous and 0.26 and 0.22 for multiparous cows. The associations between fertility traits and ES indicators indicated that negative ES during the first weeks postpartum may delay the onset of luteal activity. Milk FPR was not as good an indicator for cow ES as other indicators. According to these findings, predictions of plasma NEFA and milk FA based on milk MIR spectra of routine test-day samples and the frequent measurement of milk BHB by Herd Navigator gave equally good predictions of cow ES during the first weeks of lactation. Our results indicate that routinely measured milk traits can be used for ES evaluation in early lactation.

Practical implementation of genetic groups in single-step genomic evaluations with Woodbury matrix identity-based genomic relationship inverse.

The growing amount of genomic information in dairy cattle has increased computational and modeling challenges in the single-step evaluations. The computational challenges are due to the dense inverses of genomic (G) and pedigree (A22) relationship matrices of genotyped animals in the single-step mixed model equations. An equivalent mixed model equation is given by single-step genomic BLUP that are based on the T matrix (ssGTBLUP), where these inverses are avoided by expressing G-1 through a product of 2 rectangular matrices, and (A22)-1 through sparse matrix blocks of the inverse of full relationship matrix A-1. A proper way to account genetic groups through unknown parent groups (UPG) after the Quaas-Pollak transformation (QP) is one key factor in a single-step model. When the UPG effects are incompletely accounted, the iterative solving method may have convergence problems. In this study, we investigated computational and predictive performance of ssGTBLUP with residual polygenic (RPG) effect and UPG. The QP transformation used A-1 and, in the complete form, T and (A22)-1 matrices as well. The models were tested with official Nordic Holstein milk production test-day data and model. The results show that UPG can be easily implemented in ssGTBLUP having RPG. The complete QP transformation was computationally feasible when preconditioned conjugate gradient iteration and iteration on data without explicitly setting up G or A22 matrices were used. Furthermore, for good convergence of the preconditioned conjugate gradient method, a complete QP transformation was necessary.

Symposium review: Single-step genomic evaluations in dairy cattle.

During the last decade, genomic selection has revolutionized dairy cattle breeding. For example, Nordic dairy cows (Denmark, Finland, and Sweden) born in 2018 were >90% sired by young genomically tested bulls. Thus, the average age of sires for Red Dairy Cattle cows born in 2018 was only 3.1 yr, whereas in 2011 it was 5.7 yr. Earlier the key driver of genetic progress was the selection of progeny-tested sires, but now it is the genomic preselection of young sires. This leads to a biased estimation of genetic progress by the traditional genetic evaluations. When these are used as input for multi-step genomic evaluations also they became distorted. The only long-term solution to maintain unbiasedness is to include the genomic information in evaluations. Although means for single-step evaluation models were introduced in 2010, they have not yet been implemented in large-scale national dairy evaluations. At first, single-step evaluations were hindered by computational cost. This has been largely solved, either by sparse presentations of the inverses of the genomic relationship (G) and pedigree relationship (A22) matrices of genotyped animals needed in the single-step evaluation models based on G (ssGBLUP), or by using the single-step marker models. Approaches for G-1 are the APY-G, where the relationships among "young" animals are completely determined by their relationship to the "core" animals, and single-step evaluations where the G-1 is replaced by a computational formula based on the structure of G (ssGTBLUP). The single-step marker models include the marker effects either directly, as effects in the statistical model, or indirectly, to generate genomic relationships among genotyped animals. Concurrently with development of the algorithm, computing resources have evolved in both availability of computer memory and speed. The problems actively studied now are the same for both of the single-step approaches (GBLUP and marker models). Convergence in iterative solving seems to get worse with an increasing number of genotypes. These problems are more pronounced with low-heritability traits and in multi-trait models with high genetic correlations among traits. Problems are also related to the unbalancedness of pedigrees and diverse genetic groups. In many cases, the problem can be solved by properly accounting for contributions of the genotyped animals to genetic groups. The standard solving approach is preconditioned conjugate gradient iteration, in which the convergence has been improved by better preconditioning matrices. Another difficulty to be considered is inflation in genomic evaluations of candidate animals; genomic models seem to overvalue the genomic information. The problem is usually smaller in single-step evaluations than in multi-step evaluations but is more difficult to mitigate by ad hoc adjustments.

Using Monte Carlo method to include polygenic effects in calculation of SNP-BLUP model reliability.

An SNP-BLUP model is computationally scalable even for large numbers of genotyped animals. When genetic variation cannot be completely captured by SNP markers, a more accurate model is obtained by fitting a residual polygenic effect (RPG) as well. However, inclusion of the RPG effect increases the size of the SNP-BLUP mixed model equations (MME) by the number of genotyped animals. Consequently, the calculation of model reliabilities requiring elements of the inverted MME coefficient matrix becomes more computationally challenging with increasing numbers of genotyped animals. We present a Monte Carlo (MC)-based sampling method to estimate the reliability of the SNP-BLUP model including the RPG effect, where the MME size depends on the number of markers and MC samples. We compared reliabilities calculated using different RPG proportions and different MC sample sizes in analyzing 2 data sets. Data set 1 (data set 2) contained 19,757 (222,619) genotyped animals, with 11,729 (50,240) SNP markers, and 231,186 (13.35 million) pedigree animals. Correlations between the correct and the MC-calculated reliabilities were above 98% even with 5,000 MC samples and an 80% RPG proportion in both data sets. However, more MC samples were needed to achieve a small maximum absolute difference and mean squared error, particularly when the RPG proportion exceeded 20%. The computing time for MC SNP-BLUP was shorter than for GBLUP. In conclusion, the MC-based approach can be an effective strategy for calculating SNP-BLUP model reliability with an RPG effect included.

Metafounder approach for single-step genomic evaluations of Red Dairy cattle.

Single-step genomic BLUP (ssGBLUP) is a powerful approach for breeding value prediction in populations with a limited number of genotyped animals. However, conflicting genomic (G) and pedigree (A22) relationship matrices complicate the implementation of ssGBLUP into practice. The metafounder (MF) approach is a recently proposed solution for this problem and has been successfully used on simulated and real multi-breed pig data. Advantages of the method are easily seen across breed evaluations, where pedigrees are traced to several pure breeds, which are thereafter used as MF. Application of the MF method to ruminants is complicated due to multi-breed pedigree structures and the inability to transmit existing unknown parent groups (UPG) to MF. In this study, we apply the MF approach for ssGBLUP evaluation of Finnish Red Dairy cattle treated as a single breed. Relationships among MF were accounted for by a (co)variance matrix (Γ) computed using estimated base population allele frequencies. The attained Γ was used to calculate a relationship matrix A22Γ for the genotyped animals. We tested the influence of SNP selection on the Γ matrix by applying a minor allele frequency (MAF) threshold (ΓMAF) where accepted markers had an MAF ≥0.05. Elements in the ΓMAF matrix were slightly lower than in the Γ matrix. Correlation between diagonal elements of the genomic and pedigree relationship matrices increased from 0.53 (A22) to 0.76 ( A22Γ and [Formula: see text] ). Average diagonal elements of A22Γ and [Formula: see text] matrices increased to the same level as in the G matrix. The ssGBLUP breeding values (GEBV) were solved using either the original 236 or redefined 8 UPG, or 8 MF computed with or without the MAF threshold. For bulls, the GEBV validation test results for the 8 UPG and 8 MF gave the same validation reliability (R2; 0.31) and over-dispersion (0.73, measured by regression coefficient b1). No significant R2 increase was observed in cows. Thus, the MF greatly influenced the pedigree relationship matrices but not the GEBV. Selection of SNP according to MAF had a notable effect on the Γ matrix and made the A22 and G matrices more similar.

Reliability of breeding values for feed intake and feed efficiency traits in dairy cattle: When dry matter intake recordings are sparse under different scenarios.

Currently, routine recordings of dry matter intake (DMI) in commercial herds are practically nonexistent. Recording DMI from commercial herds is a prerequisite for the inclusion of feed efficiency (FE) traits in dairy cattle breeding goals. To develop future on-farm phenotyping strategies, recording strategies that are low cost and less demanding logistically and that give relatively accurate estimates of the animal's genetic merit are therefore needed. The objectives of this study were (1) to estimate genetic parameters for daily DMI and FE traits and use the estimated parameters to simulate daily DMI phenotypes under different DMI recording scenarios (SCN) and (2) to use the simulated data to estimate for different scenarios the associated reliability of estimated breeding value and accuracies of genomic prediction for varying sizes of reference populations. Five on-farm daily DMI recording scenarios were simulated: once weekly (SCN1), once monthly (SCN2), every 2 mo (SCN3), every 3 mo (SCN4), and every 4 mo (SCN5). To estimate reliability of estimated breeding values, DMI and FE observations and true breeding values were simulated based on variance components estimated for daily observations of Nordic Red cows. To emulate realistic on-farm recording, 5 data set replicates, each with 36,037 DMI and FE records, were simulated for real pedigree and data structure of 789 Holstein cows. Observations for the 5 DMI recording scenarios were generated by discarding data in a step-wise manner from the full simulated data per the scenario's definitions. For each of these scenarios, reliabilities were calculated as correlation between the true and estimated breeding values. Variance components and genetic parameters were estimated for daily DMI, residual feed intake (RFI), and energy conversion efficiency (ECE) fitting the random regression model. Data for variance components were from 227 primiparous Nordic Red dairy cows covering 8 to 280 d in milk. Lactation-wise heritability for DMI, RFI, and ECE was 0.33, 0.12, and 0.32, respectively, and daily heritability estimates during lactation ranged from 0.18 to 0.45, 0.08 to 0.32, and 0.08 to 0.45 for DMI, RFI, and ECE, respectively. Genetic correlations for DMI between different stages of lactation ranged from -0.50 to 0.99. The comparison of different on-farm DMI recording scenarios indicated that adopting a less-frequent recording scenario (SCN3) gave a similar level of accuracy as SCN1 when 17 more daughters are recorded per sire over the 46 needed for SCN1. Such a strategy is less demanding logistically and is low cost because fewer observations need to be collected per animal. The accuracy of genomic predictions associated with the 5 recording scenarios indicated that setting up a relatively larger reference population and adopting a less-frequent DMI sampling scenario (e.g., SCN3) is promising. When the same reference population size was considered, the genomic prediction accuracy of SCN3 was only 5.0 to 7.0 percentage points lower than that for the most expensive DMI recording strategy (SCN1). We concluded that DMI recording strategies that are sparse in terms of records per cow but with slightly more cows recorded per sire are advantageous both in genomic selection and in traditional progeny testing schemes when accuracy, logistics, and cost implications are considered.

Body and milk traits as indicators of dairy cow energy status in early lactation.

The inclusion of feed intake and efficiency traits in dairy cow breeding goals can lead to increased risk of metabolic stress. An easy and inexpensive way to monitor postpartum energy status (ES) of cows is therefore needed. Cows' ES can be estimated by calculating the energy balance from energy intake and output and predicted by indicator traits such as change in body weight (ΔBW), change in body condition score (ΔBCS), milk fat:protein ratio (FPR), or milk fatty acid (FA) composition. In this study, we used blood plasma nonesterified fatty acids (NEFA) concentration as a biomarker for ES. We determined associations between NEFA concentration and ES indicators and evaluated the usefulness of body and milk traits alone, or together, in predicting ES of the cow. Data were collected from 2 research herds during 2013 to 2016 and included 137 Nordic Red dairy cows, all of which had a first lactation and 59 of which also had a second lactation. The data included daily body weight, milk yield, and feed intake and monthly BCS. Plasma samples for NEFA were collected twice in lactation wk 2 and 3 and once in wk 20. Milk samples for analysis of fat, protein, lactose, and FA concentrations were taken on the blood sampling days. Plasma NEFA concentration was higher in lactation wk 2 and 3 than in wk 20 (0.56 ± 0.30, 0.43 ± 0.22, and 0.13 ± 0.06 mmol/L, respectively; all means ± standard deviation). Among individual indicators, C18:1 cis-9 and the sum of C18:1 in milk had the highest correlations (r = 0.73) with NEFA. Seven multiple linear regression models for NEFA prediction were developed using stepwise selection. Of the models that included milk traits (other than milk FA) as well as body traits, the best fit was achieved by a model with milk yield, FPR, ΔBW, ΔBCS, FPR × ΔBW, and days in milk. The model resulted in a cross-validation coefficient of determination (R2cv) of 0.51 and a root mean squared error (RMSE) of 0.196 mmol/L. When only milk FA concentrations were considered in the model, NEFA prediction was more accurate using measurements from evening milk than from morning milk (R2cv = 0.61 vs. 0.53). The best model with milk traits contained FPR, C10:0, C14:0, C18:1 cis-9, C18:1 cis-9 × C14:0, and days in milk (R2cv = 0.62; RMSE = 0.177 mmol/L). The most advanced model using both milk and body traits gave a slightly better fit than the model with only milk traits (R2cv = 0.63; RMSE = 0.176 mmol/L). Our findings indicate that ES of cows in early lactation can be monitored with moderately high accuracy by routine milk measurements.

Polyethylene glycol as an indigestible marker to estimate fecal output in dairy cows.

The objective of this study was to evaluate the accuracy of fecal output measurements using polyethylene glycol (PEG) as an external marker determined by near-infrared reflectance spectroscopy. In addition, the accuracy of dry matter intake predictions based on fecal output and digestibility estimated using an internal marker [indigestible neutral detergent fiber (iNDF)] was assessed. The experiment was conducted using 6 lactating dairy cows fed 2 different diets. Polyethylene glycol was administered twice daily into the rumen and the diurnal pattern of fecal concentrations and recovery in feces were determined. To evaluate the effects of alternative marker administration and sampling schemes on fecal output estimates, the passage kinetics of PEG in the digestive tract of dairy cows was determined and used for simulation models. The results indicate that PEG was completely recovered in feces and, thus, fecal output was accurately estimated using PEG. Good agreement between measured and predicted dry matter intake (standard error of prediction = 0.86 kg/d, R2 = 0.81) indicates good potential to determine feed intake using PEG in combination with iNDF. The precision of cow-specific digestibility estimates based on iNDF was unsatisfactory, but for a group of cows iNDF provided an accurate estimate of dry matter digestibility. The current study indicated that, to overcome inherent day-to-day variation in feed intake and fecal output, the minimum of 4 fecal spot samples should be collected over 4 d. Preferably, these samples should be distributed evenly over the 12-h marker administration interval to compensate for the circadian variation in fecal PEG concentrations.

Genetic background in partitioning of metabolizable energy efficiency in dairy cows.

The main objective of this study was to assess the genetic differences in metabolizable energy efficiency and efficiency in partitioning metabolizable energy in different pathways: maintenance, milk production, and growth in primiparous dairy cows. Repeatability models for residual energy intake (REI) and metabolizable energy intake (MEI) were compared and the genetic and permanent environmental variations in MEI were partitioned into its energy sinks using random regression models. We proposed 2 new feed efficiency traits: metabolizable energy efficiency (MEE), which is formed by modeling MEI fitting regressions on energy sinks [metabolic body weight (BW0.75), energy-corrected milk, body weight gain, and body weight loss] directly; and partial MEE (pMEE), where the model for MEE is extended with regressions on energy sinks nested within additive genetic and permanent environmental effects. The data used were collected from Luke's experimental farms Rehtijärvi and Minkiö between 1998 and 2014. There were altogether 12,350 weekly MEI records on 495 primiparous Nordic Red dairy cows from wk 2 to 40 of lactation. Heritability estimates for REI and MEE were moderate, 0.33 and 0.26, respectively. The estimate of the residual variance was smaller for MEE than for REI, indicating that analyzing weekly MEI observations simultaneously with energy sinks is preferable. Model validation based on Akaike's information criterion showed that pMEE models fitted the data even better and also resulted in smaller residual variance estimates. However, models that included random regression on BW0.75 converged slowly. The resulting genetic standard deviation estimate from the pMEE coefficient for milk production was 0.75 MJ of MEI/kg of energy-corrected milk. The derived partial heritabilities for energy efficiency in maintenance, milk production, and growth were 0.02, 0.06, and 0.04, respectively, indicating that some genetic variation may exist in the efficiency of using metabolizable energy for different pathways in dairy cows.

Short communication: Genomic prediction using different single-step methods in the Finnish red dairy cattle population.

Single-step genomic prediction models utilizing both genotyped and nongenotyped animals are likely to become the prevailing tool in genetic evaluations of livestock. Various single-step prediction models have been proposed, based either on estimation of individual marker effects or on direct prediction via a genomic relationship matrix. In this study, a classical pedigree-based animal model, a regular single-step genomic BLUP (ssGBLUP) model, algorithm for proven and young (APY) with 2 strategies for choosing core animals, and a single-step Bayesian regression (ssBR) model were compared for 305-d production traits (milk, fat, protein) in the Finnish red dairy cattle population. A residual polygenic effect with 10% of total genetic variance was included in the single-step models to reduce inflation of genomic predictions. Validation reliability was calculated as the squared Pearson correlation coefficient between genomically enhanced breeding value (GEBV) and yield deviation for masked records for 2,056 validation cows from the last year in the data set investigated. The results showed that gains of 0.02 to 0.04 on validation reliability were achieved by using single-step methods compared with the classical animal model. The regular ssGBLUP model and ssBR model with an extra polygenic effect yielded the same results. The APY methods yielded similar reliabilities as the regular ssGBLUP and ssBR. Exact prediction error variance of GEBV could be obtained by ssBR to avoid any approximation methods used for ssGBLUP when inversion left-hand side of mixed model equations is computationally infeasible for large data sets.

Detection of evaluation bias caused by genomic preselection.

The aim of this simulation study was to investigate whether it is possible to detect the effect of genomic preselection on Mendelian sampling (MS) means or variances obtained by the MS validation test. Genomic preselection of bull calves is 1 additional potential source of bias in international evaluations unless adequately accounted for in national evaluations. Selection creates no bias in traditional breeding value evaluation if the data of all animals are included. However, this is not the case with genomic preselection, as it excludes culled bulls. Genomic breeding values become biased if calculated using a multistep procedure instead of, for example, a single-step method. Currently, about 60% of the countries participating in international bull evaluations have already adopted genomic selection in their breeding schemes. The data sent for multiple across-country evaluation can, therefore, be very heterogeneous, and a proper validation method is needed to ensure a fair comparison of the bulls included in international genetic evaluations. To study the effect of genomic preselection, we generated a total of 50 replicates under control and genomic preselection schemes using the structures of the real data and pedigree from a medium-size cow population. A genetic trend of 15% of the genetic standard deviation was created for both schemes. In carrying out the analyses, we used 2 different heritabilities: 0.25 and 0.10. From the start of genomic preselection, all bulls were genomically preselected. Their MS deviations were inflated with a value corresponding to selection of the best 10% of genomically tested bull calves. For cows, the MS deviations were unaltered. The results revealed a clear underestimation of bulls' breeding values (BV) after genomic preselection started, as well as a notable deviation from zero both in true and estimated MS means. The software developed recently for the MS validation test already produces yearly MS means, and they can be used to devise an appropriate test. Mean squared true MS of genomically preselected bulls was clearly inflated. After correcting for the simulated preselection bias, the true genetic variance was smaller than the parametric value used to simulate BV, and also below the variance based on the estimated BV. Based on this study, the lower the trait's heritability, the stronger the bias in estimated BV and MS means and variances. Daughters of genomically preselected bulls had higher true and estimated BV compared with the control scheme and only slightly elevated MS means, but no effect on genetic variances was observed.

Validation of consistency of Mendelian sampling variance.

Experiences from international sire evaluation indicate that the multiple-trait across-country evaluation method is sensitive to changes in genetic variance over time. Top bulls from birth year classes with inflated genetic variance will benefit, hampering reliable ranking of bulls. However, none of the methods available today enable countries to validate their national evaluation models for heterogeneity of genetic variance. We describe a new validation method to fill this gap comprising the following steps: estimating within-year genetic variances using Mendelian sampling and its prediction error variance, fitting a weighted linear regression between the estimates and the years under study, identifying possible outliers, and defining a 95% empirical confidence interval for a possible trend in the estimates. We tested the specificity and sensitivity of the proposed validation method with simulated data using a real data structure. Moderate (M) and small (S) size populations were simulated under 3 scenarios: a control with homogeneous variance and 2 scenarios with yearly increases in phenotypic variance of 2 and 10%, respectively. Results showed that the new method was able to estimate genetic variance accurately enough to detect bias in genetic variance. Under the control scenario, the trend in genetic variance was practically zero in setting M. Testing cows with an average birth year class size of more than 43,000 in setting M showed that tolerance values are needed for both the trend and the outlier tests to detect only cases with a practical effect in larger data sets. Regardless of the magnitude (yearly increases in phenotypic variance of 2 or 10%) of the generated trend, it deviated statistically significantly from zero in all data replicates for both cows and bulls in setting M. In setting S with a mean of 27 bulls in a year class, the sampling error and thus the probability of a false-positive result clearly increased. Still, overall estimated genetic variance was close to the parametric value. Only rather strong trends in genetic variance deviated statistically significantly from zero in setting S. Results also showed that the new method was sensitive to the quality of the approximated reliabilities of breeding values used in calculating the prediction error variance. Thus, we recommend that only animals with a reliability of Mendelian sampling higher than 0.1 be included in the test and that low heritability traits be analyzed using bull data sets only.

Reducing bias in the dairy cattle single-step genomic evaluation by ignoring bulls without progeny.

The number of genotyped animals has increased rapidly creating computational challenges for genomic evaluation. In animal model BLUP, candidate animals without progeny and phenotype do not contribute information to the evaluation and can be discarded. In theory, genotyped candidate animal without progeny can bring information into single-step BLUP (ssGBLUP) and affect the estimation of other breeding values. We studied the effect of including or excluding genomic information of culled bull calves on genomic breeding values (GEBV) from ssGBLUP. In particular, GEBVs of genotyped bulls with daughters and GEBVs of young bulls selected into AI to be progeny tested (test bulls) were studied. The ssGBLUP evaluation was computed using Nordic test day (TD) model and TD data for the Nordic Red Dairy Cattle. The results indicate that genomic information of culled bull calves does not affect the GEBVs of progeny tested reference animals, but if genotypes of the culled bulls are used in the TD ssGBLUP, the genetic trend in the test bulls is considerably higher compared to the situation when genomic information of the culled bull calves is excluded. It seems that by discarding genomic information of culled bull calves without progeny, upward bias of GEBVs of test bulls is reduced.

Solving efficiently large single-step genomic best linear unbiased prediction models.

Single-step genomic BLUP (ssGBLUP) requires a dense matrix of the size equal to the number of genotyped animals in the coefficient matrix of mixed model equations (MME). When the number of genotyped animals is high, solving time of MME will be dominated by this matrix. The matrix is the difference of two inverse relationship matrices: genomic (G) and pedigree (A22 ). Different approaches were used to ease computations, reduce computing time and improve numerical stability. Inverse of A22 can be computed as A22-1=A22-A21A11-1A12 where Aij , i, j = 1,2, are sparse sub-matrices of A-1 , and numbers 1 and 2 refer to non-genotyped and genotyped animals, respectively. Inversion of A11 was avoided by three alternative approaches: iteration on pedigree (IOP), matrix iteration in memory (IM), and Cholesky decomposition by CHOLMOD library (CM). For the inverse of G, the APY (algorithm for proven and young) approach using Cholesky decomposition was formulated. Different approaches to choose the APY core were compared. These approaches were tested on a joint genetic evaluation of the Nordic Holstein cattle for fertility traits and had 81,031 genotyped animals. Computing time per iteration was 1.19 min by regular ssGBLUP, 1.49 min by IOP, 1.32 min by IM, and 1.21 min by CM. In comparison with the regular ssGBLUP, the total computing time decreased due to omitting the inversion of the relationship matrix A22 . When APY used 10,000 (20,000) animals in the core, the computing time per iteration was at most 0.44 (0.63) min by all the APY alternatives. A core of 10,000 animals in APY gave GEBVs sufficiently close to those by regular ssGBLUP but needed only 25% of the total computing time. The developed approaches to invert the two relationship matrices are expected to allow much higher number of genotyped animals than was used in this study.

Estimation of genetic (co)variances of Gompertz growth function parameters in pigs.

The objective of this study was to estimate genetic (co)variances for the Gompertz growth function parameters, asymptotic mature weight (A), the ratio of mature weight to birthweight (B) and rate of maturation (k), using alternative modelling approaches. The data set consisted of 51 893 live weight records from 10 201 growing pigs. The growth of each pig was modelled using the Gompertz model employing either a two-step fixed effect or mixed model approach or a one-step mixed model approach using restricted maximum likelihood for the estimation of genetic (co)variance. Heritability estimates for the Gompertz growth function parameters, A (0.40), B (0.69) and k (0.45), were greatest for the one-step approach, compared with the two-step fixed effects approach, A (0.10), B (0.33) and k (0.13), and the two-step mixed model approach, A (0.17), B (0.32) and k (0.18). Inferred genetic correlations (i.e. correlations of estimated breeding values) between growth function parameters within models ranged from -0.78 to 0.76, and across models ranged from 0.28 to 0.73 for parameter A, 0.75 to 0.88 for parameter B and 0.09 to 0.37 for parameter k. Correlations between predicted daily sire live weights based on the Gompertz growth curve parameters' estimated breeding values from 60 to 200 days of age between all three modelled approaches were moderately to strongly correlated (0.75 to 0.95). Results from this study provide heritability estimates for biologically interpretable parameters of pig growth through the quantification of genetic (co)variances, thereby facilitating the estimation of breeding values for inclusion in breeding objectives to aid in breeding and selection decisions.

Cow-specific diet digestibility predictions based on near-infrared reflectance spectroscopy scans of faecal samples.

This study was designed to obtain information on prediction of diet digestibility from near-infrared reflectance spectroscopy (NIRS) scans of faecal spot samples from dairy cows at different stages of lactation and to develop a faecal sampling protocol. NIRS was used to predict diet organic matter digestibility (OMD) and indigestible neutral detergent fibre content (iNDF) from faecal samples, and dry matter digestibility (DMD) using iNDF in feed and faecal samples as an internal marker. Acid-insoluble ash (AIA) as an internal digestibility marker was used as a reference method to evaluate the reliability of NIRS predictions. Feed and composite faecal samples were collected from 44 cows at approximately 50, 150 and 250 days in milk (DIM). The estimated standard deviation for cow-specific organic matter digestibility analysed by AIA was 12.3 g/kg, which is small considering that the average was 724 g/kg. The phenotypic correlation between direct faecal OMD prediction by NIRS and OMD by AIA over the lactation was 0.51. The low repeatability and small variability estimates for direct OMD predictions by NIRS were not accurate enough to quantify small differences in OMD between cows. In contrast to OMD, the repeatability estimates for DMD by iNDF and especially for direct faecal iNDF predictions were 0.32 and 0.46, respectively, indicating that developing of NIRS predictions for cow-specific digestibility is possible. A data subset of 20 cows with daily individual faecal samples was used to develop an on-farm sampling protocol. Based on the assessment of correlations between individual sample combinations and composite samples as well as repeatability estimates for individual sample combinations, we found that collecting up to three individual samples yields a representative composite sample. Collection of samples from all the cows of a herd every third month might be a good choice, because it would yield a better accuracy.

Modeling of daily body weights and body weight changes of Nordic Red cows.

Increased availability of automated weighing systems have made it possible to record massive amounts of body weight (BW) data in a short time. If the BW measurement is unbiased, the changes in BW reflect the energy status of the cow and can be used for management or breeding purposes. The usefulness of the BW data depends on the reliability of the measures. The noise in BW measurements can be smoothed by fitting a parametric or time series model into the BW measurements. This study examined the accuracy of different models to predict BW of the cows based on daily BW measurements and investigated the usefulness of modeling in increasing the value of BW measurements as management and breeding tools. Data included daily BW measurements, production, and intake from 230 Nordic Red dairy cows. The BW of the cows was recorded twice a day on their return from milking. In total, the data included 50,594 daily observations with 98,418 BW measurements. A clear diurnal change was present in the BW of the cows even if they had feed available 24 h. The daily average BW were used in the modeling. Five different models were tested: (1) a cow-wise fixed second-order polynomial regression model (FiX) including the exponential Wilmink term, (2) a random regression model with fixed and random animal lactation stage functions (MiX), (3) MiX with 13 periods of weighing added (PER), (4) natural cubic smoothing splines with 8 equally spaced knots (SPk8), and (5) spline model with no restriction on knots but a smoothing parameter corresponding to a fit of 5 degrees of freedom (SPdf5). In the original measured BW data, the within-animal variation was 6.4% of the total variance. Modeling decreased the within animal variation to levels of 2.9 to 5.1%. The smallest day-to-day variation and thereafter highest day-to-day repeatabilities were with PER and MiX models. The usability of modeled BW as energy balance (EB) indicator were evaluated by estimating relationships between EB, or EB indicators, and modeled BW change. In all cases the modeling increased the correlation and thus the reliability of the BW measurements. From all of the tested models, the best predictive value was attained by the random regression model with fixed and random animal lactation stage functions. Based on results, modeling of BW significantly increases the usefulness of BW as an EB predictor and management indicator.

Single-step genomic evaluation using multitrait random regression model and test-day data.

The objectives of this study were to evaluate the feasibility of use of the test-day (TD) single-step genomic BLUP (ssGBLUP) using phenotypic records of Nordic Red Dairy cows. The critical point in ssGBLUP is how genomically derived relationships (G) are integrated with population-based pedigree relationships (A) into a combined relationship matrix (H). Therefore, we also tested how different weights for genomic and pedigree relationships affect ssGBLUP, validation reliability, and validation regression coefficients. Deregressed proofs for 305-d milk, protein, and fat yields were used for a posteriori validation. The results showed that the use of phenotypic TD records in ssGBLUP is feasible. Moreover, the TD ssGBLUP model gave considerably higher validation reliabilities and validation regression coefficients than the TD model without genomic information. No significant differences were found in validation reliability between the different TD ssGBLUP models according to bootstrap confidence intervals. However, the degree of inflation in genomic enhanced breeding values is affected by the method used in construction of the H matrix. The results showed that ssGBLUP provides a good alternative to the currently used multi-step approach but there is a great need to find the best option to combine pedigree and genomic information in the genomic matrix.

Using the unified relationship matrix adjusted by breed-wise allele frequencies in genomic evaluation of a multibreed population.

The observed low accuracy of genomic selection in multibreed and admixed populations results from insufficient linkage disequilibrium between markers and trait loci. Failure to remove variation due to the population structure may also hamper the prediction accuracy. We verified if accounting for breed origin of alleles in the calculation of genomic relationships would improve the prediction accuracy in an admixed population. Individual breed proportions derived from the pedigree were used to estimate breed-wise allele frequencies (AF). Breed-wise and across-breed AF were estimated from the currently genotyped population and also in the base population. Genomic relationship matrices (G) were subsequently calculated using across-breed (GAB) and breed-wise (GBW) AF estimated in the currently genotyped and also in the base population. Unified relationship matrices were derived by combining different G with pedigree relationships in the evaluation of genomic estimated breeding values (GEBV) for genotyped and ungenotyped animals. The validation reliabilities and inflation of GEBV were assessed by a linear regression of deregressed breeding value (deregressed proofs) on GEBV, weighted by the reliability of deregressed proofs. The regression coefficients (b1) from GAB ranged from 0.76 for milk to 0.90 for protein. Corresponding b1 terms from GBW ranged from 0.72 to 0.88. The validation reliabilities across 4 evaluations with different G were generally 36, 40, and 46% for milk, protein, and fat, respectively. Unexpectedly, validation reliabilities were generally similar across different evaluations, irrespective of AF used to compute G. Thus, although accounting for the population structure in GBW tends to simplify the blending of genomic- and pedigree-based relationships, it appeared to have little effect on the validation reliabilities.

Comparison of multiplicative heterogeneous variance adjustment models for genetic evaluations.

Two heterogeneous variance adjustment methods and two variance models were compared in a simulation study. The method used for heterogeneous variance adjustment in the Nordic test-day model, which is a multiplicative method based on Meuwissen (J. Dairy Sci., 79, 1996, 310), was compared with a restricted multiplicative method where the fixed effects were not scaled. Both methods were tested with two different variance models, one with a herd-year and the other with a herd-year-month random effect. The simulation study was built on two field data sets from Swedish Red dairy cattle herds. For both data sets, 200 herds with test-day observations over a 12-year period were sampled. For one data set, herds were sampled randomly, while for the other, each herd was required to have at least 10 first-calving cows per year. The simulations supported the applicability of both methods and models, but the multiplicative mixed model was more sensitive in the case of small strata sizes. Estimation of variance components for the variance models resulted in different parameter estimates, depending on the applied heterogeneous variance adjustment method and variance model combination. Our analyses showed that the assumption of a first-order autoregressive correlation structure between random-effect levels is reasonable when within-herd heterogeneity is modelled by year classes, but less appropriate for within-herd heterogeneity by month classes. Of the studied alternatives, the multiplicative method and a variance model with a random herd-year effect were found most suitable for the Nordic test-day model for dairy cattle evaluation.