Estimating breeding values for feed efficiency in dairy cattle by regression on expected feed intake

The efficiency with which a dairy cow utilises feed for the various physiological and metabolic processes can be evaluated by metrics that contrast realised feed intake with expected feed intake. In this study, we presented a new metric - regression on expected feed intake (ReFI). This metric is based on the idea of regressing DM intake (DMI) on expected DMI using a random regression model, where energy requirement formulations are applied for the calculation of expected DMI covariables. We compared this new metric with the metrics residual feed intake (RFI) and genetic residual feed intake (gRFI), by applying them on 18 581 feed efficiency records from 654 primiparous Nordic Red dairy cows. We estimated variance components for the three metrics and their respective genetic correlations with intake and production traits. In addition, we examined the phenotypes of superior cows. With ReFI, we estimated for feed efficiency a higher genetic variation (4.7%) and heritability (0.23) compared to applying RFI or gRFI. The ReFI metric was genetically uncorrelated with DMI and negatively correlated within energy-corrected milk (ECM), whereas the RFI metric was genetically positively correlated with DMI and metabolic BW. The gRFI metric was genetically positively correlated with DMI and uncorrelated with energy sink traits. Overall, the estimated SE were large. The ReFI metric resulted in a different ranking of cows compared to those based on RFI or gRFI and was superior in selecting the most efficient animals. When the selection was based on ReFI breeding values, then the 10% most efficient cows produced 12.3% more ECM per unit metabolisable energy intake, whereas the corresponding values were only 4.3 or 5.9% when using RFI or gRFI breeding values, respectively. Based on ReFI, superior cows had also higher milk production, whereas based on RFI or gRFI milk production either decreased or was unaffected, respectively. The superiority of the ReFI metric in selecting efficient cows was due to a better modelling of the expected feed intake. The ReFI metric simplified modelling of feed utilisation efficiency in dairy cattle and resulted in breeding values that are equal to percentages of feed saved.

Genetic analyses of metabolic body weight, carcass weight and body conformation traits in Nordic dairy cattle

Improving feed efficiency in dairy cattle by animal breeding has started in the Nordic countries. One of the two traits included in the applied Saved feed index is called maintenance and it is based on the breeding values for metabolic BW (MBW). However, BW recording based on heart girth measurements is decreasing and recording based on scales is increasing only slowly, which may weaken the maintenance index in future. Therefore, the benefit of including correlated traits, like carcass weight and conformation traits, is of interest. In this study, we estimated genetic variation and genetic correlations for eight traits describing the energy requirement for maintenance in dairy cattle including: first, second and third parity MBW based on heart girth measurements, carcass weight (CARW) and predicted MBW (pMBW) based on predicted slaughter weight, and first parity conformation traits stature (ST), chest width (CW) and body depth (BD). The data consisted of 21329 records from Finnish Ayrshire and 9780 records from Holstein cows. Heritability estimates were 0.44, 0.53, 0.56, 0.52, 0.54, 0.60, 0.17 and 0.26 for MBW1, MBW2, MBW3, CARW, pMBW, ST, CW and BD, respectively. Estimated genetic correlations among MBW traits were strong (>0.95). Genetic correlations between slaughter traits (CARW and pMBW) and MBW traits were higher (from 0.77 to 0.90) than between conformation and MBW traits (from 0.47 to 0.70). Our results suggest that including information on carcass weight and body conformation as correlated traits into the maintenance index is beneficial when direct BW measurements are not available or are difficult or expensive to obtain.

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.

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.

Genetic correlations between energy status indicator traits and female fertility in primiparous Nordic Red Dairy cattle

Inclusion of feed efficiency traits into the dairy cattle breeding programmes will require considering early lactation energy status to avoid deterioration in health and fertility of dairy cows. In this regard, energy status indicator (ESI) traits, for example, blood metabolites or milk fatty acids (FAs), are of interest. These indicators can be predicted from routine milk samples by mid-IR reflectance spectroscopy (MIR). In this study, we estimated genetic variation in ESI traits and their genetic correlation with female fertility in early lactation. The data consisted of 37 424 primiparous Nordic Red Dairy cows with milk test-day records between 8 and 91 days in milk (DIM). Routine test-day milk samples were analysed by MIR using previously developed calibration equations for blood plasma non-esterified FA (NEFA), milk FAs, milk beta-hydroxybutyrate (BHB) and milk acetone concentrations. Six ESI traits were considered and included: plasma NEFA concentration (mmol/l) either predicted by multiple linear regression including DIM, milk fat to protein ratio (FPR) and FAs C10:0, C14:0, C18:1 cis-9, C14:0 * C18:1 cis-9 (NEFAFA) or directly from milk MIR spectra (NEFAMIR), C18:1 cis-9 (g/100 ml milk), FPR, BHB (mmol/l milk) and acetone (mmol/l milk). The interval from calving to first insemination (ICF) was considered as the fertility trait. Data were analysed using linear mixed models. Heritability estimates varied during the first three lactation months from 0.13 to 0.19, 0.10 to 0.17, 0.09 to 0.14, 0.07 to 0.10, 0.13 to 0.17 and 0.13 to 0.18 for NEFAMIR, NEFAFA, C18:1 cis-9, FPR, milk BHB and acetone, respectively. Genetic correlations between all ESI traits and ICF were from 0.18 to 0.40 in the first lactation period (8 to 35 DIM), in general somewhat lower (0.03 to 0.43) in the second period (36 to 63 DIM) and decreased clearly (-0.02 to 0.19) in the third period (64 to 91 DIM). Our results indicate that genetic variation in energy status of cows in early lactation can be determined using MIR-predicted indicators. In addition, the markedly lower genetic correlation between ESI traits and fertility in the third lactation month indicated that energy status should be determined from the first test-day milk samples during the first 2 months of lactation.

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.

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.

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.

Efficient single-step genomic evaluation for a multibreed beef cattle population having many genotyped animals

An equivalent computational approach called ssGTBLUP was formulated for the original single-step GBLUP (ssGBLUP). In ssGTBLUP, the genomic relationship matrix has the form = ' + , where the (centered and scaled) marker matrix has size x (numbers of genotypes and markers), and the matrix can be easily inverted. The inverse can be written as = - ' where is an by matrix. When the preconditioned conjugate gradient (PCG) method is used to solve the mixed model equations, a matrix vector product needs to be computed. In ssGBLUP, this requires multiplications, but in ssGTBLUP, the product ' has 2 multiplications and has multiplications with the constant independent of or . In an approximate approach called ssGTBLUP(p), the eigendecomposition of ' is used to reduce the number of rows in the matrix. Here, p is the percentage of total variance explained by the accepted eigenvalues. The objective of this study was to compare the performance of ssGBLUP, ssGTBLUP, ssGTBLUP(p), and the APY (algorithm for proven and young) method. In APY, the core had 50,000 (APY50K), 30,000 (APY30K), or 10,000 (APY10K) animals. The approaches were tested on the Irish beef carcass conformation genetic evaluation which has a heterogeneous multibreed population. The pedigree had 13.3 million animals. There were = 54,620 markers available from = 163,277 genotyped animals. For genotyped animals, the correlations of breeding values between ssGBLUP and ssGTBLUP(p) for the 11 traits in the model ranged from 0.999-1.000 for p = 99, 0.998-1.000 for p = 98, and 0.992-0.998 for p = 95 but were 0.994-1.000 for APY50K, 0.969-0.997 for APY30K, and 0.899-0.967 for APY10K. Computing times per iteration were 4.43, 3.30, 2.69, 2.29, 1.55, 1.76, 1.27, and 0.55 min for ssGBLUP, ssGTBLUP, ssGTBLUP(99), ssGTBLUP(98), ssGTBLUP(95), APY50K, APY30K, and APY10K, respectively. The ssGTBLUP(p) approach allowed a well-defined approximation to ssGBLUP and fast computations.

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.

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.

The estimation of genomic relationships using breedwise allele frequencies among animals in multibreed populations

Different approaches of calculating genomic measures of relationship were explored and compared with pedigree relationships (A) within and across base breeds in a crossbreed population, using genotypes for 38,194 loci of 4,106 Nordic Red dairy cattle. Four genomic relationship matrices (G) were calculated using either observed allele frequencies (AF) across breeds or within-breed AF. The G matrices were compared separately when the AF were estimated in the observed and in the base population. Breedwise AF in the current and base population were estimated using linear regression models of individual genotypes on breed composition. Different G matrices were further used to predict direct estimated genomic values using a genomic BLUP model. Higher variability existed in the diagonal elements of G across breeds (standard deviation=0.06, on average) compared with A (0.01). The use of simple observed AF across base breeds to compute G increased coefficients for individuals in distantly related populations. Estimated breedwise AF reduced differences in coefficients similarly within and across populations. The variability of the current adjusted G matrix decreased from 0.055 to 0.035 when breedwise AF were estimated from the base breed population. The direct estimated genomic values and their validation reliabilities were, however, unaffected by AF used to compute G when estimated with a genomic BLUP model, due to inclusion of breed means in the model. In multibreed populations, G adjusted with breedwise AF from the founder population may provide more consistency among relationship coefficients between genotyped and ungenotyped individuals in an across-breed single-step evaluation.

Use of random regression model as an alternative for multibreed relationship matrix

A random regression model is presented as an approximation for multibreed variance model. The approximation is derived using the splitted multibreed model where the single breeding value is split to the breed specific and their segregation terms. The random regression model allows extending the multibreed information easily to genomic data models. We present the approach by a simple example.

Genetic associations of test-day fat:protein ratio with milk yield, fertility, and udder health traits in Nordic Red cattle

Interest is growing in finding indicator traits for the evaluation of nutritional or tissue energy status of animals directly at the individual animal level. The development and subsequent use of such traits in practice demands a clear understanding of the genetic and phenotypic associations with the various production and functional traits. In this study, the relationships during lactation between milk fat:protein ratio (FPR) and production and functional traits were estimated for Nordic Red cattle, in which published information is scarce. The objectives of this study were to estimate genetic associations of FPR with milk yield (MY), fertility, and udder health traits during different stages of lactation. Traits included in the analyses were MY, 4 fertility traits-days from calving to insemination (DFI), days open (DO), number of inseminations (NI), and nonreturn rate to 56 d (NRR)-and 2 udder health traits-test-day somatic cell score (SCS) and clinical mastitis (CM). Data were from a total of 22,422 first-lactation cows. Random regression models were used to estimate genetic parameters and associations between traits. The mean FPR in first-lactation cows was 1.28 and ranged from 1.25 to 1.45. During first lactation, the heritability of FPR ranged from 0.14 to 0.25. Genetic correlations between FPR and MY in early lactation (until 50 d in milk) were positive and ranged from 0.05 to 0.22; later in lactation, they were close to zero or negative, indicating that cows may have come out of the negative state of energy balance. The strength of genetic associations between FPR and fertility traits varied during lactation. In early lactation, correlations between FPR and the interval fertility traits DFI and DO were positive and ranged from 0.14 to 0.28. Genetic correlations between FPR and the udder health traits SCS and CM in early lactation ranged from 0.09 to 0.20. Milk fat:protein ratio is a heritable trait and easily available from routine milk-recording schemes. It can be used as a low-cost monitoring tool of poor health and fertility in the most critical phases of lactation and as an important indicator trait to improve robustness in dairy cows through selection.

Different methods to calculate genomic predictions--comparisons of BLUP at the single nucleotide polymorphism level (SNP-BLUP), BLUP at the individual level (G-BLUP), and the one-step approach (H-BLUP)

Several strategies to use genomic data in predictions have been proposed. The aim of this study was to compare different genomic prediction methods. The response variables used in the genomic predictions were deregressed proofs, which were derived from 2 estimated breeding value (EBV) data sets. The full EBV data set from March 2010 included the EBV for production and mastitis traits for all Nordic red bulls. The reduced data set included the same animals as the full data set, but the EBV were predicted from a data set that excluded the last 5 yr of observations. Genomic predictions were obtained using different BLUP models: BLUP at the single nucleotide polymorphism level (SNP-BLUP), BLUP at the individual level (G-BLUP), and the one-step approach (H-BLUP). For the selection candidate bulls, the SNP-BLUP and G-BLUP models gave the same direct genomic breeding values (e.g., correlation of direct genomic breeding values between SNP-BLUP and G-BLUP for protein was 0.99), but slightly different from genomic EBV obtained from H-BLUP (correlations of SNP-BLUP or G-BLUP with H-BLUP were about 0.96). For all traits, SNP-BLUP and G-BLUP gave the same validation reliability, whereas H-BLUP led to slightly higher reliability. Therefore, the results support a slight advantage of using H-BLUP for genomic evaluation.

Change in genetic correlation due to selection using animal model evaluation

SUMMARY

Monte Carlo simulation and analytical calculations were used to study the effect of selection on genetic correlation between two traits. The simulated breeding program was based on a closed adult multiple ovulation and embryo transfer nucleus breeding scheme. Selection was on an index calculated using multi-trait animal model (AM). Analytical formulae applicable to any evaluation method were derived to predict change in genetic (co)variance due to selection under multi-trait selection using different evaluation methods. Two formulae were investigated, one assuming phenotypic selection and the other based on a recursive two-generation AM selection index. The recursive AM method approximated information due to relatives by a relationship matrix of two generations. Genetic correlation after selection was compared under different levels of initial genetic and environmental correlations with two different selection criteria. Changes in genetic correlation were similar in simulation and analytical predictions. After one round of selection the recursive AM method and the simulation gave similar predictions while the phenotypic selection predicted usually more change in genetic correlation. After several rounds of selection both analytical formulae predicted more change in genetic correlation than the simulation. ZUSAMMENFASSUNG: Änderung der genetischen Korrelation bei Selektion mit einem Tiermodell Der Selektionseffekt auf die genetische Korrelation zwischen zwei Merkmalen wurde mit Hilfe von Monte Carlo-Simulation und analytischen Berechnungen untersucht. Ein geschlossener Adulter - MOET (Multiple Ovulation and Embryo Transfer) Zuchtplan wurde simuliert. Die Selektion gründete sich auf einen Index, der die Zuchtwertschätzung des Mehrmerkmals-Tiermodells benutzte. Analytische Formeln für die Voraussage der Änderung der genetischen (Ko)varianz unter multivariate Selektion für verschiedene Zuchtwertschätzungsmethode wurden deduziert. Zwei Formeln wurden studiert, die erste nahm phänotypische Auswahl an und die andere gründete sich auf ein wiederholte Mehrmerkmals-Tiermodell von zwei Generationen. Das wiederholte Mehrmerkmals-Tiermodell approximierte die Information aus den Verwandten mit Hilfe einer Verwandtschaftsmatrix der zwei Generationen. Die genetische Korrelation nach der Selektion aus der Simulation und den analytischen Formeln wurde mit verschiedenen reellen genetischen und umweltbedingten Korrelationen mit zwei Selektionskriterien verglichen. Sie änderte sich ähnlich bei Simulation und analytischen Formeln. Nach einem Selektionszyklus kamen das wiederholte Mehrmerkmals-Tiermodell und die Simulation zu gleichen Voraussagen, aber die phänotypische Selektion sagte mehr Änderung voraus. Nach mehreren selektierten Generationen sagten die beiden analytischen Formeln mehr Änderung in der genetischen Korrelation voraus als die Simulation. RÉSUMÉ: Changement de corrélation génétique du à la sélection en utilisant une évaluation de type modèle animal Une simulation Monte Carlo et des calculs analytiques ont été utilisés pour étudier l'effet de la sélection sur la corrélation génétique entre deux caractères. Le programme de sélection simulé a été basé sur le schéma d'un noyau de sélection adulte et fermé avec superovulation et transfert embryonnaire. La sélection portait sur un indice calculé à partir d'un modèle animal multicaractères (AM). Des formules analytiques applicables à n'importe quelle méthode d'évaluation ont été développées pour prédire le changement de (co)variance génétique du à la sélection multicaractères en utilisant différentes méthodes d'évaluation. Deux formules ont été étudiées, l'une supposant une sélection phénotypique et l'autre basée sur un index de sélection de type AM sur deux générations. La méthode AM récurrente prenait en compte l'information des apparentés de manière approximative à travers la matrice de parenté sur deux générations. La corrélation génétique après sélection a été comparée à différents niveaux de corrélations génétique et environnementale pour deux critères de sélection différents. Les changements de corrélation génétique étaient similaires dans les simulations et les prédictions analytiques. Après un cycle de sélection, la méthode récurrente AM et la simulation donnaient les prédictions similaires alors que la sélection phénotypique prédisait habituellement des changements de corrélations génétiques plus importants. Après plusieurs cycles de sélection, les deux formules analytiques prédisaient des changements de corrélation plus importants que la simulation. RÉSUMÉ: Cambio en la correlación genética debido a selección usando evaluaciones con modelo animal Se estudió el efecto de la selección sobre la correlación genética entre dos caracteres utilizando simulación de Monte Carlo y cálculos analíticos. El esquema de selección simulado estuvo basado en un núcleo adulto y cerrado de ovulación multiple y transferencia de embriones. El criterio de selección fue un indice calculado a partir de un modelo animal multicarácter (AM). Se derivaron fórmulas analíticas aplicables a cualquier método de evaluación para predecir cambios debidos a selección en las (co)varianzas genéticas bajo selección multicarácter usando distintos métodos de valoración. Se investigaron dos fórmulas, una que asumía selección fenotípica y la otra basada en un índice de selección AM recurrente con dos generaciones. El método AM recurrente aproximaba la información de parientes a través de una matriz de relaciones aditivas que contemplaba dos generaciones. La correlación genética tras la selección fue comparada bajo distintos niveles de correlación genética y ambiental iniciales con dos criterios de selección diferentes. Los cambios en correlatión genética fueron similares en las predicciones analíticas y con simulación. Tras un ciclo de selección, el método AM recurrente y la simulación produjeron predicciones similares mientras que la selección fenotípica predijo, generalmente, más cambio en la correlación genética. Después de varios ciclos de selección, las dos fórmulas analíticas predijeron más cambios en la correlación genética que la simulación.

Across breed multi-trait random regression genomic predictions in the Nordic Red dairy cattle

The current study evaluates reliability of genomic predictions in selection candidates using multi-trait random regression model, which accounts for interactions between marker effects and breed of origin in the Nordic Red dairy cattle (RDC). The population structure of the RDC is admixed. Data consisted of individual animal breed proportions calculated from the full pedigree, deregressed proofs (DRP) of published estimated breeding values (EBV) for yield traits and genotypic data for 37,595 single nucleotide polymorphic markers. The analysed data included 3330 bulls in the reference population and 812 bulls that were used for validation. Direct genomic breeding values (DGV) were estimated using the model under study, which accounts for breed effects and also with GBLUP, which assume uniform population. Validation reliability was calculated as a coefficient of determination from weighted regression of DRP on DGV (rDRP,DGV 2), scaled by the mean reliability of DRP. Using the breed-specific model increased the reliability of DGV by 2 and 3% for milk and protein, respectively, when compared to homogeneous population GBLUP. The exception was for fat, where there was no gain in reliability. Estimated validation reliabilities were low for milk (0.32) and protein (0.32) and slightly higher (0.42) for fat.

Employing a Monte Carlo algorithm in expectation maximization restricted maximum likelihood estimation of the linear mixed model

Multiple-trait and random regression models have multiplied the number of equations needed for the estimation of variance components. To avoid inversion or decomposition of a large coefficient matrix, we propose estimation of variance components by Monte Carlo expectation maximization restricted maximum likelihood (MC EM REML) for multiple-trait linear mixed models. Implementation is based on full-model sampling for calculating the prediction error variances required for EM REML. Performance of the analytical and the MC EM REML algorithm was compared using a simulated and a field data set. For field data, results from both algorithms corresponded well even with one MC sample within an MC EM REML round. The magnitude of the standard errors of estimated prediction error variances depended on the formula used to calculate them and on the MC sample size within an MC EM REML round. Sampling variation in MC EM REML did not impair the convergence behaviour of the solutions compared with analytical EM REML analysis. A convergence criterion that takes into account the sampling variation was developed to monitor convergence for the MC EM REML algorithm. For the field data set, MC EM REML proved far superior to analytical EM REML both in computing time and in memory need.

Genomic prediction for Nordic Red Cattle using one-step and selection index blending

This study investigated the accuracy of direct genomic breeding values (DGV) using a genomic BLUP model, genomic enhanced breeding values (GEBV) using a one-step blending approach, and GEBV using a selection index blending approach for 15 traits of Nordic Red Cattle. The data comprised 6,631 bulls of which 4,408 bulls were genotyped using Illumina Bovine SNP50 BeadChip (Illumina, San Diego, CA). To validate reliability of genomic predictions, about 20% of the youngest genotyped bulls were taken as test data set. Deregressed proofs (DRP) were used as response variables for genomic predictions. Reliabilities of genomic predictions in the validation analyses were measured as squared correlations between DRP and genomic predictions corrected for reliability of DRP, based on the bulls in the test data sets. A set of weighting (scaling) factors was used to construct the combined relationship matrix among genotyped and nongenotyped bulls for one-step blending, and to scale DGV and its expected reliability in the selection index blending. Weighting (scaling) factors had a small influence on reliabilities of GEBV, but a large influence on the variation of GEBV. Based on the validation analyses, averaged over the 15 traits, the reliability of DGV for bulls without daughter records was 11.0 percentage points higher than the reliability of conventional pedigree index. Further gain of 0.9 percentage points was achieved by combining information from conventional pedigree index using the selection index blending, and gain of 1.3 percentage points was achieved by combining information of genotyped and nongenotyped bulls simultaneously applying the one-step blending. These results indicate that genomic selection can greatly improve the accuracy of preselection for young bulls in Nordic Red population, and the one-step blending approach is a good alternative to predict GEBV in practical genetic evaluation program.

Direct and maternal genetic effects on first litter size, maturation age, and animal size in Finnish minks

Variance components were estimated for maturing age, first litter size, and animal size in Finnish minks. The fitted animal models had direct genetic and maternal genetic effects, litter effects, and maternal environmental effects. Multivariate analysis was performed to determine covariances between the traits. Maternal effects represented a significant source of phenotypic variance in the maturation age and animal size. For litter size, maternal effects were not as clear. Moreover, in maturation age and animal size, the covariance between the direct additive effect and the maternal additive effect was negative. In addition, litter effect variances were larger than maternal variances for all traits. Therefore, it is crucial to also estimate environmental effects common to littermates for these traits. Direct heritability and the response to selection are overestimated, especially for maturation age and also for animal size, when maternal and common litter effects are not considered.

Use of Herd Solutions from a Random Regression Test-Day Model for Diagnostic Dairy Herd Management

In a random regression test-day model, environmental effects in addition to individual animal factors can be included and analyzed. Moreover, instead of herd-year classification of the management groups, the herd-test-day classification within the model better accounts for month-to-month short-term environmental variation in production and somatic cell count (SCC) traits. The herd management levels of milk yield (milk deviation from whole-country mean, kilograms/day), protein and fat concentration (protein and fat deviation, %), and SCC (SCC deviation, 1,000 cells/mL) are used in the dairy herd management Web application "Maitoisa" (in English, "Milky"). This management tool helps to recognize several management problems. For recognition of systematic patterns and single unusual test-days, a monthly time-trend analysis was developed to smooth the random fluctuations and display the yearly production pattern. In addition to analyzing single test-day deviations from the mean, modeled herd solutions assist users in identifying repeated phenomena and enable the forecasting of the management pattern for the subsequent year. The solutions are displayed either as tables or graphs plotted by calendar months. In addition to management effects of the farmer's own herd, he or she can request country or region percentiles to be displayed in the graphs. The Web service has been offered to farmers and dairy advisors since 2001, and it has proved to be a powerful tool for herd monitoring and planning.

Genetic evaluation of somatic cell score in dairy cattle considering first and later lactations as two different but correlated traits

A test-day (TD) random regression model (RRM) was described for the genetic evaluation of somatic cell score (SCS) where first and later lactations were considered as two different but correlated traits. A two-step covariance function procedure was used to estimate variance-covariances and associated genetic parameters. Analysis of estimated breeding values (EBV), ranking of top bulls and cows and some computational aspects were used to compare RRM with TD repeatability model (RPM) and lactation average model (LAM). Residuals were analysed to assess the relative fit of TD models. Comparison between RRM and RPM showed that RRM has lower mean squared error and gave better fit to the data. For young bulls and cows, the standard deviation (SD) of EBVs was highest for RRM and lowest for LAM implying efficient utilization of information on SCS, in terms of revealing more genetic variation. A much lower correlation of EBVs ranging from 0.80 to 0.92 and significant re-ranking of top bulls and cows were observed between RRM and LAM. The lower across-lactation correlation between RRM and LAM indicated that LAM is directed to give more weight to first lactation breeding values. The RRM, where SCS in the first and later lactations was considered as two different but correlated traits was able to make effective use of available information on young bulls and cows, and could offer an opportunity to breeders to utilize EBVs for first and later lactations.

Feed efficiency of rainbow trout can be improved through selection: Different genetic potential on alternative diets1

To assess the genetic potential for selection of increased feed efficiency in rainbow trout (Oncorhynchus mykiss), we estimated the heritabilities and correlations for BW, daily weight gain (DG), and daily feed intake (DFI). Body weight was recorded 5 times, and DG and DFI 3 times during a feeding trial lasting 22 mo. To test the hypothesis that phenotypic and genetic parameters were influenced by a nutritional environment, fish were fed either a modern normal protein diet (NP, 40 to 45% protein and 30 to 33% lipid) or an alternative high protein diet (HP, 50 to 56% protein, 20 to 24% lipid) in a split-family design. Results showed that there were no large differences in heritabilities between the diets. Average heritability for DFI over both diets and different fish ages was low (average h2 = 0.10), indicating that modest genetic changes in response to selection can be obtained. Average heritabilities for BW and DG over both diets and different fish ages were 0.28 and 0.33, respectively. The NP diet enabled fish to express a wide range of BW, as shown by the increased coefficients of phenotypic variation for BW. Fish fed the HP diet showed increased phenotypic variation for DFI in > 750-g fish. On the NP diet, genetic correlations of DFI with DG and BW were very strong for 750- to 2,000-g fish. In contrast, on the HP diet, the respective correlations were moderate to low, revealing more genetic potential to change growth and feed intake simultaneously in opposite directions. An analysis of the predicted selection responses showed that selection solely for high DG improved feed efficiency as a correlated genetic response. Simultaneous selection for high DG and reduced DFI, in turn, may increase genetic gain in feed efficiency by a factor of 1.2 compared with selection solely for DG. However, variation for growth and feed intake and the relationships between these traits were different in different nutritional environments, leading to divergent genetic responses on the alternative diets.

Genetic and Phenotypic Relationships Among Milk Yield and Somatic Cell Count Before and After Clinical Mastitis

This paper studies whether cows with originally lower somatic cell count (SCC) are more susceptible to clinical mastitis (CM) than cows with higher somatic cell count, and evaluates the correlations between CM, SCC, and milk yield. Data were extracted from the Finnish national milk-recording database and from the health recording system. First and second lactation records of 87,861 Ayrshire cows calving between January 1998 and December 2000 were included. Traits studied were incidence of CM, test-day SCC, and test-day milk yield before and following CM. Genetic parameters were estimated using multitrait REML with a sire model. Results did not indicate that cows with genetically low SCC would be more susceptible to CM. The genetic correlation between CM in the first and second lactation was reasonably high (0.73), suggesting that susceptibility to mastitis remains similar across lactations. The genetic correlation between CM and milk yield traits was positive (from 0.38 to 0.56), confirming the genetic antagonism between production and udder health traits. The genetic correlation between SCC and milk was positive in the first lactation, but negative, or near zero in the second lactation. This indicates that breeding for lower SCC might not affect milk production in later lactations. The results of this study support the use of SCC as an indicator of mastitis and a tool for selection for mastitis resistance.

Genetic associations of prolificacy with performance, carcass, meat quality, and leg conformation traits in the Finnish Landrace and Large White pig populations

The objective of this study was to estimate genetic associations of prolificacy traits with other traits under selection in the Finnish Landrace and Large White populations. The prolificacy traits evaluated were total number of piglets born, number of stillborn piglets, piglet mortality during suckling, age at first farrowing, and first farrowing interval. Genetic correlations were estimated with two performance traits (ADG and feed:gain ratio), with two carcass traits (lean percent and fat percent), with four meat quality traits (pH and L* values in longissimus dorsi and semimembranosus muscles), and with two leg conformation traits (overall leg action and buck-kneed forelegs). The data contained prolificacy information on 12,525 and 10,511 sows in the Finnish litter recording scheme and station testing records on 10,372 and 9,838 pigs in Landrace and Large White breeds, respectively. The genetic correlations were estimated by the restricted maximum likelihood method. The most substantial correlations were found between age at first farrowing and lean percent (0.19 in Landrace and 0.27 in Large White), and fat percent (-0.26 in Landrace and -0.18 in Large White), and between number of stillborn piglets and ADG (-0.38 in Landrace and -0.25 in Large White) and feed:gain (0.27 in Landrace and 0.12 in Large White). The correlations are indicative of the benefits of superior growth for piglets already at birth. Similarly, the correlations indicate that age at first farrowing is increasing owing to selection for carcass lean content. There was also clear favorable correlation between performance traits and piglet mortality from birth to weaning in Large White (r(g) was -0.43 between piglet mortality and ADG, and 0.42 between piglet mortality and feed:gain), but not in Landrace (corresponding correlations were 0.26 and -0.22). There was a general tendency that prolificacy traits were favorably correlated with performance traits, and unfavorably with carcass lean and fat percents, whereas there were no clear associations between prolificacy and meat quality or leg conformation. In conclusion, accuracy of estimated breeding values may be improved by accounting for genetic associations between prolificacy, carcass, and performance traits in a multitrait analysis.

Strategies for estimating the parameters needed for different test-day models

Currently, most analyses of parameters in test-day models involve two types of models: random regression, where various functions describe variability of (co)variances with regard to days in milk, and multiple traits, where observations in adjacent days in milk are treated as one trait. The methodologies used for estimation of parameters included Bayesian via Gibbs sampling, and REML in the form of derivative-free, expectation-maximization, or average-information algorithms. The first method is simpler and uses less memory but may need many rounds to produce posterior samples. In REML, however, the stopping point is well established. Because of computing limitations, the largest estimations of parameters were on fewer than 20,000 animals. The magnitude and pattern of heritabilities varied widely, which could be caused by simplifications in the model, overparameterization, small sample size, and unrepresentative samples. Patterns of heritability differ among random regression and multiple-trait models. Accurate parameters for large multi-trait random regression models may be difficult to obtain at the present time. Parameters that are sufficiently accurate in practice may be obtained outside the complete prediction model by a constructive approach, where parameters averaged over the lactation would be combined with several typical curves for (co)variances for days in milk. Obtained parameters could be used for any model, and could also aid in comparison of models.

Solving large test-day models by iteration on data and preconditioned conjugate gradient

A preconditioned conjugate gradient method was implemented into an iteration on a program for data estimation of breeding values, and its convergence characteristics were studied. An algorithm was used as a reference in which one fixed effect was solved by Gauss-Seidel method, and other effects were solved by a second-order Jacobi method. Implementation of the preconditioned conjugate gradient required storing four vectors (size equal to number of unknowns in the mixed model equations) in random access memory and reading the data at each round of iteration. The preconditioner comprised diagonal blocks of the coefficient matrix. Comparison of algorithms was based on solutions of mixed model equations obtained by a single-trait animal model and a single-trait, random regression test-day model. Data sets for both models used milk yield records of primiparous Finnish dairy cows. Animal model data comprised 665,629 lactation milk yields and random regression test-day model data of 6,732,765 test-day milk yields. Both models included pedigree information of 1,099,622 animals. The animal model ¿random regression test-day model¿ required 122 ¿305¿ rounds of iteration to converge with the reference algorithm, but only 88 ¿149¿ were required with the preconditioned conjugate gradient. To solve the random regression test-day model with the preconditioned conjugate gradient required 237 megabytes of random access memory and took 14% of the computation time needed by the reference algorithm.

Relationships between clinical mastitis, somatic cell score, and production for the first three lactations of Finnish Ayrshire

Data on 23,196 cows were extracted from the Finnish system for recording health data and merged with information on SCS and 305-d milk production to study 1) the genetic and phenotypic correlations of clinical mastitis (within 150 d postpartum) and SCS across the first three lactations and 2) the genetic relationships between the traits for individual lactations. (Co)variance components were estimated using linear multitrait REML and the expectation-maximization algorithm. Heritability estimates for separate lactations were distinctly higher for somatic cell score (0.14 to 0.19) than for clinical mastitis (0.02 to 0.05). Genetic correlations of the same traits among different lactations were positive and moderate to high, suggesting that, in practice, clinical mastitis and SCS can be considered as the same traits for different lactations. Genetic correlations of clinical mastitis and SCS varied from 0.37 for first lactation to 0.68 for third lactation, implying that clinical mastitis and SCC monitor different aspects of udder health. A clear, antagonistic genetic association existed between clinical mastitis and milk production, but the genetic correlation of SCS and milk production did not differ from 0.

Genetic variation of residual feed consumption in a selected Finnish egg-layer population

The purpose of the study was to estimate the heritability of residual feed consumption (RFC) and the genetic correlations between RFC and economically important traits. The genetic progress after four generations of selection for RFC and the changes in economically important traits were also investigated. A selection experiment for RFC was carried out from 1983 to 1987. The total data consisted of 3,750 birds and 2,661 records. The (co)variance components were calculated using derivative-free bivariate animal model restricted maximum likelihood (REML). Breeding values were estimated for calculating genetic progress in RFC and correlated responses in the other traits. The heritability of RFC calculated from the whole recorded period (16 to 42 wk) and using all 2,661 records was .46 (+/- .04). The genetic correlations between RFC and egg mass, number of eggs, egg weight, and body weight were not significant. The genetic correlation between RFC and feed consumption was .50 (+/- .04). The breeding value estimates indicated a moderate genetic progress in RFC due to selection. Feed consumption was decreased and body weight gain showed reduction in the last two generations. No change could be found in egg mass, number of eggs, egg weight, age at first egg, or body weight.

Clinical ketosis: phenotypic and genetic correlations between occurrences and with milk yield

The repeatability and heritability of ketosis were estimated using data from 28,277 Finnish Ayrshire cows. A four-trait linear model including community-year, calving age and month, genetic group, and random sire effects was used to describe first and second lactation milk yields and veterinary diagnoses of ketosis. Variance components were estimated using REML. The disease traits were also analyzed with a categorical model including the same effects except that community and year were separate factors. Variance components were estimated with marginal maximum likelihood. Genetic relationships between 339 sires analyzed were included in models. The phenotypic correlation between the first and second lactation was defined as a repeatability of trait. The lactational incidence risk of ketosis was .05 in both the first and the second lactation. Average milk production was 4956 and 5547 kg in the first and second lactations, respectively. Estimates of heritabilities were .09 and .07 for ketosis and .23 and .19 for milk in the first and second lactations, respectively. Genetic correlations between first and second lactation recordings were .64 for ketosis and .93 for milk. Repeatabilities between subsequent lactations were .36 (.13 in linear analysis) for ketosis and .68 for milk. In the first lactation, genetic relationship between milk yield and ketosis was unfavorable, but in the second lactation ketosis and milk yield were genetically and phenotypically unrelated.

Simulation study on covariance component estimation for two binary traits in an underlying continuous scale

The usefulness of the variance and covariance component estimation methods based on a threshold model was studied in a multiple-trait situation with two binary traits. Estimation equations that yield marginal maximum likelihood estimates of variance components on the underlying continuous variable scale and point estimates of location parameters with empirical Bayesian properties are described. Methods were tested on simulated data sets that were generated to exhibit three different incidences, 25, 15, and 5%. Results were compared with analyses of the same data sets with a REML method based on normal distribution and a linear model. Heritabilities and residual correlations calculated from discrete observations were transformed to underlying parameters. In estimation of heritabilities, all methods performed equally well at all incidence levels and with no detectable bias. As suggested by threshold theory, the genetic correlation was accurately estimated directly from the observations without any need of correction for incidence. Marginal maximum likelihood estimates of genetic correlations were similar to linear model estimates; discrepancies from the true parameters were consistent with both methods. In estimation of residual correlations, the method with the linear model approach yielded satisfactory estimates only at the highest incidence level, 25%. For 5% incidence, the uncorrected estimate of residual correlation was 50% less than the true value, and after correction for incidence, the parameter was overestimated by 90%. The estimates of residual correlation from the threshold model were regarded fair, except at the lowest level of incidence, where the estimate was 27% higher than the true value. Results indicated that when an accurate estimate of residual correlation is needed, the marginal maximum likelihood estimates are superior to the estimates calculated with the linear model. Using correction for the incidence level for residual correlation did not work well except at the highest incidence level.