Single-step Evaluation Research Articles

Combined single-step evaluation of functional longevity of dairy cows including correlated traits

BackgroundFor years, multiple trait genetic evaluations have been used to increase the accuracy of estimated breeding values (EBV) using information from correlated traits. In France, accurate approximations of multiple trait evaluations were implemented for traits that are described by different models by combining the results of univariate best linear unbiased prediction (BLUP) evaluations. Functional longevity (FL) is the trait that has most benefited from this approach. Currently, with many single-step (SS) evaluations, only univariate FL evaluations can be run. The aim of this study was to implement a “combined” SS (CSS) evaluation that extends the “combined” BLUP evaluation to obtain more accurate genomic (G) EBV for FL when information from five correlated traits (somatic cell score, clinical mastitis, conception rate for heifers and cows, and udder depth) is added.ResultsGEBV obtained from univariate SS (USS) evaluations and from a CSS evaluation were compared. The correlations between these GEBV showed the benefits of including information from correlated traits. Indeed, a CSS evaluation run without any performances on FL showed that the indirect information from correlated traits to evaluate FL was substantial. USS and CSS evaluations that mimic SS evaluations with data available in 2016 were compared. For each evaluation separately, the GEBV were sorted and then split into 10 consecutive groups (deciles). Survival curves were calculated for each group, based on the observed productive life of these cows as known in 2021. Regardless of their genotyping status, the worst group of heifers based on their GEBV in 2016 was well identified in the CSS evaluation and they had a substantially shorter herd life, while those in the best heifer group had a longer herd life. The gaps between groups were more important for the genotyped than the ungenotyped heifers, which indicates better prediction of future survival.ConclusionsA CSS evaluation is an efficient tool to improve FL. It allows a proper combination of information on functional traits that influence culling. In contrast, because of the strong selection intensity on young bulls for functional traits, the benefit of such a “combined” evaluation of functional traits is more modest for these males.

The marker effects of a single-step random regression model for 4 test-day traits in German Holsteins

The single-step genomic model has become the golden standard for routine evaluation in livestock species, such as Holstein dairy cattle. The single-step genomic model with direct estimation of marker effects has been proven to be efficient in accurately accounting for millions of genotype records. For diverse applications including frequent genomic evaluation updates on a weekly basis, estimates of the marker effects from the single-step evaluations play a central role in genomic prediction. In this study we focused on exploring the marker effect estimates from the single-step evaluation. Phenotypic, genotypic, and pedigree data were taken from the official evaluation for German dairy breeds in April 2021. A multilactation random regression test-day model was applied to more than 242 million test-day records separately for 4 traits: milk, fat, and protein yields, and somatic cell scores (SCS). Approximately one million genotyped Holstein animals were considered in the single-step genomic evaluations including ∼21 million animals in pedigree. Deregressed multiple across-country breeding values of Holstein bulls having daughters outside Germany were integrated into the national test-day data to increase the reliability of genomic breeding values. To assess the stability and bias of the marker effects of the single-step model, test-day records of the last 4 yr were deleted, and the integrated bulls born in the last 4 yr were truncated from the complete phenotypic dataset. Estimates of the marker effects were shown to be highly correlated, with correlations ∼0.9, between the full and truncated evaluations. Regression slope values of the marker-effect estimates from the full on the truncated evaluations were all close to their expected value, being ∼1.03. Calculated using random regression coefficients of the marker effect estimates, drastically different shapes of the genetic lactation curve were seen for 2 markers on chromosome 14 for the 4 test-day traits. The contribution of individual chromosomes to the total additive genetic variances seemed to follow the polygenic inheritance mode for protein yield and SCS. However, chromosome 14 was found to make an exceptionally large contribution to the total additive genetic variance for milk and fat yields because of markers near the major gene DGAT1. For the first lactation test-day traits, we obtained ∼0 correlations of chromosomal direct genomic values between any pair of the chromosomes; no spurious correlations were found in our analysis, thanks to the large reference population. For trait milk yield, chromosomal direct genomic values appeared to have a large variation in the between-lactation correlations among the chromosomes, especially between first and second or third lactations. The optimal features of the random regression test-day model and the single-step marker model allowed us to track the differences in the shapes of genetic lactation curves down to the individual markers. Furthermore, the single-step random regression test-day model enabled us to better understand the inheritance mode of the yield traits and SCS (e.g., variable chromosomal contributions to the total additive genetic variance and to the genetic correlations between lactations).

Efficient large-scale single-step evaluations and indirect genomic prediction of genotyped selection candidates

BackgroundSingle-step genomic best linear unbiased prediction (ssGBLUP) models allow the combination of genomic, pedigree, and phenotypic data into a single model, which is computationally challenging for large genotyped populations. In practice, genotypes of animals without their own phenotype and progeny, so-called genotyped selection candidates, can become available after genomic breeding values have been estimated by ssGBLUP. In some breeding programmes, genomic estimated breeding values (GEBV) for these animals should be known shortly after obtaining genotype information but recomputing GEBV using the full ssGBLUP takes too much time. In this study, first we compare two equivalent formulations of ssGBLUP models, i.e. one that is based on the Woodbury matrix identity applied to the inverse of the genomic relationship matrix, and one that is based on marker equations. Second, we present computationally-fast approaches to indirectly compute GEBV for genotyped selection candidates, without the need to do the full ssGBLUP evaluation.ResultsThe indirect approaches use information from the latest ssGBLUP evaluation and rely on the decomposition of GEBV into its components. The two equivalent ssGBLUP models and indirect approaches were tested on a six-trait calving difficulty model using Irish dairy and beef cattle data that include 2.6 million genotyped animals of which about 500,000 were considered as genotyped selection candidates. When using the same computational approaches, the solving phase of the two equivalent ssGBLUP models showed similar requirements for memory and time per iteration. The computational differences between them were due to the preprocessing phase of the genomic information. Regarding the indirect approaches, compared to GEBV obtained from single-step evaluations including all genotypes, indirect GEBV had correlations higher than 0.99 for all traits while showing little dispersion and level bias.ConclusionsIn conclusion, ssGBLUP predictions for the genotyped selection candidates were accurately approximated using the presented indirect approaches, which are more memory efficient and computationally fast, compared to solving a full ssGBLUP evaluation. Thus, indirect approaches can be used even on a weekly basis to estimate GEBV for newly genotyped animals, while the full single-step evaluation is done only a few times within a year.

Single-step SNPBLUP evaluation in six German beef cattle breeds.

The implementation of genomic selection for six German beef cattle populations was evaluated. Although the multiple-step implementation of genomic selection is the status quo in most national dairy cattle evaluations, the breeding structure of German beef cattle, coupled with the shortcoming and complexity of the multiple-step method, makes single step a more attractive option to implement genomic selection in German beef cattle populations. Our objective was to develop a national beef cattle single-step genomic evaluation in five economically important traits in six German beef cattle populations and investigate its impact on the accuracy and bias of genomic evaluations relative to the current pedigree-based evaluation. Across the six breeds in our study, 461,929 phenotyped and 14,321 genotyped animals were evaluated with a multi-trait single-step model. To validate the single-step model, phenotype data in the last 2 years were removed in a forward validation study. For the conventional and single-step approaches, the genomic estimated breeding values of validation animals and other animals were compared between the truncated and the full evaluations. The correlation of the GEBVs between the full and truncated evaluations in the validation animals was slightly higher in the single-step evaluation. The regression of the full GEBVs on truncated GEBVs was close to the optimal value of 1 for both the pedigree-based and the single-step evaluations. The SNP effect estimates from the truncated evaluation were highly correlated with those from the full evaluation, with values ranging from 0.79 to 0.94. The correlation of the SNP effect was influenced by the number of genotyped animals shared between the full and truncated evaluations. The regression coefficients of the SNP effect of the full evaluation on the truncated evaluation were all close to the expected value of 1, indicating unbiased estimates of the SNP markers for the production traits. The Manhattan plot of the SNP effect estimates identified chromosomal regions harbouring major genes for muscling and body weight in breeds of French origin. Based on the regression intercept and slope of the GEBVs of validation animals, the single-step evaluation was neither inflated nor deflated across the six breeds. Overall, the single-step model resulted in a more accurate and stable evaluation. However, due to the small number of genotyped individuals, the single-step method only provided slightly better results when compared to the pedigree-based method.

Genomic evaluation of carcass traits of Korean beef cattle Hanwoo using a single-step marker effect model

Hanwoo beef cattle are well known for the flavor and tenderness of their meat. Genetic improvement programs have been extremely successful over the last 40 yr. Recently, genomic selection was initiated in Hanwoo to enhance genetic progress. Routine genomic evaluation based on the single-step breeding value model was implemented in 2020 for all economically important traits. In this study, we tested a single-step marker effect model for the genomic evaluation of four carcass traits, namely, carcass weight (CW), eye muscle area, backfat thickness, and marbling score. In total, 8,023,666 animals with carcass records were jointly evaluated, including 29,965 genotyped animals. To assess the prediction stability of the single-step model, carcass data from the last 4 yr were removed in a forward validation study. The estimated genomic breeding values (GEBV) of the validation animals and other animals were compared between the truncated and full evaluations. A parallel conventional best linear unbiased prediction (BLUP) evaluation with either the full or the truncated dataset was also conducted for comparison with the single-step model. The estimates of the marker effect from the truncated evaluation were highly correlated with those from the full evaluation, ranging from 0.88 to 0.92. The regression coefficients of the estimates of the marker effect for the full and truncated evaluations were close to their expected value of 1, indicating unbiased estimates for all carcass traits. Estimates of the marker effect revealed three chromosomal regions (chromosomes 4, 6, and 14) harboring the major genes for CW in Hanwoo. For validation of cows or steers, the single-step model had a much higher R2 value for the linear regression model than the conventional BLUP model. Based on the regression intercept and slope of the validation, the single-step evaluation was neither inflated nor deflated. For genotyped animals, the estimated GEBV from the full and truncated evaluations were more correlated than the estimated breeding values from the two conventional BLUP evaluations. The single-step model provided a more accurate and stable evaluation over time.

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.

Computational strategies for the preconditioned conjugate gradient method applied to ssSNPBLUP, with an application to a multivariate maternal model

BackgroundThe single-step single nucleotide polymorphism best linear unbiased prediction (ssSNPBLUP) is one of the single-step evaluations that enable a simultaneous analysis of phenotypic and pedigree information of genotyped and non-genotyped animals with a large number of genotypes. The aim of this study was to develop and illustrate several computational strategies to efficiently solve different ssSNPBLUP systems with a large number of genotypes on current computers.ResultsThe different developed strategies were based on simplified computations of some terms of the preconditioner, and on splitting the coefficient matrix of the different ssSNPBLUP systems into multiple parts to perform its multiplication by a vector more efficiently. Some matrices were computed explicitly and stored in memory (e.g. the inverse of the pedigree relationship matrix), or were stored using a compressed form (e.g. the Plink 1 binary form for the genotype matrix), to permit the use of efficient parallel procedures while limiting the required amount of memory. The developed strategies were tested on a bivariate genetic evaluation for livability of calves for the Netherlands and the Flemish region in Belgium. There were 29,885,286 animals in the pedigree, 25,184,654 calf records, and 131,189 genotyped animals. The ssSNPBLUP system required around 18 GB Random Access Memory and 12 h to be solved with the most performing implementation.ConclusionsBased on our proposed approaches and results, we showed that ssSNPBLUP provides a feasible approach in terms of memory and time requirements to estimate genomic breeding values using current computers.

Technical note: Methods for interim prediction of single-step breeding values for young animals

Single-step genomic evaluations have the advantage of simultaneously combining all pedigree, phenotypic, and genotypic information available. However, systems with a large number of genotyped animals have some computational challenges. In many genomic breeding programs, genomic predictions of young animals should become available for selection decisions in the shortest time possible, which requires either a very effective estimation or an approximation with negligible loss in accuracy. We investigated different procedures for predicting breeding values of young genotyped animals without setting up the full single-step system augmented for the additional genotypes. Methods were based on transmitting the information from single-step breeding values of genotyped animals that took part in the previous full run to young animals, either through genomic relationships or through a marker-based model. The different procedures were tested on real data from the April 2017 run of the German-Austrian official genomic evaluation for Fleckvieh. The data set included 62,559 genotyped animals and was used to run single-step evaluations for 23 conformation traits. A further data set comprising 1,768 young animals was used for interim prediction and we called it the validation set. The reference values for validation were the predicted breeding values of the young animals from a full single-step run containing the genotypes of all 64,327 animals. Correlations between the approximated predictions and those from the full single-step run also containing genotypes from young animals averaged 0.9932 for the best method (from 0.990 to 0.995 across traits). In conclusion, prediction of single-step breeding values for young animals can be well approximated using systems of size equal to the number of markers.

An innovative method for nuclear emergency source term evaluation based on pressure vessel water level

In the event of severe accidents in nuclear power plants (NPPs), timely and accurate evaluation of the source term released from the reactor can provide technical support for a nuclear emergency response. Currently, the method for source term evaluation during a nuclear emergency in NPP is mainly based on the core damage assessment technique. The first step in the evaluation process is core damage assessment; and the second step is source term evaluation, based on core damage state and NUREG-1465 reference guide. In this paper, a nuclear emergency source term evaluation method (RVLST) based on measured reactor pressure vessel water level is presented. The single-step evaluation process combines pressure vessel water level monitoring system, core degradation model, and fission product release model. The feasibility, computational speed and accuracy of RVLST are compared with the methods in IAEA-TECDOC-955/NUREG-1465, IAEA-TECDOC-1127 and MELCOR using source term released into the containment in a large break loss of coolant accident (LBLOCA) in the AP1000 nuclear power plant, and the results obtained by the four methods were comparatively analyzed. The results show that the release fraction of noble gases calculated by RVLST is close to the one calculated by the IAEA-TECDOC-955/NUREG-1465 method and MELCOR. Moreover, compared with the results for Cesium (Cs) calculated with the IAEA-TECDOC-955/NUREG-1465 method, the calculations obtained from the RVLST are closer to those derived from MELCOR. Also, more conservative calculations were obtained from RVLST than those calculated with IAEA-TECDOC-955/NUREG-1465 and MELCOR for halogen Iodine (I) concentration.

Short communication: The role of genotypes from animals without phenotypes in single-step genomic evaluations

In a 2-step genomic system, genotypes of animals without phenotypes do not influence genomic prediction of other animals, but that might not be the case in single-step systems. We investigated the effects of including genotypes from culled bulls on the reliability of genomic predictions from single-step evaluations. Four scenarios with a constant amount of phenotypic information and increasing numbers of genotypes from culled bulls were simulated and compared with respect to prediction reliability. With increasing numbers of genotyped culled bulls, there was a corresponding increase in prediction reliability. For instance, in our simulation scenario the reliability for selection candidates was twice as large when all culled bulls from the last 4 generations were included in the analysis. Single-step evaluations imply the imputation of all nongenotyped animals in the pedigree. We showed that this imputation was increasingly more accurate as increasingly more genotypic information from the culled bulls was taken into account. This resulted in higher prediction reliabilities. The extent of the benefit from including genotypes from culled bulls might be more relevant for small populations with low levels of reliabilities.

Single-step SNP-BLUP with on-the-fly imputed genotypes and residual polygenic effects

BackgroundSingle-step genomic best linear unbiased prediction (BLUP) evaluation combines relationship information from pedigree and genomic marker data. The inclusion of the genomic information into mixed model equations requires the inverse of the combined relationship matrix {mathbf{H}}, which has a dense matrix block for genotyped animals.MethodsTo avoid inversion of dense matrices, single-step genomic BLUP can be transformed to single-step single nucleotide polymorphism BLUP (SNP-BLUP) which have observed and imputed marker coefficients. Simple block LDL type decompositions of the single-step relationship matrix {mathbf{H}} were derived to obtain different types of linearly equivalent single-step genomic mixed model equations with different sets of reparametrized random effects. For non-genotyped animals, the imputed marker coefficient terms in the single-step SNP-BLUP were calculated on-the-fly during the iterative solution using sparse matrix decompositions without storing the imputed genotypes. Residual polygenic effects were added to genotyped animals and transmitted to non-genotyped animals using relationship coefficients that are similar to imputed genotypes. The relationships were further orthogonalized to improve convergence of iterative methods.ResultsAll presented single-step SNP-BLUP models can be solved efficiently using iterative methods that rely on iteration on data and sparse matrix approaches. The efficiency, accuracy and iteration convergence of the derived mixed model equations were tested with a small dataset that included 73,579 animals of which 2885 were genotyped with 37,526 SNPs.ConclusionsInversion of the large and dense genomic relationship matrix was avoided in single-step evaluation by using fully orthogonalized single-step SNP-BLUP formulations. The number of iterations until convergence was smaller in single-step SNP-BLUP formulations than in the original single-step GBLUP when heritability was low, but increased above that of the original single-step when heritability was high.

Effect of cow reference group on validation reliability of genomic evaluation

We studied the effect of including genomic data for cows in the reference population of single-step evaluations. Deregressed individual cow genetic evaluations (DRP) from milk production evaluations of Nordic Red Dairy cattle were used to estimate the single-step breeding values. Validation reliability and bias of the evaluations were calculated with four data sets including different amount of DRP record information from genotyped cows in the reference population. The gain in reliability was from 2% to 4% units for the production traits, depending on the used DRP data and the amount of genomic data. Moreover, inclusion of genotyped bull dams and their genotyped daughters seemed to create some bias in the single-step evaluation. Still, genotyping cows and their inclusion in the reference population is advantageous and should be encouraged.

Correction: Compatibility of pedigree-based and marker-based relationship matrices for single-step genetic evaluation

Correction: Compatibility of pedigree-based and marker-based relationship matrices for single-step genetic evaluation

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.

AB0605 Evaluation of three screening questionnaires for use in identifying symptomatic knee osteoarthritis in the general population

BackgroundKnee Osteoarthritis (OA) causes large economic burden worldwide. Accurate prevalence estimates helps evaluation of its impact and guide resource allocation. Screening questionnaires with reasonable accuracy offer less costly alternative to...

A Common Dataset for Genomic Analysis of Livestock Populations

Although common datasets are an important resource for the scientific community and can be used to address important questions, genomic datasets of a meaningful size have not generally been available in livestock species. We describe a pig dataset that PIC (a Genus company) has made available for comparing genomic prediction methods. We also describe genomic evaluation of the data using methods that PIC considers best practice for predicting and validating genomic breeding values, and we discuss the impact of data structure on accuracy. The dataset contains 3534 individuals with high-density genotypes, phenotypes, and estimated breeding values for five traits. Genomic breeding values were calculated using BayesB, with phenotypes and de-regressed breeding values, and using a single-step genomic BLUP approach that combines information from genotyped and un-genotyped animals. The genomic breeding value accuracy increased with increased trait heritability and with increased relationship between training and validation. In nearly all cases, BayesB using de-regressed breeding values outperformed the other approaches, but the single-step evaluation performed only slightly worse. This dataset was useful for comparing methods for genomic prediction using real data. Our results indicate that validation approaches accounting for relatedness between populations can correct for potential overestimation of genomic breeding value accuracies, with implications for genotyping strategies to carry out genomic selection programs.

Efficient computation of the genomic relationship matrix and other matrices used in single‐step evaluation

Genomic evaluations can be calculated using a unified procedure that combines phenotypic, pedigree and genomic information. Implementation of such a procedure requires the inverse of the relationship matrix based on pedigree and genomic relationships. The objective of this study was to investigate efficient computing options to create relationship matrices based on genomic markers and pedigree information as well as their inverses. SNP maker information was simulated for a panel of 40 K SNPs, with the number of genotyped animals up to 30 000. Matrix multiplication in the computation of the genomic relationship was by a simple 'do' loop, by two optimized versions of the loop, and by a specific matrix multiplication subroutine. Inversion was by a generalized inverse algorithm and by a LAPACK subroutine. With the most efficient choices and parallel processing, creation of matrices for 30 000 animals would take a few hours. Matrices required to implement a unified approach can be computed efficiently. Optimizations can be either by modifications of existing code or by the use of efficient automatic optimizations provided by open source or third-party libraries.

Combination of the material force concept and the extended finite element method for mixed mode crack growth simulations

AbstractA novel approach to simulate crack growth within an extended finite element framework is presented. The introduced approach combines the material force concept and the extended finite element method (xFEM) that is not straight forward and faces the major problem that a crack tip node, which is required for the evaluation of the material force, is not available within an xFEM framework.The introduced concept enables an efficient single step evaluation of the crack state and the crack growth direction based on a continuum mechanics approach and represents an alternative to the common procedure of using the stress intensity factor solution within a stress or energy‐based empirical formulation for the determination of the crack growth direction. Two different approaches are introduced that evaluate the crack tip material force within the xFEM based on a domain or contour approach, both providing equivalent results. After an evaluation of the method, a major focus is set on crack growth investigations with increased complexity, including mixed mode loading and crack interaction with other discontinuities. The influence of different evaluation parameters is studied by comparing the results with empirical, experimental and alternative numerical solutions and confirms the applicability and capability of the proposed combination of both concepts. Copyright © 2010 John Wiley & Sons, Ltd.

Hot topic: A unified approach to utilize phenotypic, full pedigree, and genomic information for genetic evaluation of Holstein final score

The first national single-step, full-information (phenotype, pedigree, and marker genotype) genetic evaluation was developed for final score of US Holsteins. Data included final scores recorded from 1955 to 2009 for 6,232,548 Holsteins cows. BovineSNP50 (Illumina, San Diego, CA) genotypes from the Cooperative Dairy DNA Repository (Beltsville, MD) were available for 6,508 bulls. Three analyses used a repeatability animal model as currently used for the national US evaluation. The first 2 analyses used final scores recorded up to 2004. The first analysis used only a pedigree-based relationship matrix. The second analysis used a relationship matrix based on both pedigree and genomic information (single-step approach). The third analysis used the complete data set and only the pedigree-based relationship matrix. The fourth analysis used predictions from the first analysis (final scores up to 2004 and only a pedigree-based relationship matrix) and prediction using a genomic based matrix to obtain genetic evaluation (multiple-step approach). Different allele frequencies were tested in construction of the genomic relationship matrix. Coefficients of determination between predictions of young bulls from parent average, single-step, and multiple-step approaches and their 2009 daughter deviations were 0.24, 0.37 to 0.41, and 0.40, respectively. The highest coefficient of determination for a single-step approach was observed when using a genomic relationship matrix with assumed allele frequencies of 0.5. Coefficients for regression of 2009 daughter deviations on parent-average, single-step, and multiple-step predictions were 0.76, 0.68 to 0.79, and 0.86, respectively, which indicated some inflation of predictions. The single-step regression coefficient could be increased up to 0.92 by scaling differences between the genomic and pedigree-based relationship matrices with little loss in accuracy of prediction. One complete evaluation took about 2h of computing time and 2.7 gigabytes of memory. Computing times for single-step analyses were slightly longer (2%) than for pedigree-based analysis. A national single-step genetic evaluation with the pedigree relationship matrix augmented with genomic information provided genomic predictions with accuracy and bias comparable to multiple-step procedures and could account for any population or data structure. Advantages of single-step evaluations should increase in the future when animals are pre-selected on genotypes.

A novel zeolite based stationary phases for in situ synthesis and evaluation of porphyrins and calix (4) pyrroles

The application of zeolite based molecular sieves as catalysts and sorbents in thin layer chromatography (TLC) has been investigated for a single step evaluation of porphyrins and calix (4) pyrroles by in situ synthesis from pyrrole with aromatic aldehydes and ketones under microwave irradiation. The molecular sieves used were microporous zeolites such as HZSM-5, HY, Hβ and mesoporous MCM-41 material and the results are compared. Among the various sorbents studied, MCM-41 proves to be the potential candidate and offered quantitative conversions. This glass-backed zeolite coated TLC plate presumably acted as a reactor and facilitated simultaneous chromatographic separation of the macrocycles as well. The process is simple, economically viable, rapid, selective, solvent free and finds a novel application in high through put parallel synthesis and chromatographic screening in a single step.