Pedigree-based Relationship Matrices Research Articles

The Estimation of Genetic Parameters for Chronic Progressive Lymphedema and Body Traits in the Rhenish German Draught Horse.

Chronic progressive lymphedema (CPL) is a prevalent and progressive disease in Rhenish German draught horses. The objective of our follow-up study was to evaluate the heritability of this disease in Rhenish German draught horses using pedigree-based and genomic relationship matrices. We employed linear and threshold animal models. Models included the random animal effect and effects of breeding association, coat colour, sex, and age within sex, and farm-related factors, on CPL scores. In addition, we estimated heritabilities in models assuming censoring for data when horses were below an age of 1-15 years. The heritabilities of CPL scores across all ages were 0.595 ± 0.131 and 0.482 ± 0.105 in the threshold and linear animal model with pedigree-based relationship matrices, respectively. The restriction of data to horses with a minimum age at examination or accounting for censored data in younger animals showed an increase in heritabilities of CPL scores up to 0.788 ± 0.168 (threshold model) and 0.752 ± 0.153 (linear model) at an age of 7-8 years. Analyses including genomic relationship matrices yielded very similar estimates, but with smaller standard errors than pedigree-based analyses. Heritabilities in threshold models for CPL prevalence (CPL-bin-score) and the number of affected limbs (CPL-bin-sum) were 0.176-0.189 ± 0.061-0.064 and 0.375-0.433 ± 0.164-0.170, respectively. We were able to show moderately to highly positive genetic correlations between the CPL score and cannon bone circumference (0.529-0.825), height at withers (0.338-0.555), and skinfold thickness (0.241-0.517). Using the dichotomous trait for the CPL score and the genomic relationship matrix resulted in corresponding estimates of 0.868, 0.793, and 0.784, respectively. This study showed the great importance of additive genetic variation influencing the expression of chronic progressive lymphedema in Rhenish German draught horses. Therefore, further research is warranted to implement breeding programmes in a small breeding population that exploit the potential of additive genetic differences among animals for reducing the prevalence and severity of lesions of this incurable disease.

Genomic selection for resistance to mammalian bark stripping and associated chemical compounds in radiata pine.

The integration of genomic data into genetic evaluations can facilitate the rapid selection of superior genotypes and accelerate the breeding cycle in trees. In this study, 390 trees from 74 control-pollinated families were genotyped using a 36K Axiom SNP array. A total of 15,624 high-quality SNPs were used to develop genomic prediction models for mammalian bark stripping, tree height, and selected primary and secondary chemical compounds in the bark. Genetic parameters from different genomic prediction methods-single-trait best linear unbiased prediction based on a marker-based relationship matrix (genomic best linear unbiased prediction), multitrait single-step genomic best linear unbiased prediction, which integrated the marker-based and pedigree-based relationship matrices (single-step genomic best linear unbiased prediction) and the single-trait generalized ridge regression-were compared to equivalent single- or multitrait pedigree-based approaches (ABLUP). The influence of the statistical distribution of data on the genetic parameters was assessed. Results indicated that the heritability estimates were increased nearly 2-fold with genomic models compared to the equivalent pedigree-based models. Predictive accuracy of the single-step genomic best linear unbiased prediction was higher than the ABLUP for most traits. Allowing for heterogeneity in marker effects through the use of generalized ridge regression did not markedly improve predictive ability over genomic best linear unbiased prediction, arguing that most of the chemical traits are modulated by many genes with small effects. Overall, the traits with low pedigree-based heritability benefited more from genomic models compared to the traits with high pedigree-based heritability. There was no evidence that data skewness or the presence of outliers affected the genomic or pedigree-based genetic estimates.

Updating genetic relationship matrices and their inverses: a methodology note

Most of the calculations for genetic relationship matrices and their inverses utilized in recent (t + 1) evaluations for populations of interest can be avoided by updating these matrices at t evaluations for only new animals. This study describes and develops existing methods for updating pedigree-based and marker-based relationship matrices and their inverses. Updating some of the matrices could benefit from parallel computing.

Controlling bias in genomic breeding values for young genotyped bulls

The objectives of this study were to investigate bias in genomic predictions for dairy cattle and to find a practical approach to reduce the bias. The simulated data included phenotypes, pedigrees, and genotypes, mimicking a dairy cattle population (i.e., cows with phenotypes and bulls with no phenotypes) and assuming selection by breeding values or no selection. With the simulated data, genomic estimated breeding values (GEBV) were calculated with a single-step genomic BLUP and compared with true breeding values. Phenotypes and genotypes were simulated in 10 generations and in the last 4 generations, respectively. Phenotypes in the last generation were removed to predict breeding values for those individuals using only genomic and pedigree information. Complete pedigrees and incomplete pedigrees with 50% missing dams were created to construct the pedigree-based relationship matrix with and without inbreeding. With missing dams, unknown parent groups (UPG) were assigned in relationship matrices. Regression coefficients (b1) and coefficients of determination (R2) of true breeding values on (G)EBV were calculated to investigate inflation and accuracy in GEBV for genotyped animals, respectively. In addition to the simulation study, 18 linear type traits of US Holsteins were examined. For the 18 type traits, b1 and R2 of GEBV with full data sets on GEBV with partial data sets for young genotyped bulls were calculated. The results from the simulation study indicated inflation in GEBV for genotyped males that were evaluated with only pedigree and genomic information under BLUP selection. However, when UPG for only pedigree-based relationships were included, the inflation was reduced, accuracy was highest, and genetic trends had no bias. For the linear type traits, when UPG for only pedigree-based relationships were included, the results were generally in agreement with those from the simulation study, implying less bias in genetic trends. However, when including no UPG, UPG in pedigree-based relationships, or UPG in genomic relationships, inflation and accuracy in GEBV were similar. The results from the simulation and type traits suggest that UPG must be defined accurately to be estimable and inbreeding should be included in pedigree-based relationships. In dairy cattle, known pedigree information with inbreeding and estimable UPG plays an important role in improving compatibility between pedigree-based and genomic relationship matrices, resulting in more reliable genomic predictions.

Estimates of genetic trend for single-step genomic evaluations

BackgroundA common measure employed to evaluate the efficacy of livestock improvement schemes is the genetic trend, which is calculated as the means of predicted breeding values for animals born in successive time periods. This implies that different cohorts refer to the same base population. For genetic evaluation schemes integrating genomic information with records for all animals, genotyped or not, this is often not the case: expected means for pedigree founders are zero whereas values for genotyped animals are expected to sum to zero at the (mean) time corresponding to the frequencies that are used to center marker allele counts when calculating genomic relationships.MethodsThe paper examines estimates of genetic trends from single-step genomic evaluations. After a review of methods which propose to align pedigree-based and genomic relationship matrices, simulation is used to illustrate the effects of alignments and choice of assumed gene frequencies on trajectories of genetic trends.ResultsThe results show that methods available to alleviate differences between the founder populations implied by the two types of relationship matrices perform well; in particular, the meta-founder approach is advantageous. An application to data from routine genetic evaluation of Australian sheep is shown, confirming their effectiveness for practical data.ConclusionsAligning pedigree and genomic relationship matrices for single step genetic evaluation for populations under selection is essential. Fitting meta-founders is an effective and simple method to avoid distortion of estimates of genetic trends.

Weighting genomic and genealogical information for genetic parameter estimation and breeding value prediction in tropical beef cattle.

A combined matrix that exploits genealogy together with marker-based information could improve the selection of elite individuals in breeding programs. We present genetic parameters for adaptive and growth traits in beef cattle by exploring linear combinations of pedigree-based (A) and marker-based (G) relationship matrices. We use a data set with 2,111 Brahman (BB) and 2,550 Tropical Composite (TC) cattle with genotypes for 729,068 SNP, and phenotypes for five traits. A weighted relationship matrix (WRM) combining G and A was constructed as WRM = λG + (1 - λ)A. The weight (λ) was explored at values from 0.0 to 1.0, at 0.1 intervals. Additionally, four alternative G matrices, in the WRM, were evaluated according to the selection of SNP used to generate them: 1) Gw: all autosomal SNP with minor allele frequency (MAF) > 1%; 2) Gg: autosomal SNP with MAF > 1% and mapped inside to gene coding regions; 3) Gp: autosomal SNP with MAF > 1% and previously reported to have significant pleiotropic effect in these two populations; and 4) Gc: autosomal SNP with MAF > 1% and with significant correlated effects previously reported in both BB and TC populations. In addition, two A matrices were evaluated: 1) A: all relationships between animals were considered after tracing back known ancestors; and 2) Ad: a distorted A matrix where a random 1% of the off-diagonal nonzero values were set to zero to simulate relationship errors. Five independent Ad matrices were explored each with a different random 1% of relationships masked. Criteria for comparing the resulting WRM included estimates of heritability (h2) and cross-validation accuracy (ACC) of genomic estimated breeding values. The choice of WRM had a greater impact on h2 than on ACC estimates. The 1% errors introduced in pedigree relationships generated large distortion in genetic parameters and ACC estimates. However, employing a λ > 0.7 was an efficient mechanism to compensate for the errors in A. Additionally, although significant (P-value < 0.0001), we found no consistent relationship between the type of SNP used to compute G and h2 or ACC estimates. We devised the optimal value of λ for maximum h2 and ACC at λ = 0.7 suggesting a 70% and 30% weighting to genomic and genealogical information, respectively, as an optimal strategy to compensate for pedigree errors, to improve genetic parameters estimates and lead to more accurate selection decisions.

Relevance of genetic relationship in GWAS and genomic prediction.

The objective of this study was to analyze the relevance of relationship information on the identification of low heritability quantitative trait loci (QTLs) from a genome-wide association study (GWAS) and on the genomic prediction of complex traits in human, animal and cross-pollinating populations. The simulation-based data sets included 50 samples of 1000 individuals of seven populations derived from a common population with linkage disequilibrium. The populations had non-inbred and inbred progeny structure (50 to 200) with varying number of members (5 to 20). The individuals were genotyped for 10,000 single nucleotide polymorphisms (SNPs) and phenotyped for a quantitative trait controlled by 10 QTLs and 90 minor genes showing dominance. The SNP density was 0.1cM and the narrow sense heritability was 25%. The QTL heritabilities ranged from 1.1 to 2.9%. We applied mixed model approaches for both GWAS and genomic prediction using pedigree-based and genomic relationship matrices. For GWAS, the observed false discovery rate was kept below the significance level of 5%, the power of detection for the low heritability QTLs ranged from 14 to 50%, and the average bias between significant SNPs and a QTL ranged from less than 0.01 to 0.23cM. The QTL detection power was consistently higher using genomic relationship matrix. Regardless of population and training set size, genomic prediction provided higher prediction accuracy of complex trait when compared to pedigree-based prediction. The accuracy of genomic prediction when there is relatedness between individuals in the training set and the reference population is much higher than the value for unrelated individuals.

GenoMatrix: A Software Package for Pedigree-Based and Genomic Prediction Analyses on Complex Traits.

Genomic and pedigree-based best linear unbiased prediction methodologies (G-BLUP and P-BLUP) have proven themselves efficient for partitioning the phenotypic variance of complex traits into its components, estimating the individuals' genetic merits, and predicting unobserved (or yet-to-be observed) phenotypes in many species and fields of study. The GenoMatrix software, presented here, is a user-friendly package to facilitate the process of using genome-wide marker data and parentage information for G-BLUP and P-BLUP analyses on complex traits. It provides users with a collection of applications which help them on a set of tasks from performing quality control on data to constructing and manipulating the genomic and pedigree-based relationship matrices and obtaining their inverses. Such matrices will be then used in downstream analyses by other statistical packages. The package also enables users to obtain predicted values for unobserved individuals based on the genetic values of observed related individuals. GenoMatrix is available to the research community as a Windows 64bit executable and can be downloaded free of charge at: http://compbio.ufl.edu/software/genomatrix/.

Estimates of genetic variance and variance of predicted genetic merits using pedigree or genomic relationship matrices in six Brown Swiss cattle populations for different traits

The amount of variance captured in genetic estimations may depend on whether a pedigree-based or genomic relationship matrix is used. The purpose of this study was to investigate the genetic variance as well as the variance of predicted genetic merits (PGM) using pedigree-based or genomic relationship matrices in Brown Swiss cattle. We examined a range of traits in six populations amounting to 173 population-trait combinations. A main aim was to determine how using different relationship matrices affect variance estimation. We calculated ratios between different types of estimates and analysed the impact of trait heritability and population size. The genetic variances estimated by REML using a genomic relationship matrix were always smaller than the variances that were similarly estimated using a pedigree-based relationship matrix. The variances from the genomic relationship matrix became closer to estimates from a pedigree relationship matrix as heritability and population size increased. In contrast, variances of predicted genetic merits obtained using a genomic relationship matrix were mostly larger than variances of genetic merit predicted using pedigree-based relationship matrix. The ratio of the genomic to pedigree-based PGM variances decreased as heritability and population size rose. The increased variance among predicted genetic merits is important for animal breeding because this is one of the factors influencing genetic progress.

Combining Genomic and Genealogical Information in a Reproducing Kernel Hilbert Spaces Regression Model for Genome-Enabled Predictions in Dairy Cattle

Genome-enhanced genotypic evaluations are becoming popular in several livestock species. For this purpose, the combination of the pedigree-based relationship matrix with a genomic similarities matrix between individuals is a common approach. However, the weight placed on each matrix has been so far established with ad hoc procedures, without formal estimation thereof. In addition, when using marker- and pedigree-based relationship matrices together, the resulting combined relationship matrix needs to be adjusted to the same scale in reference to the base population. This study proposes a semi-parametric Bayesian method for combining marker- and pedigree-based information on genome-enabled predictions. A kernel matrix from a reproducing kernel Hilbert spaces regression model was used to combine genomic and genealogical information in a semi-parametric scenario, avoiding inversion and adjustment complications. In addition, the weights on marker- versus pedigree-based information were inferred from a Bayesian model with Markov chain Monte Carlo. The proposed method was assessed involving a large number of SNPs and a large reference population. Five phenotypes, including production and type traits of dairy cattle were evaluated. The reliability of the genome-based predictions was assessed using the correlation, regression coefficient and mean squared error between the predicted and observed values. The results indicated that when a larger weight was given to the pedigree-based relationship matrix the correlation coefficient was lower than in situations where more weight was given to genomic information. Importantly, the posterior means of the inferred weight were near the maximum of 1. The behavior of the regression coefficient and the mean squared error was similar to the performance of the correlation, that is, more weight to the genomic information provided a regression coefficient closer to one and a smaller mean squared error. Our results also indicated a greater accuracy of genomic predictions when using a large reference population.

Empirical comparison of association and admixture mapping for body weight using F&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; mice data set

Abstract. Recent advances in molecular genetics have provided hundreds of thousands of single nucleotide polymorphisms (SNPs) to detect mutations in genes related with complex traits. Undetected shared ancestry within samples of individuals could lead to the detection of false genomic signals in association mapping. Pedigree-based relationship matrices or genomic relationship matrices could be used in a mixed model to predict and correct for genetic stratifications. Genotypic information of founder populations could also be used to explore patterns of inheritance for complex traits by admixture mapping. An F2 population was created using M16 and ICR mouse lines for studying body weight at 8 weeks of age. Genotypes were collected for 1813 SNPs for each animal, including the founders. Bayesian residuals were used for population stratification in the admixture model. Association and admixture mapping detected similar genomic signals from chromosome 10. Our results provide empirical proof that gene flow from ancestral populations could be traced by admixture mapping with founder genotypes.

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

Genomic evaluation of both purebred and crossbred performances

BackgroundFor a two-breed crossbreeding system, Wei and van der Werf presented a model for genetic evaluation using information from both purebred and crossbred animals. The model provides breeding values for both purebred and crossbred performances. Genomic evaluation incorporates marker genotypes into a genetic evaluation system. Among popular methods are the so-called single-step methods, in which marker genotypes are incorporated into a traditional animal model by using a combined relationship matrix that extends the marker-based relationship matrix to non-genotyped animals. However, a single-step method for genomic evaluation of both purebred and crossbred performances has not been developed yet.ResultsAn extension of the Wei and van der Werf model that incorporates genomic information is presented. The extension consists of four steps: (1) the Wei van der Werf model is reformulated using two partial relationship matrices for the two breeds; (2) marker-based partial relationship matrices are constructed; (3) marker-based partial relationship matrices are adjusted to be compatible to pedigree-based partial relationship matrices and (4) combined partial relationship matrices are constructed using information from both pedigree and marker genotypes. The extension of the Wei van der Werf model can be implemented using software that allows inverse covariance matrices in sparse format as input.ConclusionsA method for genomic evaluation of both purebred and crossbred performances was developed for a two-breed crossbreeding system. The method allows information from crossbred animals to be incorporated in a coherent manner for such crossbreeding systems.

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

BackgroundSingle-step methods provide a coherent and conceptually simple approach to incorporate genomic information into genetic evaluations. An issue with single-step methods is compatibility between the marker-based relationship matrix for genotyped animals and the pedigree-based relationship matrix. Therefore, it is necessary to adjust the marker-based relationship matrix to the pedigree-based relationship matrix. Moreover, with data from routine evaluations, this adjustment should in principle be based on both observed marker genotypes and observed phenotypes, but until now this has been overlooked. In this paper, I propose a new method to address this issue by 1) adjusting the pedigree-based relationship matrix to be compatible with the marker-based relationship matrix instead of the reverse and 2) extending the single-step genetic evaluation using a joint likelihood of observed phenotypes and observed marker genotypes. The performance of this method is then evaluated using two simulated datasets.ResultsThe method derived here is a single-step method in which the marker-based relationship matrix is constructed assuming all allele frequencies equal to 0.5 and the pedigree-based relationship matrix is constructed using the unusual assumption that animals in the base population are related and inbred with a relationship coefficient γ and an inbreeding coefficient γ / 2. Taken together, this γ parameter and a parameter that scales the marker-based relationship matrix can handle the issue of compatibility between marker-based and pedigree-based relationship matrices. The full log-likelihood function used for parameter inference contains two terms. The first term is the REML-log-likelihood for the phenotypes conditional on the observed marker genotypes, whereas the second term is the log-likelihood for the observed marker genotypes. Analyses of the two simulated datasets with this new method showed that 1) the parameters involved in adjusting marker-based and pedigree-based relationship matrices can depend on both observed phenotypes and observed marker genotypes and 2) a strong association between these two parameters exists. Finally, this method performed at least as well as a method based on adjusting the marker-based relationship matrix.ConclusionsUsing the full log-likelihood and adjusting the pedigree-based relationship matrix to be compatible with the marker-based relationship matrix provides a new and interesting approach to handle the issue of compatibility between the two matrices in single-step genetic evaluation.

Comparison on genomic predictions using three GBLUP methods and two single-step blending methods in the Nordic Holstein population

BackgroundA single-step blending approach allows genomic prediction using information of genotyped and non-genotyped animals simultaneously. However, the combined relationship matrix in a single-step method may need to be adjusted because marker-based and pedigree-based relationship matrices may not be on the same scale. The same may apply when a GBLUP model includes both genomic breeding values and residual polygenic effects. The objective of this study was to compare single-step blending methods and GBLUP methods with and without adjustment of the genomic relationship matrix for genomic prediction of 16 traits in the Nordic Holstein population.MethodsThe data consisted of de-regressed proofs (DRP) for 5 214 genotyped and 9 374 non-genotyped bulls. The bulls were divided into a training and a validation population by birth date, October 1, 2001. Five approaches for genomic prediction were used: 1) a simple GBLUP method, 2) a GBLUP method with a polygenic effect, 3) an adjusted GBLUP method with a polygenic effect, 4) a single-step blending method, and 5) an adjusted single-step blending method. In the adjusted GBLUP and single-step methods, the genomic relationship matrix was adjusted for the difference of scale between the genomic and the pedigree relationship matrices. A set of weights on the pedigree relationship matrix (ranging from 0.05 to 0.40) was used to build the combined relationship matrix in the single-step blending method and the GBLUP method with a polygenetic effect.ResultsAveraged over the 16 traits, reliabilities of genomic breeding values predicted using the GBLUP method with a polygenic effect (relative weight of 0.20) were 0.3% higher than reliabilities from the simple GBLUP method (without a polygenic effect). The adjusted single-step blending and original single-step blending methods (relative weight of 0.20) had average reliabilities that were 2.1% and 1.8% higher than the simple GBLUP method, respectively. In addition, the GBLUP method with a polygenic effect led to less bias of genomic predictions than the simple GBLUP method, and both single-step blending methods yielded less bias of predictions than all GBLUP methods.ConclusionsThe single-step blending method is an appealing approach for practical genomic prediction in dairy cattle. Genomic prediction from the single-step blending method can be improved by adjusting the scale of the genomic relationship matrix.

Bias in genomic predictions for populations under selection

Prediction of genetic merit or disease risk using genetic marker information is becoming a common practice for selection of livestock and plant species. For the successful application of genome-wide marker-assisted selection (GWMAS), genomic predictions should be accurate and unbiased. The effect of selection on bias and accuracy of genomic predictions was studied in two simulated animal populations under weak or strong selection and with several heritabilities. Prediction of genetic values was by best-linear unbiased prediction (BLUP) using data either from relatives summarized in pseudodata for genotyped individuals (multiple-step method) or using all available data jointly (single-step method). The single-step method combined genomic- and pedigree-based relationship matrices. Predictions by the multiple-step method were biased. Predictions by a single-step method were less biased and more accurate but under strong selection were less accurate. When genomic relationships were shifted by a constant, the single-step method was unbiased and the most accurate. The value of that constant, which adjusts for non-random selection of genotyped individuals, can be derived analytically.

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.