Yvonne C. J. Wientjes

The Effect of Linkage Disequilibrium and Family Relationships on the Reliability of Genomic Prediction

Although the concept of genomic selection relies on linkage disequilibrium (LD) between quantitative trait loci and markers, reliability of genomic predictions is strongly influenced by family relationships. In this study, we investigated the effects of LD and family relationships on reliability of genomic predictions and the potential of deterministic formulas to predict reliability using population parameters in populations with complex family structures. Five groups of selection candidates were simulated by taking different information sources from the reference population into account: (1) allele frequencies, (2) LD pattern, (3) haplotypes, (4) haploid chromosomes, and (5) individuals from the reference population, thereby having real family relationships with reference individuals. Reliabilities were predicted using genomic relationships among 529 reference individuals and their relationships with selection candidates and with a deterministic formula where the number of effective chromosome segments (Me) was estimated based on genomic and additive relationship matrices for each scenario. At a heritability of 0.6, reliabilities based on genomic relationships were 0.002 ± 0.0001 (allele frequencies), 0.022 ± 0.001 (LD pattern), 0.018 ± 0.001 (haplotypes), 0.100 ± 0.008 (haploid chromosomes), and 0.318 ± 0.077 (family relationships). At a heritability of 0.1, relative differences among groups were similar. For all scenarios, reliabilities were similar to predictions with a deterministic formula using estimated Me. So, reliabilities can be predicted accurately using empirically estimated Me and level of relationship with reference individuals has a much higher effect on the reliability than linkage disequilibrium per se. Furthermore, accumulated length of shared haplotypes is more important in determining the reliability of genomic prediction than the individual shared haplotype length.

Empirical and deterministic accuracies of across-population genomic prediction

BackgroundDifferences in linkage disequilibrium and in allele substitution effects of QTL (quantitative trait loci) may hinder genomic prediction across populations. Our objective was to develop a deterministic formula to estimate the accuracy of across-population genomic prediction, for which reference individuals and selection candidates are from different populations, and to investigate the impact of differences in allele substitution effects across populations and of the number of QTL underlying a trait on the accuracy.MethodsA deterministic formula to estimate the accuracy of across-population genomic prediction was derived based on selection index theory. Moreover, accuracies were deterministically predicted using a formula based on population parameters and empirically calculated using simulated phenotypes and a GBLUP (genomic best linear unbiased prediction) model. Phenotypes of 1033 Holstein-Friesian, 105 Groninger White Headed and 147 Meuse-Rhine-Yssel cows were simulated by sampling 3000, 300, 30 or 3 QTL from the available high-density SNP (single nucleotide polymorphism) information of three chromosomes, assuming a correlation of 1.0, 0.8, 0.6, 0.4, or 0.2 between allele substitution effects across breeds. The simulated heritability was set to 0.95 to resemble the heritability of deregressed proofs of bulls.ResultsAccuracies estimated with the deterministic formula based on selection index theory were similar to empirical accuracies for all scenarios, while accuracies predicted with the formula based on population parameters overestimated empirical accuracies by ~25 to 30%. When the between-breed genetic correlation differed from 1, i.e. allele substitution effects differed across breeds, empirical and deterministic accuracies decreased in proportion to the genetic correlation. Using a multi-trait model, it was possible to accurately estimate the genetic correlation between the breeds based on phenotypes and high-density genotypes. The number of QTL underlying the simulated trait did not affect the accuracy.ConclusionsThe deterministic formula based on selection index theory estimated the accuracy of across-population genomic predictions well. The deterministic formula using population parameters overestimated the across-population genomic accuracy, but may still be useful because of its simplicity. Both formulas could accommodate for genetic correlations between populations lower than 1. The number of QTL underlying a trait did not affect the accuracy of across-population genomic prediction using a GBLUP method.

An Equation to Predict the Accuracy of Genomic Values by Combining Data from Multiple Traits, Populations, or Environments

Predicting the accuracy of estimated genomic values using genome-wide marker information is an important step in designing training populations. Currently, different deterministic equations are available to predict accuracy within populations, but not for multipopulation scenarios where data from multiple breeds, lines or environments are combined. Therefore, our objective was to develop and validate a deterministic equation to predict the accuracy of genomic values when different populations are combined in one training population. The input parameters of the derived prediction equation are the number of individuals and the heritability from each of the populations in the training population; the genetic correlations between the populations, i.e., the correlation between allele substitution effects of quantitative trait loci; the effective number of chromosome segments across predicted and training populations; and the proportion of the genetic variance in the predicted population captured by the markers in each of the training populations. Validation was performed based on real genotype information of 1033 Holstein–Friesian cows that were divided into three different populations by combining half-sib families in the same population. Phenotypes were simulated for multiple scenarios, differing in heritability within populations and in genetic correlations between the populations. Results showed that the derived equation can accurately predict the accuracy of estimating genomic values for different scenarios of multipopulation genomic prediction. Therefore, the derived equation can be used to investigate the potential accuracy of different multipopulation genomic prediction scenarios and to decide on the most optimal design of training populations.

Impact of QTL properties on the accuracy of multi-breed genomic prediction

BackgroundAlthough simulation studies show that combining multiple breeds in one reference population increases accuracy of genomic prediction, this is not always confirmed in empirical studies. This discrepancy might be due to the assumptions on quantitative trait loci (QTL) properties applied in simulation studies, including number of QTL, spectrum of QTL allele frequencies across breeds, and distribution of allele substitution effects. We investigated the effects of QTL properties and of including a random across- and within-breed animal effect in a genomic best linear unbiased prediction (GBLUP) model on accuracy of multi-breed genomic prediction using genotypes of Holstein-Friesian and Jersey cows.MethodsGenotypes of three classes of variants obtained from whole-genome sequence data, with moderately low, very low or extremely low average minor allele frequencies (MAF), were imputed in 3000 Holstein-Friesian and 3000 Jersey cows that had real high-density genotypes. Phenotypes of traits controlled by QTL with different properties were simulated by sampling 100 or 1000 QTL from one class of variants and their allele substitution effects either randomly from a gamma distribution, or computed such that each QTL explained the same variance, i.e. rare alleles had a large effect. Genomic breeding values for 1000 selection candidates per breed were estimated using GBLUP modelsincluding a random across- and a within-breed animal effect.ResultsFor all three classes of QTL allele frequency spectra, accuracies of genomic prediction were not affected by the addition of 2000 individuals of the other breed to a reference population of the same breed as the selection candidates. Accuracies of both single- and multi-breed genomic prediction decreased as MAF of QTL decreased, especially when rare alleles had a large effect. Accuracies of genomic prediction were similar for the models with and without a random within-breed animal effect, probably because of insufficient power to separate across- and within-breed animal effects.ConclusionsAccuracy of both single- and multi-breed genomic prediction depends on the properties of the QTL that underlie the trait. As QTL MAF decreased, accuracy decreased, especially when rare alleles had a large effect. This demonstrates that QTL properties are key parameters that determine the accuracy of genomic prediction.

Using selection index theory to estimate consistency of multi-locus linkage disequilibrium across populations

BackgroundThe potential of combining multiple populations in genomic prediction is depending on the consistency of linkage disequilibrium (LD) between SNPs and QTL across populations. We investigated consistency of multi-locus LD across populations using selection index theory and investigated the relationship between consistency of multi-locus LD and accuracy of genomic prediction across different simulated scenarios. In the selection index, QTL genotypes were considered as breeding goal traits and SNP genotypes as index traits, based on LD among SNPs and between SNPs and QTL. The consistency of multi-locus LD across populations was computed as the accuracy of predicting QTL genotypes in selection candidates using a selection index derived in the reference population. Different scenarios of within and across population genomic prediction were evaluated, using all SNPs or only the four neighboring SNPs of a simulated QTL. Phenotypes were simulated using different numbers of QTL underlying the trait. The relationship between the calculated consistency of multi-locus LD and accuracy of genomic prediction using a GBLUP type of model was investigated.ResultsThe accuracy of predicting QTL genotypes, i.e. the measure describing consistency of multi-locus LD, was much lower for across population scenarios compared to within population scenarios, and was lower when QTL had a low MAF compared to QTL randomly selected from the SNPs. Consistency of multi-locus LD was highly correlated with the realized accuracy of genomic prediction across different scenarios and the correlation was higher when QTL were weighted according to their effects in the selection index instead of weighting QTL equally. By only considering neighboring SNPs of QTL, accuracy of predicting QTL genotypes within population decreased, but it substantially increased the accuracy across populations.ConclusionsConsistency of multi-locus LD across populations is a characteristic of the properties of the QTL in the investigated populations and can provide more insight in underlying reasons for a low empirical accuracy of across population genomic prediction. By focusing in genomic prediction models only on neighboring SNPs of QTL, multi-locus LD is more consistent across populations since only short-range LD is considered, and accuracy of predicting QTL genotypes of individuals from another population is increased.

Across population genomic prediction scenarios in which Bayesian variable selection outperforms GBLUP

BackgroundThe use of information across populations is an attractive approach to increase the accuracy of genomic prediction for numerically small populations. However, accuracies of across population genomic prediction, in which reference and selection individuals are from different populations, are currently disappointing. It has been shown for within population genomic prediction that Bayesian variable selection models outperform GBLUP models when the number of QTL underlying the trait is low. Therefore, our objective was to identify across population genomic prediction scenarios in which Bayesian variable selection models outperform GBLUP in terms of prediction accuracy. In this study, high density genotype information of 1033 Holstein Friesian, 105 Groningen White Headed, and 147 Meuse-Rhine-Yssel cows were used. Phenotypes were simulated using two changing variables: (1) the number of QTL underlying the trait (3000, 300, 30, 3), and (2) the correlation between allele substitution effects of QTL across populations, i.e. the genetic correlation of the simulated trait between the populations (1.0, 0.8, 0.4).ResultsThe accuracy obtained by the Bayesian variable selection model was depending on the number of QTL underlying the trait, with a higher accuracy when the number of QTL was lower. This trend was more pronounced for across population genomic prediction than for within population genomic prediction. It was shown that Bayesian variable selection models have an advantage over GBLUP when the number of QTL underlying the simulated trait was small. This advantage disappeared when the number of QTL underlying the simulated trait was large. The point where the accuracy of Bayesian variable selection and GBLUP became similar was approximately the point where the number of QTL was equal to the number of independent chromosome segments (Me) across the populations.ConclusionBayesian variable selection models outperform GBLUP when the number of QTL underlying the trait is smaller than Me. Across populations, Me is considerably larger than within populations. So, it is more likely to find a number of QTL underlying a trait smaller than Me across populations than within population. Therefore Bayesian variable selection models can help to improve the accuracy of across population genomic prediction.

Multi-population Genomic Relationships for Estimating Current Genetic Variances Within and Genetic Correlations Between Populations

Relationships between individuals are important to estimate genetic variances within a population and covariances between populations. Here, Wientjes..... Different methods are available to calculate multi-population genomic relationship matrices. Since those matrices differ in base population, it is anticipated that the method used to calculate genomic relationships affects the estimate of genetic variances, covariances, and correlations. The aim of this article is to define the multi-population genomic relationship matrix to estimate current genetic variances within and genetic correlations between populations. The genomic relationship matrix containing two populations consists of four blocks, one block for population 1, one block for population 2, and two blocks for relationships between the populations. It is known, based on literature, that by using current allele frequencies to calculate genomic relationships within a population, current genetic variances are estimated. In this article, we theoretically derived the properties of the genomic relationship matrix to estimate genetic correlations between populations and validated it using simulations. When the scaling factor of across-population genomic relationships is equal to the product of the square roots of the scaling factors for within-population genomic relationships, the genetic correlation is estimated unbiasedly even though estimated genetic variances do not necessarily refer to the current population. When this property is not met, the correlation based on estimated variances should be multiplied by a correction factor based on the scaling factors. In this study, we present a genomic relationship matrix which directly estimates current genetic variances as well as genetic correlations between populations.

Multibreed genomic prediction using multitrait genomic residual maximum likelihood and multitask Bayesian variable selection

Genomic prediction is applicable to individuals of different breeds. Empirical results to date, however, show limited benefits in using information on multiple breeds in the context of genomic prediction. We investigated a multitask Bayesian model, presented previously by others, implemented in a Bayesian stochastic search variable selection (BSSVS) model. This model allowed for evidence of quantitative trait loci (QTL) to be accumulated across breeds or for both QTL that segregate across breeds and breed-specific QTL. In both cases, single nucleotide polymorphism effects were estimated with information from a single breed. Other models considered were a single-trait and multitrait genomic residual maximum likelihood (GREML) model, with breeds considered as different traits, and a single-trait BSSVS model. All single-trait models were applied to each of the 2 breeds separately and to the pooled data of both breeds. The data used included a training data set of 6,278 Holstein and 722 Jersey bulls, as well as 374 Jersey validation bulls. All animals had genotypes for 474,773 single nucleotide polymorphisms after editing and phenotypes for milk, fat, and protein yields. Using the same training data, BSSVS consistently outperformed GREML. The multitask BSSVS, however, did not outperform single-trait BSSVS, which used pooled Holstein and Jersey data for training. Thus, the rigorous assumption that the traits are the same in both breeds yielded a slightly better prediction than a model that had to estimate the correlation between the breeds from the data. Adding the Holstein data significantly increased the accuracy of the single-trait GREML and BSSVS in predicting the Jerseys for milk and protein, in line with estimated correlations between the breeds of 0.66 and 0.47 for milk and protein yields, whereas only the BSSVS model significantly improved the accuracy for fat yield with an estimated correlation between breeds of only 0.05. The relatively high genetic correlations for milk and protein yields, and the superiority of the pooling strategy, is likely the result of the observed admixture between both breeds in our data. The Bayesian model was able to detect several QTL in Holsteins, which likely enabled it to outperform GREML. The inability of the multitask Bayesian models to outperform a simple pooling strategy may be explained by the fact that the pooling strategy assumes equal effects in both breeds; furthermore, this assumption may be valid for moderate- to large-sized QTL, which are important for multibreed genomic prediction.

Required marker properties for unbiased estimates of the genetic correlation between populations

Populations generally differ in environmental and genetic factors, which can create differences in allele substitution effects between populations. Therefore, a single genotype may have different additive genetic values in different populations. The correlation between the two additive genetic values of a single genotype in both populations is known as the additive genetic correlation between populations and can differ from one. Our objective was to investigate whether differences in linkage disequilibrium (LD) and allele frequencies of markers and causal loci between populations affect bias of the estimated genetic correlation. We simulated two populations that were separated for 50 generations. Markers and causal loci were selected to either have similar or different allele frequencies in the two populations. Differences in consistency of LD between populations were obtained by using different marker density panels. Results showed that when the difference in allele frequencies of causal loci between populations was reflected by the markers, genetic correlations were only slightly underestimated using markers. This was even the case when LD patterns, measured by LD statistic r, were different between populations. When the difference in allele frequencies of causal loci between populations was not reflected by the markers, genetic correlations were severely underestimated. We conclude that for an unbiased estimate of the genetic correlation between populations, marker allele frequencies should reflect allele frequencies of causal loci so that marker-based relationships can accurately predict the relationships at causal loci, i.e. E(Gcausal loci|Gmarkers) ≠ Gmarkers. Differences in LD between populations have little effect on the estimated genetic correlation.

Properties Of Genomic Relationships For Estimating Current Genetic Variances Within And Genetic Correlations Between Populations

Different methods are available to calculate multi-population genomic relationship matrices. Since those matrices differ in base population, it is anticipated that the method used to calculate the genomic relationship matrix affect the estimate of genetic variances, covariances and correlations. The aim of this paper is to define a multi-population genomic relationship matrix to estimate current genetic variances within and genetic correlations between populations. The genomic relationship matrix containing two populations consists of four blocks, one block for population 1, one block for population 2, and two blocks for relationships between the populations. It is known, based on literature, that current genetic variances are estimated when the current population is used as base population of the relationship matrix. In this paper, we theoretically derived the properties of the genomic relationship matrix to estimate genetic correlations and validated it using simulations. When the scaling factors of the genomic relationship matrix fulfill the property , the genetic correlation is estimated even though estimated variance components are not necessarily related to the current population. When this property is not met, the correlation based on estimated variance components should be multiplied by to rescale the genetic correlation. In this study we present a genomic relationship matrix which directly results in current genetic variances as well as genetic correlations between populations.