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

The 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. The 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. Consistency 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.

Wientjes YC ，Veerkamp RF ，Calus MP 《BMC GENETICS》

Empirical and deterministic accuracies of across-population genomic prediction.

Differences 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. A 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. Accuracies 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. The 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.

Wientjes YC ，Veerkamp RF ，Bijma P ，Bovenhuis H ，Schrooten C ，Calus MP ... -  《-》

Contributions of linkage disequilibrium and co-segregation information to the accuracy of genomic prediction.

Traditional genomic prediction models using multiple regression on single nucleotide polymorphisms (SNPs) genotypes exploit associations between genotypes of quantitative trait loci (QTL) and SNPs, which can be created by historical linkage disequilibrium (LD), recent co-segregation (CS) and pedigree relationships. Results from field data analyses show that prediction accuracy is usually much higher for individuals that are close relatives of the training population than for distantly related individuals. A possible reason is that historical LD between QTL and SNPs is weak and, for close relatives, prediction accuracy of SNP models is mainly contributed by pedigree relationships and CS. Information from pedigree relationships decreases fast over generations and only contributes to within-family prediction. Information from CS is affected by family structures and effective population size, and can have a substantial contribution to prediction accuracy when modeled explicitly. In this study, a method to explicitly model CS was developed by following the transmission of putative QTL alleles using allele origins at SNPs. Bayesian hierarchical models that combine information from LD and CS (LD-CS model) were developed for genomic prediction in pedigree populations. Contributions of LD and CS information to prediction accuracy across families and generations without retraining were investigated in simulated half-sib datasets and deep pedigrees with different recent effective population sizes, respectively. Results from half-sib datasets showed that when historical LD between QTL and SNPs is low, accuracy of the LD model decreased when the training data size is increased by adding independent sire families, but accuracies from the CS and LD-CS models increased and plateaued rapidly. Results from deep pedigree datasets show that the LD model had high accuracy across generations only when historical LD between QTL and SNPs was high. Modeling CS explicitly resulted in higher accuracy than the LD model across generations when the mating design generated many close relatives. Our results suggest that modeling CS explicitly improves accuracy of genomic prediction when historical LD between QTL and SNPs is low. Modeling both LD and CS explicitly is expected to improve accuracy when recent effective population size is small, or when the training data include many independent families.

Sun X ，Fernando R ，Dekkers J 《-》

Accuracy of prediction of simulated polygenic phenotypes and their underlying quantitative trait loci genotypes using real or imputed whole-genome markers in cattle.

More accurate genomic predictions are expected when the effects of QTL (quantitative trait loci) are predicted from markers in close physical proximity to the QTL. The objective of this study was to quantify to what extent whole-genome methods using 50 K or imputed 770 K SNPs (single nucleotide polymorphisms) could predict single or multiple QTL genotypes based on SNPs in close proximity to those QTL. Phenotypes with a heritability of 1 were simulated for 2677 Hereford animals genotyped with the BovineSNP50 BeadChip. Genotypes for the high-density 770 K SNP panel were imputed using Beagle software. Various Bayesian regression methods were used to predict single QTL or a trait influenced by 42 such QTL. We quantified to what extent these predictions were based on SNPs in close proximity to the QTL by comparing whole-genome predictions to local predictions based on estimates of the effects of variable numbers of SNPs i.e. ±1, ±2, ±5, ±10, ±50 or ±100 that flanked the QTL. Prediction accuracies based on local SNPs using whole-genome training for single QTL with the 50 K SNP panel and BayesC0 ranged from 0.49 (±1 SNP) to 0.75 (±100 SNPs). The minimum number of local SNPs for an accurate prediction is ±10 SNPs. Prediction accuracies that were based on local SNPs only were higher than those based on whole-genome SNPs for both 50 K and 770 K SNP panels. For the 770 K SNP panel, prediction accuracies were higher than 0.70 and varied little i.e. between 0.73 (±1 SNP) and 0.77 (±5 SNPs). For the summed 42 QTL, prediction accuracies were generally higher than for single QTL regardless of the number of local SNPs. For QTL with low minor allele frequency (MAF) compared to QTL with high MAF, prediction accuracies increased as the number of SNPs around the QTL increased. These results suggest that with both 50 K and imputed 770 K SNP genotypes the level of linkage disequilibrium is sufficient to predict single and multiple QTL. However, prediction accuracies are eroded through spuriously estimated effects of SNPs that are distant from the QTL. Prediction accuracies were higher with the 770 K than with the 50 K SNP panel.

Hassani S ，Saatchi M ，Fernando RL ，Garrick DJ ... -  《-》

Accuracy of Genomic Prediction in Synthetic Populations Depending on the Number of Parents, Relatedness, and Ancestral Linkage Disequilibrium.

Synthetics play an important role in quantitative genetic research and plant breeding, but few studies have investigated the application of genomic prediction (GP) to these populations. Synthetics are generated by intermating a small number of parents ([Formula: see text] and thereby possess unique genetic properties, which make them especially suited for systematic investigations of factors contributing to the accuracy of GP. We generated synthetics in silico from [Formula: see text]2 to 32 maize (Zea mays L.) lines taken from an ancestral population with either short- or long-range linkage disequilibrium (LD). In eight scenarios differing in relatedness of the training and prediction sets and in the types of data used to calculate the relationship matrix (QTL, SNPs, tag markers, and pedigree), we investigated the prediction accuracy (PA) of Genomic best linear unbiased prediction (GBLUP) and analyzed contributions from pedigree relationships captured by SNP markers, as well as from cosegregation and ancestral LD between QTL and SNPs. The effects of training set size [Formula: see text] and marker density were also studied. Sampling few parents ([Formula: see text]) generates substantial sample LD that carries over into synthetics through cosegregation of alleles at linked loci. For fixed [Formula: see text], [Formula: see text] influences PA most strongly. If the training and prediction set are related, using [Formula: see text] parents yields high PA regardless of ancestral LD because SNPs capture pedigree relationships and Mendelian sampling through cosegregation. As [Formula: see text] increases, ancestral LD contributes more information, while other factors contribute less due to lower frequencies of closely related individuals. For unrelated prediction sets, only ancestral LD contributes information and accuracies were poor and highly variable for [Formula: see text] due to large sample LD. For large [Formula: see text], achieving moderate accuracy requires large [Formula: see text], long-range ancestral LD, and high marker density. Our approach for analyzing PA in synthetics provides new insights into the prospects of GP for many types of source populations encountered in plant breeding.

Schopp P ，Müller D ，Technow F ，Melchinger AE ... -  《-》