Empirical and deterministic accuracies of across-population genomic prediction

Background

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.

Methods

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.

Results

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.

Conclusions

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.     

Phagocytosis of bacteria by polymorphonuclear leukocytes: a freeze-fracture, scanning electron microscope, and thin-section investigation of membrane structure

The changes in membrane structure of rabbit polymorphonuclear (PMN) leukocytes during bacterial phagocytosis was investigated with scanning electron microscope (SEM), thin-section, and freeze-fracture techniques. SEM observations of bacterial attachment sites showed the involvement of limited areas of PMN membrane surface (0.01-0.25μm(2)). Frequently, these areas of attachment were located on membrane extensions. The membrane extensions were present before, during, and after the engulfment of bacteria, but were diminished in size after bacterial engulfment. In general, the results obtained with SEM and thin-section techniques aided in the interpretation of the three-dimensional freeze-fracture replicas. Freeze-fracture results revealed the PMN leukocytes had two fracture faces as determined by the relative density of intramembranous particles (IMP). Membranous extensions of the plasma membrane, lysosomes, and phagocytic vacuoles contained IMP's with a distribution and density similar to those of the plasma membrane. During phagocytosis, IMPs within the plasma membrane did not undergo a massive aggregation. In fact, structural changes within the membranes were infrequent and localized to regions such as the attachment sites of bacteria, the fusion sites on the plasma membrane, and small scale changes in the phagocytic vacuole membrane during membrane fusion. During the formation of the phagocytic vacuole, the IMPs of the plasma membrane appeared to move in with the lipid bilayer while maintaining a distribution and density of IMPs similar to those of the plasma membranes. Occasionally, IMPs were aligned to linear arrays within phagocytic vacuole membranes. This alignment might be due to an interaction with linearly arranged motile structures on the side of the phagocytic vacuole membranes. IMP-free regions were observed after fusion of lysosomes with the phagocytic vacuoles or plasma membrane. These IMP-free areas probably represent sites where membrane fusion occurred between lysosomal membrane and phagocytic vacuole membrane or plasma membrane. Highly symmetrical patterns of IMPs were not observed during lysosomal membrane fusion.     

Effects of data structure on the estimation of covariance functions to describe genotype by environment interactions in a reaction norm model

Covariance functions have been proposed to predict breeding values and genetic (co)variances as a function of phenotypic within herd-year averages (environmental parameters) to include genotype by environment interaction. The objective of this paper was to investigate the influence of definition of environmental parameters and non-random use of sires on expected breeding values and estimated genetic variances across environments. Breeding values were simulated as a linear function of simulated herd effects. The definition of environmental parameters hardly influenced the results. In situations with random use of sires, estimated genetic correlations between the trait expressed in different environments were 0.93, 0.93 and 0.97 while simulated at 0.89 and estimated genetic variances deviated up to 30% from the simulated values. Non random use of sires, poor genetic connectedness and small herd size had a large impact on the estimated covariance functions, expected breeding values and calculated environmental parameters. Estimated genetic correlations between a trait expressed in different environments were biased upwards and breeding values were more biased when genetic connectedness became poorer and herd composition more diverse. The best possible solution at this stage is to use environmental parameters combining large numbers of animals per herd, while losing some information on genotype by environment interaction in the data.     

Accuracy of imputation to whole-genome sequence data in Holstein Friesian cattle

Background

The use of whole-genome sequence data can lead to higher accuracy in genome-wide association studies and genomic predictions. However, to benefit from whole-genome sequence data, a large dataset of sequenced individuals is needed. Imputation from SNP panels, such as the Illumina BovineSNP50 BeadChip and Illumina BovineHD BeadChip, to whole-genome sequence data is an attractive and less expensive approach to obtain whole-genome sequence genotypes for a large number of individuals than sequencing all individuals. Our objective was to investigate accuracy of imputation from lower density SNP panels to whole-genome sequence data in a typical dataset for cattle.

Methods

Whole-genome sequence data of chromosome 1 (1737 471 SNPs) for 114 Holstein Friesian bulls were used. Beagle software was used for imputation from the BovineSNP50 (3132 SNPs) and BovineHD (40 492 SNPs) beadchips. Accuracy was calculated as the correlation between observed and imputed genotypes and assessed by five-fold cross-validation. Three scenarios S40, S60 and S80 with respectively 40%, 60%, and 80% of the individuals as reference individuals were investigated.

Results

Mean accuracies of imputation per SNP from the BovineHD panel to sequence data and from the BovineSNP50 panel to sequence data for scenarios S40 and S80 ranged from 0.77 to 0.83 and from 0.37 to 0.46, respectively. Stepwise imputation from the BovineSNP50 to BovineHD panel and then to sequence data for scenario S40 improved accuracy per SNP to 0.65 but it varied considerably between SNPs.

Conclusions

Accuracy of imputation to whole-genome sequence data was generally high for imputation from the BovineHD beadchip, but was low from the BovineSNP50 beadchip. Stepwise imputation from the BovineSNP50 to the BovineHD beadchip and then to sequence data substantially improved accuracy of imputation. SNPs with a low minor allele frequency were more difficult to impute correctly and the reliability of imputation varied more. Linkage disequilibrium between an imputed SNP and the SNP on the lower density panel, minor allele frequency of the imputed SNP and size of the reference group affected imputation reliability.     

Genomic prediction of breeding values using previously estimated SNP variances

Background

Genomic prediction requires estimation of variances of effects of single nucleotide polymorphisms (SNPs), which is computationally demanding, and uses these variances for prediction. We have developed models with separate estimation of SNP variances, which can be applied infrequently, and genomic prediction, which can be applied routinely.

Methods

SNP variances were estimated with Bayes Stochastic Search Variable Selection (BSSVS) and BayesC. Genome-enhanced breeding values (GEBV) were estimated with RR-BLUP (ridge regression best linear unbiased prediction), using either variances obtained from BSSVS (BLUP-SSVS) or BayesC (BLUP-C), or assuming equal variances for each SNP. Datasets used to estimate SNP variances comprised (1) all animals, (2) 50% random animals (RAN50), (3) 50% best animals (TOP50), or (4) 50% worst animals (BOT50). Traits analysed were protein yield, udder depth, somatic cell score, interval between first and last insemination, direct longevity, and longevity including information from predictors.

Results

BLUP-SSVS and BLUP-C yielded similar GEBV as the equivalent Bayesian models that simultaneously estimated SNP variances. Reliabilities of these GEBV were consistently higher than from RR-BLUP, although only significantly for direct longevity. Across scenarios that used data subsets to estimate GEBV, observed reliabilities were generally higher for TOP50 than for RAN50, and much higher than for BOT50. Reliabilities of TOP50 were higher because the training data contained more ancestors of selection candidates. Using estimated SNP variances based on random or non-random subsets of the data, while using all data to estimate GEBV, did not affect reliabilities of the BLUP models. A convergence criterion of 10⁻⁸ instead of 10⁻¹⁰ for BLUP models yielded similar GEBV, while the required number of iterations decreased by 71 to 90%. Including a separate polygenic effect consistently improved reliabilities of the GEBV, but also substantially increased the required number of iterations to reach convergence with RR-BLUP. SNP variances converged faster for BayesC than for BSSVS.

Conclusions

Combining Bayesian variable selection models to re-estimate SNP variances and BLUP models that use those SNP variances, yields GEBV that are similar to those from full Bayesian models. Moreover, these combined models yield predictions with higher reliability and less bias than the commonly used RR-BLUP model.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-014-0052-x) contains supplementary material, which is available to authorized users.     

A dye-binding induced conformational transition of poly-(methacrylic acid) by Auramine O in aqueous solutions. I. Experimental results

Binding of auramine O to poly-(methacrylic acid) (PMA) has been established over a large range of C⁰_p/C⁰_d values using spectroscopic methods (UV absorption and visible fluorescence emission spectra), equilibrium and sedimentation dialysis, potentiometric and viscosimetric titrations. All the results show qualitative agreement with those obtained previously with the system crystal violet-PMA although the binding seems to be less strong for auramine O than for crystal violet. From dialysis experiments binding isotherms were obtained at three different degrees of neutralization α'; at α' = 0.10 the results could be fitted to a Langmuir isotherm but at α' equal to 0.40 and 0.65 deviations with respect to such an isotherm occur. The results of potentiometric and viscosimetric titrations confirm that the conformational transition which the dye-free PMA exhibits upon ionization is affected by the dye binding. The region in which the conformational transion occurs is broadened and is less sharply defined in the presence of auramine O.     

Estimation of prediction error variances via Monte Carlo sampling methods using different formulations of the prediction error variance

Calculation of the exact prediction error variance covariance matrix is often computationally too demanding, which limits its application in REML algorithms, the calculation of accuracies of estimated breeding values and the control of variance of response to selection. Alternatively Monte Carlo sampling can be used to calculate approximations of the prediction error variance, which converge to the true values if enough samples are used. However, in practical situations the number of samples, which are computationally feasible, is limited. The objective of this study was to compare the convergence rate of different formulations of the prediction error variance calculated using Monte Carlo sampling. Four of these formulations were published, four were corresponding alternative versions, and two were derived as part of this study. The different formulations had different convergence rates and these were shown to depend on the number of samples and on the level of prediction error variance. Four formulations were competitive and these made use of information on either the variance of the estimated breeding value and on the variance of the true breeding value minus the estimated breeding value or on the covariance between the true and estimated breeding values.