A comparison of principal component regression and genomic REML for genomic prediction across populations

Background

Genomic prediction faces two main statistical problems: multicollinearity and n ≪ p (many fewer observations than predictor variables). Principal component (PC) analysis is a multivariate statistical method that is often used to address these problems. The objective of this study was to compare the performance of PC regression (PCR) for genomic prediction with that of a commonly used REML model with a genomic relationship matrix (GREML) and to investigate the full potential of PCR for genomic prediction.

Methods

The PCR model used either a common or a semi-supervised approach, where PC were selected based either on their eigenvalues (i.e. proportion of variance explained by SNP (single nucleotide polymorphism) genotypes) or on their association with phenotypic variance in the reference population (i.e. the regression sum of squares contribution). Cross-validation within the reference population was used to select the optimum PCR model that minimizes mean squared error. Pre-corrected average daily milk, fat and protein yields of 1609 first lactation Holstein heifers, from Ireland, UK, the Netherlands and Sweden, which were genotyped with 50 k SNPs, were analysed. Each testing subset included animals from only one country, or from only one selection line for the UK.

Results

In general, accuracies of GREML and PCR were similar but GREML slightly outperformed PCR. Inclusion of genotyping information of validation animals into model training (semi-supervised PCR), did not result in more accurate genomic predictions. The highest achievable PCR accuracies were obtained across a wide range of numbers of PC fitted in the regression (from one to more than 1000), across test populations and traits. Using cross-validation within the reference population to derive the number of PC, yielded substantially lower accuracies than the highest achievable accuracies obtained across all possible numbers of PC.

Conclusions

On average, PCR performed only slightly less well than GREML. When the optimal number of PC was determined based on realized accuracy in the testing population, PCR showed a higher potential in terms of achievable accuracy that was not capitalized when PC selection was based on cross-validation. A standard approach for selecting the optimal set of PC in PCR remains a challenge.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-014-0060-x) contains supplementary material, which is available to authorized users.     

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.     

The influence of landscape configuration and environment on population genetic structure in a sedentary passerine: insights from loci located in different genomic regions

The study of the factors structuring genetic variation can help to infer the neutral and adaptive processes shaping the demographic and evolutionary trajectories of natural populations. Here, we analyse the role of isolation by distance (IBD), isolation by resistance (IBR, defined by landscape composition) and isolation by environment (IBE, estimated as habitat and elevation dissimilarity) in structuring genetic variation in 25 blue tit (Cyanistes caeruleus) populations. We typed 1385 individuals at 26 microsatellite loci classified into two groups by considering whether they are located into genomic regions that are actively (TL; 12 loci) or not (NTL; 14 loci) transcribed to RNA. Population genetic differentiation was mostly detected using the panel of NTL. Landscape genetic analyses showed a pattern of IBD for all loci and the panel of NTL, but genetic differentiation estimated at TL was only explained by IBR models considering high resistance for natural vegetation and low resistance for agricultural lands. Finally, the absence for IBE suggests a lack of divergent selection pressures associated with differences in habitat and elevation. Overall, our study shows that markers located in different genomic regions can yield contrasting inferences on landscape‐level patterns of realized gene flow in natural populations.     

The origin and impact of embryonic aneuploidy

Despite the clinical importance of aneuploidy, surprisingly little is known concerning its impact during the earliest stages of human development. This study aimed to shed light on the genesis, progression, and survival of different types of chromosome anomaly from the fertilized oocyte through the final stage of preimplantation development (blastocyst). 2,204 oocytes and embryos were examined using comprehensive cytogenetic methodology. A diverse array of chromosome abnormalities was detected, including many forms never recorded later in development. Advancing female age was associated with dramatic increase in aneuploidy rate and complex chromosomal abnormalities. Anaphase lag and congression failure were found to be important malsegregation causing mechanisms in oogenesis and during the first few mitotic divisions. All abnormalities appeared to be tolerated until activation of the embryonic genome, after which some forms started to decline in frequency. However, many aneuploidies continued to have little impact, with affected embryos successfully reaching the blastocyst stage. Results from the direct analyses of female meiotic divisions and early embryonic stages suggest that chromosome errors present during preimplantation development have origins that are more varied than those seen in later pregnancy, raising the intriguing possibility that the source of aneuploidy might modulate impact on embryo viability. The results of this study also narrow the window of time for selection against aneuploid embryos, indicating that most survive until the blastocyst stage and, since they are not detected in clinical pregnancies, must be lost around the time of implantation or shortly thereafter.     

Nonessential Sites Improve Phosphorylation Switch

Multisite phosphorylation is a common form of posttranslational protein regulation which has been used to increase the switchlike behavior of the protein response to increasing kinase concentrations. In this letter, we show that the switchlike response of multisite phosphoproteins is strongly enhanced by nonessential phosphorylation sites, a mechanism that is robust to parameter changes and easily implemented in nature. We obtained analytic estimates for the Hill exponent (or coefficient) of the switchlike response, and we observed that a tradeoff exists between the switch and the kinase threshold for activation. This also suggests a possible evolutionary mechanism for the relatively large numbers of phosphorylation sites found in various proteins.     

Mitochondrial DNA diversity in wild boar from the Primorsky Krai Region (East Russia)

We have studied the cytochrome B gene and control region DNA variability in 14 wild boars from the Primorsky Region, in the far east corner of Russia. Variability was low (π = 0.00248 overall) compared with the usual estimates in these loci, indicating that this is a rather closed population. Seven haplotypes were found, and one was identical to a Chinese wild boar. Phylogeographically, the sequences clustered among several Asian clades, primarily Chinese domestic pigs and Japanese and Chinese wild boars, and are positioned within the D2 clade reported by Larson et al. [ Science 307 , 2005; 1618 ]. Although North Korean pigs should be studied, our data suggest that the Primorsky mtDNA signature is absent from domestic pigs. Sequences are available through GenBank identifiers HM010461 – HM010488 .