Genomic best linear unbiased prediction method including imprinting effects for genomic evaluation

Background

Genomic best linear unbiased prediction (GBLUP) is a statistical method used to predict breeding values using single nucleotide polymorphisms for selection in animal and plant breeding. Genetic effects are often modeled as additively acting marker allele effects. However, the actual mode of biological action can differ from this assumption. Many livestock traits exhibit genomic imprinting, which may substantially contribute to the total genetic variation of quantitative traits. Here, we present two statistical models of GBLUP including imprinting effects (GBLUP-I) on the basis of genotypic values (GBLUP-I1) and gametic values (GBLUP-I2). The performance of these models for the estimation of variance components and prediction of genetic values across a range of genetic variations was evaluated in simulations.

Results

Estimates of total genetic variances and residual variances with GBLUP-I1 and GBLUP-I2 were close to the true values and the regression coefficients of total genetic values on their estimates were close to 1. Accuracies of estimated total genetic values in both GBLUP-I methods increased with increasing degree of imprinting and broad-sense heritability. When the imprinting variances were equal to 1.4% to 6.0% of the phenotypic variances, the accuracies of estimated total genetic values with GBLUP-I1 exceeded those with GBLUP by 1.4% to 7.8%. In comparison with GBLUP-I1, the superiority of GBLUP-I2 over GBLUP depended strongly on degree of imprinting and difference in genetic values between paternal and maternal alleles. When paternal and maternal alleles were predicted (phasing accuracy was equal to 0.979), accuracies of the estimated total genetic values in GBLUP-I1 and GBLUP-I2 were 1.7% and 1.2% lower than when paternal and maternal alleles were known.

Conclusions

This simulation study shows that GBLUP-I1 and GBLUP-I2 can accurately estimate total genetic variance and perform well for the prediction of total genetic values. GBLUP-I1 is preferred for genomic evaluation, while GBLUP-I2 is preferred when the imprinting effects are large, and the genetic effects differ substantially between sexes.     

Restricted best linear unbiased prediction and a selection model

Summary An equivalence between restricted best linear unbiased prediction (and thus restricted selection index) and a particular example of a selection model is presented. Specifically, the equivalence is between restricted selection and a model of selection on the residuals of the general mixed linear model. This result illustrates that restricted selection acts by nonrandomly sampling those genes that act pleiotropically in multiple trait genetic models. An expression for a mixed linear model which includes restrictions is also presented.     

Evaluation of the best linear unbiased prediction method for breeding values of fruit-quality traits in citrus

Fruit-quality trait improvement is an important objective in citrus breeding; however, fruit breeding programs often accumulate highly unbalanced phenotypic records, which are a serious obstacle in comparing and selecting genotypes. The best linear unbiased prediction (BLUP) method can be used to overcome these difficulties, but few fruit breeding programs have adopted the method, and to our knowledge, the method has not yet been used to predict breeding values of traits based on pedigree information and genetic correlations between traits in citrus. Accordingly, we used the BLUP method to predict the breeding values of nine fruit-quality traits (fruit weight, fruit skin color, fruit surface texture, peelability, flesh color, pulp firmness, segment firmness, sugar content, and acid content) utilizing phenotypic records collected over several years as part of the citrus breeding program conducted at the Kuchinotsu branch of the National Institute of Fruit Tree Science in Japan. Although the accumulated phenotypic records were highly unbalanced, the BLUP method was able to predict the breeding values of all 2122 genotypes (111 parental cultivars and 2011 F₁ offspring from 126 pair-cross families), as well as estimates of several genetic parameters, including narrow-sense heritability and phenotypic and genotypic correlations. These findings demonstrate the utility of the BLUP method in citrus crossbreeding and provide predicted breeding values, which can be used to select superior genotypes in the Kuchinotsu Citrus Breeding Program and related genetic selection endeavors.     

Estimation of long-term genetic improvement for gerbera using the best linear unbiased prediction (BLUP) procedure

Long-term genetic improvement is measured by the selection response predicted from estimates of narrow-sense heritability. Accurate estimates of selection response require partitioning the change of population mean into genetic and environmental components. A selection experiment for cut-flower yield was conducted for 16 generations in the Davis population of gerbera (Gerbera hybrida, Compositae). Breeding values were estimated for individual plants in the population using the best linear unbiased prediction (BLUP) procedure. Genetic change in each generation was calculated from the breeding values of individual plants. The results of this study indicate that long-term selection was successful and necessary for the genetic improvement in cut-flower yield. Genetic improvement in mean breeding value over 16 generations was 33 flowers. Mean breeding values increased monotonically with an S-shape pattern while environmental effects fluctuated from generation to generation. Results predict that cut-flower yield in the Davis population of gerbera will continue to respond to selection.     

Empirical best linear unbiased prediction in cultivar trials using factor-analytic variance-covariance structures

 Results of multi-environment trials to evaluate new plant cultivars may be displayed in a two-way table of genotypes by environments. Different estimators are available to fill the cells of such tables. It has been shown previously that the predictive accuracy of the simple genotype by environment mean is often lower than that of other estimators, e.g. least-squares estimators based on multiplicative models, such as the additive main effects multiplicative interaction (AMMI) model, or empirical best-linear unbiased predictors (BLUPs) based on a two-way analysis-of-variance (ANOVA) model. This paper proposes a method to obtain BLUPs based on models with multiplicative terms. It is shown by cross-validation using five real data sets (oilseed rape, Brassica napus L.) that the predictive accuracy of BLUPs based on models with multiplicative terms may be better than that of least-squares estimators based on the same models and also better than BLUPs based on ANOVA models. Received: 18 October 1997 / Accepted: 31 March 1998     

Prediction of maize double-cross hybrids using the best linear unbiased prediction with microsatellite marker information

We examined the usefulness of the best linear unbiased prediction associated with molecular markers for prediction of untested maize double-cross hybrids. Ten single-cross hybrids from different commercial backgrounds were crossed using a complete diallel design. These 10 single-cross hybrids were genotyped with 20 microsatellite markers. The best linear unbiased prediction associated with microsatellite information gave relatively good prediction ability of the double-cross hybrid performance, with correlations between observed phenotypic values and genotypic prediction values varying from 0.27 to 0.54. Taking into account the predictions of specific combing ability, the correlation between observed and predicted specific combining ability varied from 0.50 to 0.88. Based on these results, we infer that it is feasible to predict maize double-cross hybrids with different unbalance degrees without including any prior information about parental inbreed lines or single-cross hybrid performance.     

Asymptotic rates of response from forest tree breeding strategies using best linear unbiased prediction

 Genetic gain equations are developed for selection on multiple traits using either multi- or univariate best linear unbiased predictors (BLUP) and for selection under controlled and open pollination and polymix mating schemes. The equations assume an infinite population and account for the effects of selection. A comparison with simulated populations under the same mating schemes show that the gain equations predict selection response well, with the predictions having some upward bias. The gain equations are used to compare across mating schemes, to compare univariate to multivariate analyses, and to measure the reduction in the rate of genetic gain due to selection disequilibrium. Results show controlled pollination schemes can offer as much as a 56% advantage in genetic gain relative to open pollination. The reduction in the rate of genetic gain due to selection disequilibrium is approximately 27% under controlled pollination for the breeding goals studied. The results show a limited benefit in using multivariate analyses for predicting breeding values. Received: 20 April 1997 / Accepted: 8 October 1997     

Testcross additive and dominance effects in best linear unbiased prediction of maize single-cross performance

Best linear unbiased prediction (BLUP) has been found to be useful in maize (Zea mays L.) breeding. The advantage of including both testcross additive and dominance effects (Intralocus Model) in BLUP, rather than only testcross additive effects (Additive Model), has not been clearly demonstrated. The objective of this study was to compare the usefulness of Intralocus and Additive Models for BLUP of maize single-cross performance. Multilocation data from 1990 to 1995 were obtained from the hybrid testing program of Limagrain Genetics. Grain yield, moisture, stalk lodging, and root lodging of untested single crosses were predicted from (1) the performance of tested single crosses and (2) known genetic relationships among the parental inbreds. Correlations between predicted and observed performance were obtained with a delete-one cross-validation procedure. For the Intralocus Model, the correlations ranged from 0.50 to 0.66 for yield, 0.88 to 0.94 for moisture, 0.47 to 0.69 for stalk lodging, and 0.31 to 0.45 for root lodging. The BLUP procedure was consistently more effective with the Intralocus Model than with the Additive Model. When the Additive Model was used instead of the Intralocus Model, the reductions in the correlation were largest for root lodging (0.06–0.35), smallest for moisture (0.00–0.02), and intermediate for yield (0.02–0.06) and stalk lodging (0.02–0.08). The ratio of dominance variance (v _D) to total genetic variance (v _G) was highest for root lodging (0.47) and lowest for moisture (0.10). The Additive Model may be used if prior information indicates that V_D for a given trait has little contribution to V_G. Otherwise, the continued use of the Intralocus Model for BLUP of single-cross performance is recommended.     

Genetic evaluation by best linear unbiased prediction using marker and trait information in a multibreed population.

Genetic evaluation by best linear unbiased prediction (BLUP) requires modeling genetic means, variances, and covariances. This paper presents theory to model means, variances, and covariances in a multibreed population, given marker and breed information, in the presence of gametic disequilibrium between the marker locus (ML) and linked quantitative trait locus (MQTL). Theory and algorithms are presented to construct the matrix of conditional covariances between relatives (Gv) for the MQTL effects in a multibreed population and to obtain the inverse of Gv efficiently. Theory presented here accounts for heterogeneity of variances among pure breeds and for segregation variances between pure breeds. A numerical example was used to illustrate how the theory and algorithms can be used for genetic evaluation by BLUP using marker and trait information in a multibreed population.     

Prediction of rates of inbreeding in populations selected on best linear unbiased prediction of breeding value

Predictions for the rate of inbreeding (DeltaF) in populations with discrete generations undergoing selection on best linear unbiased prediction (BLUP) of breeding value were developed. Predictions were based on the concept of long-term genetic contributions using a recently established relationship between expected contributions and rates of inbreeding and a known procedure for predicting expected contributions. Expected contributions of individuals were predicted using a linear model, u(i)(()(x)()) = alpha + betas(i), where s(i) denotes the selective advantage as a deviation from the contemporaries, which was the sum of the breeding values of the individual and the breeding values of its mates. The accuracy of predictions was evaluated for a wide range of population and genetic parameters. Accurate predictions were obtained for populations of 5-20 sires. For 20-80 sires, systematic underprediction of on average 11% was found, which was shown to be related to the goodness of fit of the linear model. Using simulation, it was shown that a quadratic model would give accurate predictions for those schemes. Furthermore, it was shown that, contrary to random selection, DeltaF less than halved when the number of parents was doubled and that in specific cases DeltaF may increase with the number of dams.     

Predicting biological networks from genomic data

Continuing improvements in DNA sequencing technologies are providing us with vast amounts of genomic data from an ever-widening range of organisms. The resulting challenge for bioinformatics is to interpret this deluge of data and place it back into its biological context. Biological networks provide a conceptual framework with which we can describe part of this context, namely the different interactions that occur between the molecular components of a cell. Here, we review the computational methods available to predict biological networks from genomic sequence data and discuss how they relate to high-throughput experimental methods.     

Predicting clinical outcomes in neuroblastoma with genomic data integration

Background

Neuroblastoma is a heterogeneous disease with diverse clinical outcomes. Current risk group models require improvement as patients within the same risk group can still show variable prognosis. Recently collected genome-wide datasets provide opportunities to infer neuroblastoma subtypes in a more unified way. Within this context, data integration is critical as different molecular characteristics can contain complementary signals. To this end, we utilized the genomic datasets available for the SEQC cohort patients to develop supervised and unsupervised models that can predict disease prognosis.

Results

Our supervised model trained on the SEQC cohort can accurately predict overall survival and event-free survival profiles of patients in two independent cohorts. We also performed extensive experiments to assess the prediction accuracy of high risk patients and patients without MYCN amplification. Our results from this part suggest that clinical endpoints can be predicted accurately across multiple cohorts. To explore the data in an unsupervised manner, we used an integrative clustering strategy named multi-view kernel k-means (MVKKM) that can effectively integrate multiple high-dimensional datasets with varying weights. We observed that integrating different gene expression datasets results in a better patient stratification compared to using these datasets individually. Also, our identified subgroups provide a better Cox regression model fit compared to the existing risk group definitions.

Conclusion

Altogether, our results indicate that integration of multiple genomic characterizations enables the discovery of subtypes that improve over existing definitions of risk groups. Effective prediction of survival times will have a direct impact on choosing the right therapies for patients.

Reviewers

This article was reviewed by Susmita Datta, Wenzhong Xiao and Ziv Shkedy.

     

Marker-assisted prediction of non-additive genetic values

It has become increasingly clear from systems biology arguments that interaction and non-linearity play an important role in genetic regulation of phenotypic variation for complex traits. Marker-assisted prediction of genetic values assuming additive gene action has been widely investigated because of its relevance in artificial selection. On the other hand, it has been less well-studied when non-additive effects hold. Here, we explored a nonparametric model, radial basis function (RBF) regression, for predicting quantitative traits under different gene action modes (additivity, dominance and epistasis). Using simulation, it was found that RBF had better ability (higher predictive correlations and lower predictive mean square errors) of predicting merit of individuals in future generations in the presence of non-additive effects than a linear additive model, the Bayesian Lasso. This was true for populations undergoing either directional or random selection over several generations. Under additive gene action, RBF was slightly worse than the Bayesian Lasso. While prediction of genetic values under additive gene action is well handled by a variety of parametric models, nonparametric RBF regression is a useful counterpart for dealing with situations where non-additive gene action is suspected, and it is robust irrespective of mode of gene action.     

Finalizing host range determination of a weed biological control pathogen with best linear unbiased predictors and damage assessment

Colletotrichum gloeosporioides f. sp. salsolae (Penz.) Penz. & Sacc. in Penz. (CGS) is a facultative parasitic fungus being evaluated as a classical biological control agent of Russian thistle or tumbleweed (Salsola tragus L.). In initial host range determination tests, Henderson’s mixed model equations (MME) were used to generate best linear unbiased predictors (BLUPs) of disease severity reaction to CGS among 89 species of plants related to S. tragus. The MME provided: (1) disease assessments for rare and difficult or impossible to grow species, (2) environmentally independent measures of disease severity, (3) measures of disease severity for species versus a sample of material tested in a greenhouse, (4) objective indicators of susceptible and non-susceptible species, (5) a means to objectively compare disease on targets versus non-targets. Of the 89 species evaluated by the MME, eight native N. American species were predicted to be susceptible. As a result of these predictions, these eight species were further evaluated to determine the amount of actual damage caused by CGS. This was done by comparing root and shoot areas and weights between non-inoculated plants and plants inoculated with CGS. Results showed that several of the species exhibited some minor reduction in root weight and root area, but none of the species had any damage to above-ground plant parts. This supports the BLUP output in the initial host range determination tests. As a result of both analyses, there is no evidence that CGS would cause any non-target effects in nature.     

Trends in population parameters and best linear unbiased prediction of progeny performance in a European F2 maize population under modified recurrent full-sib selection

Recurrent selection is a cyclic breeding procedure designed to improve the mean of a population for the trait(s) under selection. Starting from an F₂ population of European flint maize (Zea mays L.) intermated for three generations, we conducted seven cycles of a modified recurrent full-sib (FS) selection scheme. The objectives of our study were to (1) monitor trends across selection cycles in the estimates of the population mean, additive and dominance variances, (2) compare predicted and realized selection responses, and (3) investigate the usefulness of best linear unbiased prediction (BLUP) of progeny performance under the recurrent FS selection scheme applied. Recurrent FS selection was conducted at three locations using a selection rate of 25% for a selection index, based on grain yield and grain moisture. Recombination was performed according to a pseudo-factorial mating scheme, where the selected FS families were divided into an upper-ranking group of parents mated to the lower-ranking group. Variance components were estimated with restricted maximum likelihood. Average grain yield increased 9.1% per cycle, average grain moisture decreased 1.1% per cycle, and the selection index increased 11.2% per cycle. For the three traits we observed, no significant changes in additive and dominance variances occurred, suggesting future selection response at or near current rates of progress. Predictions of FS family performance in Cn+1 based on mean performance of parental FS families in Cn were of equal or higher precision as those based on the mean additive genetic BLUP of their parents, and corresponding correlations were of moderate size only for grain moisture. The significant increase in grain yield combined with the decrease in grain moisture suggest that the F₂ source population with use of a pseudo-factorial mating scheme is an appealing alternative to other types of source materials and random mating schemes commonly used in recurrent selection.