Estimating Additive and Non-Additive Genetic Variances and Predicting Genetic Merits Using Genome-Wide Dense Single Nucleotide Polymorphism Markers

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Abstract

Non-additive genetic variation is usually ignored when genome-wide markers are used to study the genetic architecture and genomic prediction of complex traits in human, wild life, model organisms or farm animals. However, non-additive genetic effects may have an important contribution to total genetic variation of complex traits. This study presented a genomic BLUP model including additive and non-additive genetic effects, in which additive and non-additive genetic relation matrices were constructed from information of genome-wide dense single nucleotide polymorphism (SNP) markers. In addition, this study for the first time proposed a method to construct dominance relationship matrix using SNP markers and demonstrated it in detail. The proposed model was implemented to investigate the amounts of additive genetic, dominance and epistatic variations, and assessed the accuracy and unbiasedness of genomic predictions for daily gain in pigs. In the analysis of daily gain, four linear models were used: 1) a simple additive genetic model (MA), 2) a model including both additive and additive by additive epistatic genetic effects (MAE), 3) a model including both additive and dominance genetic effects (MAD), and 4) a full model including all three genetic components (MAED). Estimates of narrow-sense heritability were 0.397, 0.373, 0.379 and 0.357 for models MA, MAE, MAD and MAED, respectively. Estimated dominance variance and additive by additive epistatic variance accounted for 5.6% and 9.5% of the total phenotypic variance, respectively. Based on model MAED, the estimate of broad-sense heritability was 0.506. Reliabilities of genomic predicted breeding values for the animals without performance records were 28.5%, 28.8%, 29.2% and 29.5% for models MA, MAE, MAD and MAED, respectively. In addition, models including non-additive genetic effects improved unbiasedness of genomic predictions.

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Hot topic: a unified approach to utilize phenotypic, full pedigree, and genomic information for genetic evaluation of Holstein final score.

I. Aguilar, I Misztal, D Johnson … (2010)

The first national single-step, full-information (phenotype, pedigree, and marker genotype) genetic evaluation was developed for final score of US Holsteins. Data included final scores recorded from 1955 to 2009 for 6,232,548 Holsteins cows. BovineSNP50 (Illumina, San Diego, CA) genotypes from the Cooperative Dairy DNA Repository (Beltsville, MD) were available for 6,508 bulls. Three analyses used a repeatability animal model as currently used for the national US evaluation. The first 2 analyses used final scores recorded up to 2004. The first analysis used only a pedigree-based relationship matrix. The second analysis used a relationship matrix based on both pedigree and genomic information (single-step approach). The third analysis used the complete data set and only the pedigree-based relationship matrix. The fourth analysis used predictions from the first analysis (final scores up to 2004 and only a pedigree-based relationship matrix) and prediction using a genomic based matrix to obtain genetic evaluation (multiple-step approach). Different allele frequencies were tested in construction of the genomic relationship matrix. Coefficients of determination between predictions of young bulls from parent average, single-step, and multiple-step approaches and their 2009 daughter deviations were 0.24, 0.37 to 0.41, and 0.40, respectively. The highest coefficient of determination for a single-step approach was observed when using a genomic relationship matrix with assumed allele frequencies of 0.5. Coefficients for regression of 2009 daughter deviations on parent-average, single-step, and multiple-step predictions were 0.76, 0.68 to 0.79, and 0.86, respectively, which indicated some inflation of predictions. The single-step regression coefficient could be increased up to 0.92 by scaling differences between the genomic and pedigree-based relationship matrices with little loss in accuracy of prediction. One complete evaluation took about 2h of computing time and 2.7 gigabytes of memory. Computing times for single-step analyses were slightly longer (2%) than for pedigree-based analysis. A national single-step genetic evaluation with the pedigree relationship matrix augmented with genomic information provided genomic predictions with accuracy and bias comparable to multiple-step procedures and could account for any population or data structure. Advantages of single-step evaluations should increase in the future when animals are pre-selected on genotypes. Copyright 2010 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

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Increased accuracy of artificial selection by using the realized relationship matrix.

B. Hayes, P M Visscher, M. E. Goddard (2009)

Dense marker genotypes allow the construction of the realized relationship matrix between individuals, with elements the realized proportion of the genome that is identical by descent (IBD) between pairs of individuals. In this paper, we demonstrate that by replacing the average relationship matrix derived from pedigree with the realized relationship matrix in best linear unbiased prediction (BLUP) of breeding values, the accuracy of the breeding values can be substantially increased, especially for individuals with no phenotype of their own. We further demonstrate that this method of predicting breeding values is exactly equivalent to the genomic selection methodology where the effects of quantitative trait loci (QTLs) contributing to variation in the trait are assumed to be normally distributed. The accuracy of breeding values predicted using the realized relationship matrix in the BLUP equations can be deterministically predicted for known family relationships, for example half sibs. The deterministic method uses the effective number of independently segregating loci controlling the phenotype that depends on the type of family relationship and the length of the genome. The accuracy of predicted breeding values depends on this number of effective loci, the family relationship and the number of phenotypic records. The deterministic prediction demonstrates that the accuracy of breeding values can approach unity if enough relatives are genotyped and phenotyped. For example, when 1000 full sibs per family were genotyped and phenotyped, and the heritability of the trait was 0.5, the reliability of predicted genomic breeding values (GEBVs) for individuals in the same full sib family without phenotypes was 0.82. These results were verified by simulation. A deterministic prediction was also derived for random mating populations, where the effective population size is the key parameter determining the effective number of independently segregating loci. If the effective population size is large, a very large number of individuals must be genotyped and phenotyped in order to accurately predict breeding values for unphenotyped individuals from the same population. If the heritability of the trait is 0.3, and N(e)=100, approximately 12474 individuals with genotypes and phenotypes are required in order to predict GEBVs of un-phenotyped individuals in the same population with an accuracy of 0.7 [corrected].

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Technical note: Derivation of equivalent computing algorithms for genomic predictions and reliabilities of animal merit.

I Strandén, D Garrick (2009)

Conventional prediction of dairy cattle merit involves setting up and solving linear equations with the number of unknowns being the number of animals, typically millions, multiplied by the number of traits being simultaneously assessed. The coefficient matrix has been large and sparse and iteration on data has been the method of choice, whereby the coefficient matrix is not stored but recreated as needed. In contrast, genomic prediction involves assessment of the merit of genome fragments characterized by single nucleotide polymorphism genotypes, currently some 50,000, which can then be used to predict the merit of individual animals according to the fragments they have inherited. The prediction equations for chromosome fragments typically have fewer than 100,000 unknowns, but the number of observations used to predict the fragment effects can be one-tenth the number of fragments. The coefficient matrix tends to be dense and the resulting system of equations can be ill behaved. Equivalent computing algorithms for genomic prediction were derived. The number of unknowns in the equivalent system grows with number of genotyped animals, usually bulls, rather than the number of chromosome fragment effects. In circumstances with fewer genotyped animals than single nucleotide polymorphism genotypes, these equivalent computations allow the solving of a smaller system of equations that behaves numerically better. There were 3 solving strategies compared: 1 method that formed and stored the coefficient matrix in memory and 2 methods that iterate on data. Finally, formulas for reliabilities of genomic predictions of merit were developed.

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Author and article information

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: Role: Editor

Journal

Journal ID (nlm-ta): PLoS One

Journal ID (iso-abbrev): PLoS ONE

Journal ID (publisher-id): plos

Journal ID (pmc): plosone

Title: PLoS ONE

Publisher: Public Library of Science (San Francisco, USA )

ISSN (Electronic): 1932-6203

Publication date Collection: 2012

Publication date (Electronic): 13 September 2012

Volume: 7

Issue: 9

Electronic Location Identifier: e45293

Affiliations

[1 ]Department of Molecular Biology and Genetics, Aarhus University, AU-Foulum, Tjele, Denmark

[2 ]Pig Research Centre, Danish Agricultural & Food Council, Copenhagen, Denmark

[3 ]School of Animal Biology, University of Western Australia, Crawley, Western Australia, Australia

University of Chicago, United States of America

Author notes

* E-mail: guosheng.su@ 123456agrsci.dk

Competing Interests: The authors have declared that no competing interests exist.

Conceived and designed the experiments: GS OFC MSL. Performed the experiments: GS. Analyzed the data: GS. Contributed reagents/materials/analysis tools: GS TO MH. Wrote the paper: GS OFC MSL.

Article

Publisher ID: PONE-D-12-16944

DOI: 10.1371/journal.pone.0045293

PMC ID: 3441703

PubMed ID: 23028912

SO-VID: 068c112d-9af9-4e3c-9f85-6d2d5200dce0

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This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

History

Date received : 13 June 2012

Date accepted : 14 August 2012

Page count

Pages: 7

Funding

The work was performed in the project (grant no. 3405-11-0279) funded by the Danish Ministry of Food, Agriculture and Fisheries, Pig Research Centre and Aarhus University. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Estimating Additive and Non-Additive Genetic Variances and Predicting Genetic Merits Using Genome-Wide Dense Single Nucleotide Polymorphism Markers

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Most cited references 24

Hot topic: a unified approach to utilize phenotypic, full pedigree, and genomic information for genetic evaluation of Holstein final score.

Increased accuracy of artificial selection by using the realized relationship matrix.

Technical note: Derivation of equivalent computing algorithms for genomic predictions and reliabilities of animal merit.

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