Realized Genomic Relationships and Genomic BLUP Fikret Isik Associate Professor September 16,...

Genomic BLUP - UofCopenhagen 1

Realized Genomic Relationships and Genomic BLUP

Fikret IsikAssociate Professor

September 16, 2013

Cooperative Tree Improvement ProgramNorth Carolina State University, Raleigh, USA


Outline

• Background• Realized genomic relationships

– G matrix– H matrix

• Genomic BLUP• Empirical Examples from Pinus taeda L.

September 16, 2013


Expected covariances

• Additive genetic relationships (covariances) derived from a pedigree are based on probabilities that gene pairs are identical by descent (IBD)

• For example, the average genetic covariance between full-sibs is 0.5 because full-sibs are expected to share 50% of their genome that is IBD

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Genetic merit

• In the classic “infinitesimal model” of quantitative genetics, breeding value is considered to be the sum of thousands of allelic effects.

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Traditional genetic evaluation

• Infinitesimal model has been very successful to predict genetic merit of individuals in animal- and plant-improvement programs

• This model does not trace individual alleles (black box) (VanRaden 2008).

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Tracing loci

• “Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful” George Box.

• In real genomes, those alleles are physically located at loci whose transmission can be traced through genetic markers.

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The real deficiency of model

• Genetic relationships derived from pedigree ignore the random sampling of the two possible alleles from each parent at each locus during meiosis (Avendano et al. 2005).

• In the absence of phenotype, selection is not possible in a cross.

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Mendelian segregation effect (m)

• When gametes are produced (by meiosis) allele pairs segregate, leaving each cell with a single allele (Mendel’s law of segregation).

• Each progeny receives 50% of parental DNA, random sampling of parent alleles at each locus during meiosis

• The genetic merit: 0.5 (uj + uk) + mi where j, k are parents of i

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Genetic similarities

• van Arendonk et al. (1994) suggested that large numbers of DNA markers covering the genome could measure genetic similarity more accurately than a pedigree-based relationship

• because the genetic covariances would be based on the actual proportion of the genome that is IBD between any two individuals.

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Realized genomic relationships

• Genetic markers could estimate proportion of chromosome segments shared by individuals including identification of genes IBS (VanRaden, 2008)

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Genomic predictions

• Selection based on realized genomic relationships can produce more accurate predictions than the pedigree-based method

• because genomic selection can exploit variation created by Mendelian segregation during gamete formation (Goddard and Hayes 2007)

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Genomic predictions (cont.)

• Such methods do not require known location of markers in the genome or

• do not require estimation of relative effects of individual QTL on the trait.

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Matrix of gene content (M) The product of M matrix with its transpose M´ is MM’ matrix

• Diagonal: Counts the # of homozygous loci for each individual.

• Off-diagonal: Measure the number of alleles shared by relatives

individual 1 individual 2 individual 3

(VanRaden, 2008, Forni et al. 2011)

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Realized genomic relations matrix

(VanRaden 2008)

• Dividing by scales G to be analogues to the A matrix

• p_i are the observed MAF of all genotyped individuals regardless of inbreeding and selection

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ZZ’ = (M – P) (M – P)’


Assumptions of GS

• QTL explaining genetic variation are in LD with genetic markers (Meuwissen et al. 2001).

• We do not know the frequency of alleles IBS are actually are IBD, especially in outbred populations (Legarra et al. 2009).

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Inverse of G matrix

• The genomic matrix is positive semidefinite but it can be singular (no unique solution) if– Number of loci is limited – Subjects have identical genotypes across all loci– Number of markers is smaller than the number of

individuals genotyped

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Inverse of G matrix

• To avoid potential problems G can be weighted

• Gr is unweighted genomic matrix• A is numerator relationship matrix among only

genotyped animals• w is weight - This value is not critical between

values of 0.95 and 0.98 (Aguilar et al. 2010)

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Hybrid genetic relationship matrices

• Genotyping may not be reasonable for all the population due to high cost and logistic limitations, particularly for tree breeding populations.

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Hybrid genetic relationships

• vanRaden and (2008) and Legarra et al. (2009) proposed combining numerator relationships matrix (A) derived from pedigree with the genomic relationship matrix (G) into a single matrix (H = A+G ) to use in predictions.

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A modified animal model

• In H matrix, genomic information is transmitted to the covariances among all non-genotyped individuals (Legarra et al. 2009).

• The H matrix is a joint distribution of genotyped and non-genotyped genetic values

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Construction of H matrix

• Instead of A-1, genomic analysis uses

• is contribution of genomic relationships in H

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A22 for the genotyped individuals

Misztal et al. 2009, VanRaden 2008


Predictions of genetic merit of trees using G and H matrices

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Genomic BLUP

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Genomic estimated breeding values using selection index equations

Markers effects can be estimated by substituting the Z’ to the leftmost G


Mixed models for GBLUP

y = Xb + Zu + e • Xb is the mean (other fixed effects could be added)• Z is incidence matrix for marker effects• u is vector of additive genetics effects that

correspond to allele substitution effects for each marker

• We let the sum Zu across all marker loci (m) to be equal to the vector of breeding values Za = u

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(VanRaden 2008)


Mixed model equations for GBLUP

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Lambda is defined as the sum across loci 2Σpi1-pi times the ratio of error and additive genetic variance


Emprical results from Pinus taeda L.

September 16, 2013

Genomic BLUP - UofCopenhagen 27September 16, 2013


0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

Additive genetic covariance

A

Pedigree-based relationships

mean = 0.54

min = 0.41

max = 0.62

N = 3,998

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for 305 progeny, from 9 families


0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

Realized genomic covariance

G

Genomic relationships

mean = 0.53

min = 0

max = 0.95

N = 1,967

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for 165 trees, from 9 families


Predictions from ABLUP-GBLUP

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Zapata-Valenzuela et al. 2013


Accuracies of the predictions

Training / validation r(ABLUP) r(GBLUP)

84 / 81 0.60 0.71148 / 17 0.61 0.76

Accuracies of predictions from markers (GBLUP) are higher than accuracies of predictions from pedigree based models (ABLUP)

September 16, 2013

Zapata-Valenzuela et al. 2013 Genes Genomes Genetics.

32September 16, 2013 Genomic BLUP - UofCopenhagen

Zapata-Valenzuela et al. 2013 Genes Genomes Genetics.

Markers are capturing the Mendelian sampling effect


Predictions from blended genomic relationship in Pinus taeda

Manuscript in preparation

September 16, 2013

Funda Ogut, (NCSU Crop science)


Actual data (Mid-parent EBVs)

ABLUP: Predictions of full-sib progeny within nine families.

No phenotype was available and predictions are mid-parent breeding values

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

-3-2

-10

12

ABLUP_ide

TB

V_

ide

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Actual data (Mid-parent EBVs)ABLUP: Predictions of full-sib progeny within nine families

Not much segregation within a cross

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

-3-2

-10

12

ABLUP_ide

TB

V_

ide

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Actual data-TBVs and EBVsHBLUPDark blue dots: Non-genotyped

Red dots: predictions from HBLUP

-3 -2 -1 0 1 2 3

-3-2

-10

12

HBLUP_GOF

TB

V_

ide

r=0.73

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HBLUP models captures Mendelian segregation effect (different BV) within full-sib crosses.


Summary

• Realized genomic relationships allow capturing the Mendelian sampling effect for within-family (forward) selection without phenotype

• An important advantage to control inbreeding and increase genetic gain across multiple generations in forest tree breeding compared to the traditional evaluation

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Summary (cont.)

• HBLUP uses all the available genomic, pedigree and phenotype information in one step for genomic predictions

• Implementation is straightforward• Standard software available for linear mixed

models can be used to solve for mixed model equations while accounting for experimental design factors, such as location and age

September 16, 2013

Realized Genomic Relationships and Genomic BLUP Fikret Isik Associate Professor September 16,...

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