Software for Incorporating Marker Data in Genetic

Evaluations

Kathy Hanford

U.S. Meat Animal Research Center

Agricultural Research Service

U.S. Department of Agriculture

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Outline Introduction Mixed Models Incorporating Random

QTL Effects Current/Future Modification to

MTDFREMLQ Practical Limitations of MTDFREMLQ Applications

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Introduction

Genetic evaluation genetic improvement of quantitative traits

through selection currently use polygenic model

genes at many loci each with a small effect measure the cumulative effect analysis with mixed models –software available

add genomic information

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Introduction

Two phases in application of genomic data to livestock improvement

1) Statistical analysis of genomic information to determine the potential importance of that information (i.e. use of genetic markers to quantify the effects of QTL on traits of economic importance)

2) Include marker information in the genetic evaluation of potential parents to determine which will have the best progeny (Marker Assisted Selection)

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Introduction QTL Identification

methods needed for outbred populations daughter and granddaughter designs

– many half-sib families with QTL effects being estimated for each half-sib family

Fernando and Grossman

– works with the outbred population as a whole, using both pedigree and marker information. Need complete marker data

other methods– such as MCMC, primarily been used only in

simulations

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Mixed Model Incorporating Random QTL Effects

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e

vu

RVar(e)MVar(v)AVar(u)

e vZu ZX y

,, VG

v 2nx1 vector of QTL alleleic effects  

(a i=vp i+vm i+u i, v i=[vp i,vm i]’ )

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BLUP equations for Fernando and Grossman model

yRZ

yRZ

yRX

v

u

VMZRZZRZXRZ

ZRZGAZRZXRZ

ZRXZRXXRX'

1

1

1

1

1

1111

1111

111

'

'

'

'''

'''

''

v

u

vvuvv

vuuuu

vu

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Numerator Relationship Matrix (A)

The probability that alleles are IBD Probability between two half sibs is .25

Need the inverse of A depends on pedigree information Computed directly (Henderson, 1976) Relatively few nonzero elements (sparse)

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Gametic (QTL) Correlation Matrix (M)

The probability that alleles are IBD Need the inverse of M

depends on pedigree information depends on probabilities QTL alleles are

IBD Computed directly if complete marker

information (Abdel-Azim and Freeman, 2001)

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Practical Issues in Calculating the QTL Correlation Matrix Outbred population

Sparse marker information Individuals with missing or incomplete marker

data Some of which will be incorrect

Large complex pedigrees (inbreeding and loops)

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Complex PedigreeA B

C D

E

??

A1A2

A1A2

A1A2

Software•MCMC

•LOKI•DET

•Pong-Wong,et al.•Allelic Peeling

•GenoProb

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Size Considerations Each additional QTL increases the

number of equations by 2 times the number of animals in the pedigree

Sparse matrix storage Only store nonzero elements Polygenic (A-1) grows by 4 times the

number of animals Gametic (M-1) grows by 15 times the

number of animals

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MTDFREML

Multiple Trait Derivative-free Restricted (or residual) Maximum Likelihood

A set of programs to obtain estimates of variances and covariances

USDA/ARS – Dale Van Vleck Keith Boldman, Lisa Kriese, Curt Van

Tassell, Steve Kachman, Joerg Dodenhoff

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MTDFREML MTDFNRM – Calculate and output the

inverse of the numerator relationship matrix

MTDFPREP – Set up the model for the analysis

MTDFRUN – Run the analysis using the files produced by MTDFNRM and MTDFPREP to obtain (co)variance estimates and breeding values

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Current Modifications to MTDFREML to Incorporate QTL effects

(MTDFREMLQ) MTDFNRMQ – modified to calculate inverse

of QTL correlation matrix (M-1) from IBD probability file (produced by Genoprob, Loki, etc) Non-inbred pedigree when marker data are

incomplete Inbred pedigree when marker data are complete Genetic groups arising from different populations

with different prior selection

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Current Modifications to MTDFREMLQ (cont.)

MTDFPRPQ – modified to include multiple QTL in the model (validated for single QTL) Multiple trait Gametic imprinting (coded, not validated)

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Current Modifications to MTDFREMLQ (cont.)

MTDFRUNQ – modified to include M-1 and associated between trait (co)variances for each QTL (V-1) Assumes independence between two

QTLs

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Further Modifications to MTDFREMLQ Include inbred pedigree when marker

data are incomplete (approximate M-1) Calculate standard errors for the

parameters using the delta method Currently in MTDFREML In the testing/debugging stage

appears to work for single-trait, single-QTL and two-trait, single-QTL cases.

still need to test for multiple-QTL

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Practical Limitations of MTDFREMLQ Memory Limitations/animal/traits/qtl50,000 1Trait 2 Traits 3 Traits 4 Traits

1 qtl <268M 324M 778M 1.6G

2 qtls <268M 552M 1.5G

3 qtls <268M 919M

4 qtls 314M 1.4G

5 qtls 430M

20,000 3 Traits 4 Traits 5 Traits

1 qtl 362M 698M 1.2G

2 qtls 642M 1.3G

3 qtls 1.1G

100,000 1 Trait 2 Traits

1 qtl <268M 562M

2 qtls <268M 1.0G

3 qtls 376M

4 qtls 542M

5 qtls 775MTime Limitations

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Applications QTL detection

Find and utilize QTL in a breed and include that information in national genetic evaluation.

Marker Assisted Selection Experimental herds

The twinning herd at MARC– Currently producing about 50% twin calving

compared to a normal range of 1-3%– ~6000 in genetic evaluation, marker data from 1994

on over 3000 animals in regions of 3 QTLs

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