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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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2 Outline Introduction Mixed Models Incorporating Random QTL Effects Current/Future Modification to MTDFREMLQ Practical Limitations of MTDFREMLQ Applications

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3 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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4 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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5 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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6 Mixed Model Incorporating Random QTL Effects v 2nx1 vector of QTL alleleic effects (a i =v p i +v m i +u i, v i =[v p i,v m i ]’ )

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7 BLUP equations for Fernando and Grossman model

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8 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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9 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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10 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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11 Complex Pedigree AB C D E ?? A1A2A1A2 A1A2A1A2 A1A2A1A2 Software MCMC LOKI DET Pong-Wong,et al. Allelic Peeling GenoProb

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12 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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13 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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14 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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15 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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16 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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17 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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18 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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19 Practical Limitations of MTDFREMLQ Memory Limitations/animal/traits/qtl 50,0001Trait2 Traits3 Traits4 Traits 1 qtl<268M324M778M1.6G 2 qtls<268M552M1.5G 3 qtls<268M919M 4 qtls314M1.4G 5 qtls430M 20,0003 Traits4 Traits5 Traits 1 qtl362M698M1.2G 2 qtls642M1.3G 3 qtls1.1G 100,000 1 Trait2 Traits 1 qtl<268M562M 2 qtls<268M1.0G 3 qtls376M 4 qtls542M 5 qtls775M Time Limitations

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20 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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