Bayesian integration of external information into the single step approach for genomically enhanced prediction of breeding values

Bayesian integration of external

information into the single step

approach for genomically enhanced

prediction of breeding values

J. Vandenplas, I. Misztal, P. Faux, N.

Gengler

•

_{Unbiased EBV if genomic, pedigree and}

phenotypic information considered simultaneously

•

_Problem

– _{Only records related to selected animals available} – _{Bias due to genomic pre-selection}

•

_{Single step genomic evaluation (ssGBLUP)}

– _{Simultaneous combination of genomic, pedigree and} phenotypic information (=internal information)

– _{No integration of external information (e.g. MACE-EBV)}

•

_{Integration of a priori known external information}

into ssGBLUP

– _{By a Bayesian approach}

– _{To avoid multi-step methods} – _{By considering}

• _{simplifications of computational burden,}

• _{a correct propagation of external information,}

• _{and no multiple considerations of contributions due to} relationships.

Methods

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_{Bayesian approach}

_{(Dempfle, 1977; Legarra et al., 2007)}

•

_{2 groups of animals}

1) animals I = internal animals with only records in  Ia: non genotyped animals

Ib: genotyped animals

2) animals E = external animals with records in and possible records in

 Ea: non genotyped animals Eb: genotyped animals

I

y

E

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Methods

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_{An internal evaluation}

– _{All animals Ia, Ib, Ea, Eb} – _Only – _{instead of} where ) G , MVN(μ ) y u p(ˆ_{I E}  _E *

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Methods

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_{An unknown external ssGBLUP}

– _{All animals Ia, Ib, E}

– _{Genomic information included in}

– _{Only ( precorrected for fixed effects)}

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Methods

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_Problem

– _{Unknown external ssGBLUP}

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_Available

– _{External genetic evaluation of animals Ea and Eb}

• _{without animals Ia and Ib} • _{without genomic information}

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Methods

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_{Substitution in the unknown external ssGBLUP}

– _and * E 1 EE

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Methods

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_Finally,

_internal

_{evaluation = ssGBLUP}

integrating external information

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Methods

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_{Approximations and simplifications of}

computational burden

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Methods

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_{Approximations and simplifications of}

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Simulation