Use of Cluster Analysis for Identifying Metafounders

In the metafounder approach, the relationship matrix of metafounders, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>Γ</mml:mi></mml:mrow> <mml:annotation>$$ \boldsymbol{\Gamma} $$</mml:annotation></mml:semantics> </mml:math> is used to transfer information on relationships between pedigree founders into the numerator relationship matrix <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>A</mml:mi></mml:mrow> <mml:annotation>$$ \mathbf{A} $$</mml:annotation></mml:semantics> </mml:math> , creating matrix <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msup><mml:mi>A</mml:mi> <mml:mi>Γ</mml:mi></mml:msup> </mml:mrow> <mml:annotation>$$ {\mathbf{A}}^{\boldsymbol{\Gamma}} $$</mml:annotation></mml:semantics> </mml:math> . Commonly metafounders are defined based on the available information of the animal (e.g., country, sex, breed) similar to unknown parent groups (UPG). This limits the ability of metafounders to correctly reflect the population structure. In Single-Step Models, hidden stratification in the population may cause inconsistencies between matrix <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>A</mml:mi></mml:mrow> <mml:annotation>$$ \mathbf{A} $$</mml:annotation></mml:semantics> </mml:math> and the genomic relationship matrix <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>G</mml:mi></mml:mrow> <mml:annotation>$$ \mathbf{G} $$</mml:annotation></mml:semantics> </mml:math> when they are combined into matrix <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>H</mml:mi></mml:mrow> <mml:annotation>$$ \mathbf{H} $$</mml:annotation></mml:semantics> </mml:math> . Reliable information on the true structure in a population can be obtained from genotypes. In this study, we investigate an approach to transfer information on population structure from the genotyped animals to the ungenotyped ancestors. We used an unsupervised clustering approach to assign pedigree founders to metafounders and performed Single-Step genomic evaluation for an increasing number of metafounders (nMF) assumed. The optimum nMF to model was determined by harmonising the trend in inbreeding in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>G</mml:mi></mml:mrow> <mml:annotation>$$ \mathbf{G} $$</mml:annotation></mml:semantics> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msup><mml:mi>A</mml:mi> <mml:mi>Γ</mml:mi></mml:msup> </mml:mrow> <mml:annotation>$$ {\mathbf{A}}^{\boldsymbol{\Gamma}} $$</mml:annotation></mml:semantics> </mml:math> and by monitoring of elements in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>Γ</mml:mi></mml:mrow> <mml:annotation>$$ \boldsymbol{\Gamma} $$</mml:annotation></mml:semantics> </mml:math> . A semi-stochastic simulation based on real genotypes from Fleckvieh was used to investigate two scenarios: a trait with a strong genetic trend and a trait with no genetic trend. The quality of the prediction was determined by a regression of true breeding value as obtained from the simulation on estimated breeding value. The modelling of metafounders defined by population structure analysis led to a slight reduction in prediction quality in a trait with no trend, but was still stable in the range of the optimum nMF. In a trait with a strong genetic trend, prediction qualtity was improved compared to a common Single-Step model. The largest improvement was achieved in the range of the proposed optimum nMF.