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Approximating prediction error variances for multiple trait sire evaluations.

S A Greenhalgh, R L Quaas, L D van Vleck

    Journal of Dairy Science
    |November 1, 1986
    PubMed
    Summary
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    Accurate prediction error variances in animal breeding are crucial. New approximations using more coefficient matrix information improve accuracy for multiple trait models, aiding sire evaluation.

    Area of Science:

    • Animal Breeding and Genetics
    • Quantitative Genetics
    • Statistical Modeling

    Background:

    • Mixed model equations are essential for genetic evaluations.
    • Calculating prediction error variances (PEVs) from large coefficient matrices can be computationally challenging.
    • Traditional approximations for PEVs may lack accuracy with complex relationships and multiple traits.

    Purpose of the Study:

    • To evaluate the accuracy of different approximations for prediction error variances (PEVs) in multiple trait mixed models.
    • To compare these approximations against actual PEVs using real-world dairy bull data.
    • To identify the most reliable approximation method for practical application in genetic evaluations.

    Main Methods:

    • Compared six approximation methods for PEVs against actual PEVs.

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  • Utilized multiple trait evaluations for milk, fat, protein, and dollar value.
  • Included sire relationships and data from 229 Ayrshire and 248 Brown Swiss bulls.

    • Main Results:

    • All tested approximations underestimated actual PEVs.
    • Most approximations, excluding the selection index, showed high correlations (.90 to .99) with actual PEVs.
    • Approximations incorporating more coefficient matrix information demonstrated higher accuracy.

    Conclusions:

    • Approximations for PEVs are necessary due to computational demands of large matrices.
    • The approximation using the most coefficient matrix information is recommended for its high correlation and closeness to actual PEVs.
    • Accurate PEVs are vital for reliable genetic evaluations and selection decisions in livestock.