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Normality and Skewness of Genetic Evaluations

Normality and Skewness of Genetic Evaluations. Effects of Skewness. Number of extreme bulls Rankings are ok within countries Problems when EBVs with differing skewness merged across countries Linear vs non-linear models Economic contribution to index

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Normality and Skewness of Genetic Evaluations

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  1. Normality and Skewness of Genetic Evaluations

  2. Effects of Skewness • Number of extreme bulls • Rankings are ok within countries • Problems when EBVs with differing skewness merged across countries • Linear vs non-linear models • Economic contribution to index • Values linear on underlying or observed scale?

  3. Observed vs Underlying EBV

  4. Skewness

  5. Data and Methods • May 2006 MACE evaluations • All traits (except conf.) on all scales • Only bulls with domestic data • Skewness computed within year • Removed birth year trend by linear regression • Removal had little effect for traits with small genetic trends

  6. Protein, SCS, Longevity Skewness (Within year, for countries sampling most bulls) 1 Protein obtained from Denmark-Finland-Sweden joint evaluation

  7. Calving Ease Skewness (Within year) Observed scale Pilot run 1 Protein obtained from Denmark-Finland-Sweden joint evaluation

  8. Stillbirth and Mastitis Skewness (Within year) Underlying scale Observed scale

  9. Fertility Skewness • Heifer conception rate • Range -.23 to .11 • Days to first insemination • Range -.33 to -.09 • Cow conception rate • Range -.20 to .10 • Calving interval or days open • Range -.35 to -.04

  10. Extreme Calving Ease Bulls • USA compared to foreign bulls • Slightly poorer for direct and better for maternal calving ease on average • Percent of extreme 100 bulls across scales • 45% (direct) and 32% (maternal) of BEST • 20 % (direct) and 21% (maternal) of WORST • 34 % (direct) and 22% (maternal) of ALL bulls • Unskewed EBVs are an advantage • Economics linear on observed scale?

  11. Transformations • Cumulative normal density • Converts underlying to observed scale EBVs in threshold models • Exponential (Manly, 1976) • [exp(a EBV) – 1] / a • Choose a to make skewness = 0

  12. Conclusions • Skewness differs by trait • Yield and longevity fairly normal • SCS always moderately skewed • Calving traits, stillbirth most skewed • Underlying vs observed scale • Nonlinear transformations useful • Consistent skewness is desired

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