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 Values linear on underlying or observed scale?
Observed vs Underlying EBV
Skewness
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
Protein, SCS, Longevity Skewness (Within year, for countries sampling most bulls) Ctry Pro SCS Long USA -.16 -.26 .03 POL .93 DEU .13 -.01 NZL -.10 -.29 .09 FRA -.05 -.23 .06 GBR -.48 -.25 -.06 NLD -.13 -.24 -.15 JPN .18 DNK1 .10 -.20 -.03 ESP -.33 -.30 ITA .27 -.17 -.36 CZE -.07 -.81 CAN .20 .00 HUN -.22 AUS -.19 -.09 ISR .02 -.27 1 Protein obtained from Denmark-Finland-Sweden joint evaluation
Calving Ease Skewness (Within year) Ctry Dir Mat Modl USA -.18 -.08 Thr SWE -.69 -.53 FRA -.29 -.01 FIN -.65 -.67 NLD -.37 -.21 ISR -.59 -.81 DNK1 -.55 -.17 CHE -.80 -.30 ITA -.12 -.16 CAN -.47 -.34 AUS -.60 -.42 DEU -.48 -.84 Observed scale Pilot run 1 Protein obtained from Denmark-Finland-Sweden joint evaluation
Stillbirth and Mastitis Skewness (Within year) Clinical Ctry Direct Maternal Mastitis NLD -.48 -.62 DNK -.54 -.47 -.21 SWE -.41 -.63 -.23 FIN -.52 -.69 -.24 ISR -.94 CHE -.86 -.06 USA -.10 -.32 Underlying scale Observed scale
Fertility Skewness Heifer conception rate Days to first insemination 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
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?
Transformations Cumulative normal density Exponential (Manly, 1976) Converts underlying to observed scale EBVs in threshold models Exponential (Manly, 1976) [exp(a EBV) – 1] / a Choose a to make skewness = 0
Conclusions Skewness differs by trait Underlying vs observed scale 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