Normality and Skewness of Genetic Evaluations

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Normality and Skewness of Genetic Evaluations
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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?

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Observed vs Underlying EBV
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Skewness
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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

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Protein, SCS, Longevity Skewness (Within year,
for countries sampling most bulls)
Ctry Pro SCS Long Ctry Pro SCS Long
USA -.16 -.26 .03 POL .93
DEU .13 -.16 -.01 NZL -.10 -.29 .09
FRA -.05 -.23 .06 GBR -.48 -.25 -.06
NLD -.13 -.24 -.15 JPN .18 -.25
DNK1 .10 -.20 -.03 ESP .03 -.33 -.30
ITA .27 -.17 -.36 CZE -.07 -.81
CAN .20 -.33 .00 HUN .20 -.22
AUS .06 -.19 -.09 ISR .02 -.27 -.06
1 Protein obtained from Denmark-Finland-Sweden
joint evaluation
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Calving Ease Skewness (Within year)
Ctry Dir Mat Modl Ctry Dir Mat Modl
USA -.18 -.08 Thr SWE -.69 -.53
FRA -.29 -.01 Thr FIN -.65 -.67
NLD -.37 -.21 ISR -.59 -.81
DNK1 -.55 -.17 CHE -.80 -.30
ITA -.12 -.16 Thr
CAN -.47 -.34
AUS -.60 USA -.69 -.42 Thr
DEU -.48 -.84
Observed scale Pilot run
1 Protein obtained from Denmark-Finland-Sweden
joint evaluation
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Stillbirth and Mastitis Skewness (Within year)
Stillbirth Stillbirth Clinical
Ctry Direct Maternal Mastitis
NLD -.48 -.62
DNK -.54 -.47 -.21
SWE -.41 -.63 -.23
FIN -.52 -.69 -.24
ISR -.52 -.94
CHE -.86 -.06
USA -.10 -.23
USA -.32 -.69
Underlying scale Observed scale
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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

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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?

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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

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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