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)
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

7. 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

8. 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

9. 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

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 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

12. 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