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2010 ADSA2010 ADSA --ASAS Joint ASAS Joint AnnualAnnual MeetingMeeting
Denver, July 12Denver, July 12 --1616
Heterogeneity of residualvariances of milk fatty acids in
dairy cattle
V. M.-R. Arnould 1,2,* , H. Soyeurt 2,3, S. Vanderick² , N. Gengler² ,³
1 CONVIS, Ettelbruck, Luxembourg2 University of Liège, Gembloux Agro-Bio Tech, Belgium
3 National Fund for Scientific Research (FNRS), Brussels , Belgium* Supported by the National Research Fund, Luxembourg (AFR PHD-09-
119RE)
�� CRACRA--WW– Frédéric Dehareng – Pierre Dardenne
�� ComitComitéé du Lait du Lait – Didier Veselko – Emile Piraux
�� AWEAWE– Carlo Bertozzi – Laurent Laloux
Collaborations
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
� Routine genetic evaluation for milk fatty acids is under development in the Walloon Region of Belgium
� The model used in genetic evaluations isa multi-trait random regression test-day model (RRTDM) (Auvray and Gengler, 2002)
Context
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
� Genetic evaluation modely=Xtt+Q(Wth+Ztg+Ztp)+e
Context
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
Fixed effects :- herd * test date- stage of lactation- gestation stage- lactation stage*calving season*breed*calvingperiod regressed on age at calving
�Genetic evaluation modely=Xtt+Q(Wth+Ztg+Ztp)+e
Context
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
Random regression effects :- herd × period of calving- additive genetic- permanent environmental
Random residuals
� Genetic evaluation model y=Xtt+Q(Wth+Ztg+Ztp)+e
Context
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
Matrices :- X, W, Z are incidence matrices, - Q is the covariate matrix for the second orderLegendre polynomials.
� Accuracy of estimated breeding values is one major component in designing breeding programs
� In mixed models, it is often assumed that the residualvariance is the same for all observations (Rönnegard et al., 2010)
� BUT: variation of the residual variances seems to be quitecommon
� BUT: Assuming a homogeneous residual variance couldaffect the genetic evaluation (Takma, 2009)
� � so, it could be important to include the heterogeneity of residual variance in the used model
Context
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
To test the heterogeneity of residual variances for
- Milk, fat and protein yields
- Monounsaturated and saturated fatty acids
�Indirectly, to study the goodness of fit of the
model (average residuals)
General objective
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
� Dataset
–First lactation
–Traits involved in the genetic evaluation :Milk, fat and protein yields (kg/day)
(Milk, qFAT and qPROT)
� +/- 6,687,000 records
–Traits not involved in the genetic evaluation : content of
saturated and monounsaturated fatty acids in milk (g/dl of milk)
(SAT and MONO)
� +/- 220,000 records
Materials & Methods
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
� Residuals:
� Observed values – Estimated values
�Squared residuals ≈ residual variance
�Studied effects are:
–The month of test date
–The calving month
–The year of test date
–The age at calving
–And the stage of lactation
Materials & Methods
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
Studied traits
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
0.24
0.49
0.22
0.29
6.83
SD
1.15220,396MONO (%)
2.79220,397SAT (%)
0.566,727,524qPROT(kg/day)
0.686,746,993qFAT (kg/day)
16.966,749,239MILK (kg/day)
MeanNTrait
Residuals
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
0.09
0.17
0.05
0.07
1.35
SD
0.00220,396MONO (%)
0.00220,397SAT (%)
0.006,727,524qPROT(kg/day)
0.006,746,993qFAT (kg/day)
0.006,749,239MILK (kg/day)
MeanNTrait
Results --- Squared residuals
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
0.0218
0.0615
0.0120
0.0208
9.774
SD
0.0089220,396MONO (%²)
0.0276220,397SAT (%²)
0.00236,727,524qPROT (kg²/day²)
0.00516,746,993qFAT (kg²/day²)
1.8216,749,239MILK (kg²/day²)
MeanNTrait
Results --- Month of test-date
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
***Milk
***qFAT
***SAT
***qPROT
***MONO
Month of test dateP value
The effect of month of test date on squaredresiduals is highlysignificant for all traits
Results --- Month of test-date
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
•Peak during the spring (April � June)
•Lowest values during the summer
•Similar trend for milk, fat and proteinyields and for SAT vs MONO (smoother)
Results --- Calving month
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
***Milk
***qFAT
***SAT
***qPROT
***MONO
Calving monthP value
The effect of calvingmonth on squaredresiduals is highlysignificant for all traits
Results --- Month of test-date
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
•Peak in August
•Lowest values during the spring (April � June)
•Vs Month of calving effect
•Similar trend for milk, fat and proteinyields vs for SAT and MONO (smoother)
Results --- Year of test date
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
***Milk
***qFAT
***qPROT
Year of test dateP value
The effect of year of test date on squaredresiduals is highlysignificant for milk, fat and protein yields
Results --- Year of test date
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
Trend of squared residuals for milk yield according to year of test date
0
0.5
1
1.5
2
2.5
3
1980
1983
1986
1989
1992
1995
1998
2001
2004
2007
Year of Test Date
squa
red
resi
dual
s fo
r m
ilk y
ield
squared residuals_MILK
P value Linear: ***
P value Quadratic: ***
P value Cubic: ***
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
2008
Year of Test Date
Squ
ared
Res
idua
ls
squared residuals_FAT squared residuals_PROT
Results --- Year of test date
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
Trend of squared residuals for fat and protein yields according to year of test date
******Cubic
******Quadratic
******Linear
PROTFATP value
Results --- Age at calving
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
NSMilk
NSqFAT
NSSAT
NSqPROT
NSMONO
Age at calvingP value
The effect of age atcalving on squaredresiduals is not significant for any traits
Results --- Stage of lactation
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
***Milk
***qFAT
***SAT
***qPROT
***MONO
DIMP valueThe effect of stage of lactation on squaredresiduals is highlysignificant for all traits
Results --- Stage of lactation
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
Trend of squared residuals for milk yield according to the stage of lactation
0
0.5
1
1.5
2
2.5
5-20
36-5
066
-80
96-1
1012
6-14
015
6-17
018
6-20
021
6-23
024
6-26
027
6-29
030
6-32
033
6-35
0
Classes of days in milk
Squ
ared
res
idua
ls
squared residuals_MILK
P value Linear: ***
P value Quadratic: ***
P value Cubic: ***
P value Quartic: ***
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
5-20
36-5
066
-80
96-1
1012
6-14
015
6-17
018
6-20
021
6-23
024
6-26
027
6-29
030
6-32
033
6-35
0
Classes of days in milk
Squ
ared
res
idua
ls
squared residuals_FAT squared residuals_PROT
Results --- Stage of lactation
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
Trend of squared residuals for fat and protein yields according to the stage of lactation
******Quartic
******Cubic
******Quadratic
******Linear
PROTFATP value
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
5-20
36-5
066
-80
96-1
1012
6-14
015
6-17
018
6-20
021
6-23
024
6-26
027
6-29
030
6-32
033
6-35
0
Classes of days in milk
Squ
ared
res
idua
ls
squared residuals_SAT squared residuals_MONO
Results --- Stage of lactation
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
Trend of squared residuals for SAT and MONO according to the stage of lactation
***Cubic
****Quadratic
NS***Linear
MONOSATP value
� Means of residuals were stable and close to zero for all traits
� Trends of squared residuals: differences between milk, fat and protein yields and SAT and MONO
� � Introduction of heterogeneous residualvariance could be interesting for the accurate model definition
Conclusions
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
� How to introduce this heterogeneity?
� Suggestion : introduction of correction of variability of squared variances according to stages of lactation
Conclusions
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
� AFR – FNR (AFR PHD-09-119RE)� Walloon Region (D31-1178/S1 and D31-1224/S1)
� FP7 European Project RobustMilk(www.robustmilk.eu)
� FNRS (F.4552.05, 2.4507.02 F (2) and 2.4623.08)
Acknowledgment
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16
Author Contact
2010 ADSA-ASAS Joint Annual Meeting --- Denver, July 12-16