84 E
. Gerber Olsson et al. Livestock Production Science 65 2000 81 –89 Table 3
Number of horses N , means, standard deviations S.D., minimum Min and maximum Max values and coefficients of variation CV for the average scores of different traits in the combined data set from the stallion performance test SPT and riding horse quality test
RHQT
Trait average score N
Mean S.D.
Min Max
CV Gaits RHQT
6674 6.52
0.89 3.00
9.33 13.7
Jumping RHQT 6674
6.79 1.50
0.50 10.00
22.1 Conformation RHQT
6674 7.47
0.49 5.00
9.60 6.6
Gaits SPT 136
6.83 0.92
4.33 9.67
13.5 Jumping SPT
136 6.24
1.63 1.00
10.00 26.2
another jumping test under rider. All tests at the the random effect of the kth tested stallion, mean50
2
different ages were included and means were calcu- and variance5 As ; pe
is the random effect of the
a kl
lated for each created trait. The trait ‘conformation’ permanent environment, mean50 and variance5
2
in the RHQT data was defined as the average of five s ; e
is the random residual effect, mean50 and
pe ijkl
2
scores comprising type, head-neck-body, legs, walk variance5s .
e
and trot at hand. Table 3 contains means and Repeatability for the traits scored in the SPT was
2 2
2 2
2
standard deviations for the traits scored. estimated
as s 1 s s
where s 5 s 1
a pe
P P
a 2
2 2
s 1
s , and s is the additive genetic variance.
pe e
a
Standard errors of the variance and covariance components were provided by the DMU programme
3. Methods
and standard errors for heritabilities, repeatabilities and genetic correlations were approximated by using
A multivariate animal model was used to estimate Taylor series expansions.
repeatabilities and covariance components for the Bivariate analyses with an animal model were
traits in the SPT. For estimation of covariance performed to estimate covariances for the average
components the traits were analysed five by five scores of the traits in the combined data from the
and or four by four, due to restrictions in computer RHQT and SPT. For the analysis the derivative free
capacity. The model included the additive relation- REML programme by Meyer 1993 was used. The
ship matrix A with information about sires and animal model used for traits in RHQT contained the
maternal grandsires. Only pedigree information from fixed effects of year and place of scoring and the
males was available. Parameters were estimated by random effects of the breeding values of the in-
use of restricted maximum likelihood REML pro- dividual horses tested as follows:
cedures using the DMU computer programme pack- age Jensen and Madsen, 1994.
Y 5 m 1 year 2 place 1 horse 1 e Model 2
ij i
ij ij
To estimate repeatabilities and covariance com- ponents for the traits in the data from the stallion
where Y is the average score of each trait for the performance test the following animal model was
ij
ijth horse; m is the population mean; year2place is used:
i
the fixed effect of ith year and place of testing Y
5 m 1 age 1 year 1 stallion 1 pe
ijkl i
j k
kl
i 51, . . . , 211; horse is the random effect of the
ij
breeding value of the ijth tested horse, mean50 and 1
e Model 1
ijkl 2
variance5 As ; e is the random residual effect,
a ij
2
where, Y is the score of each trait for the ijlth test
mean50 and variance5s .
ijkl e
of the kth stallion; m is the population mean; age is For SPT traits in the data the animal model used
i
the fixed effect of the ith age i 53.5, 4.0, 4.5, 5.0, included the fixed effects of year of birth of the
5.5 of the stallion at test; year is the fixed effect of stallion and the random effect of the individual
j
jth year of testing j 5 79, 80 . . . , 93; stallion is stallion’s breeding value.
k
E . Gerber Olsson et al. Livestock Production Science 65 2000 81 –89
85 Table 4
Y 5 m 1 year of birth 1 stallion 1 e Model 3
ij i
ij ij
2
Heritabilities h , standard errors S.E. and repeatabilities t of traits scored in the stallion performance test
2
where Y is the score of each trait for the ijth
ij
Trait h S.E.
t S.E.
stallion; m is the population mean; year of birth is
j
Walk 0.46 0.13
0.77 0.03
the fixed effect of ith year of birth i 5 82, 83 . . . ,
Trot 0.37 0.11
0.77 0.03
89; stallion is the random effect of the breeding
Gallop 0.39 0.11
0.75 0.03
ij
value of the ijth tested stallion, mean50 and addi-
Free jumping 0.47 0.13
0.58 0.04
a
2
Temp. free jumping 0.23 0.14
0.38 0.07
tive genetic variance5 As ; e is the random re-
a ij
2
Jumping under rider 0.32 0.14
0.47 0.06
sidual effect, mean50 and variance5s .
e
Temp. jumping under rider 0.33 0.23
0.43 0.09
In model 1 an age effect was considered, but not
a
Temp., temperament and general appearance.
in model 3 as the traits in the latter case consisted of average values of several observations measured at
different ages. It was assumed that the environmental correlation between the SPT and RHQT traits was
the heritability estimates for gaits and jumping zero, as the traits were recorded on different in-
estimated by Bruns et al. 1985, Huizinga et al. dividuals and at different occasions. Estimates of the
1991a,b, von Velsen-Zerweck 1998 and Friemel sampling variance was not obtainable by this version
et al. 1998. of the derivative free REML programme.
The heritability estimates for temperament and general appearance for free jumping were lower than
the corresponding estimate for free jumping ability. The explanation for this may be that the tempera-
4. Results and discussion
