Page 58 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

where d, as defined earlier, equals , or 1 if both, one or no parents are known,
3
1
2 4
respectively. Using the parameters for Example 3.1 and assuming both parents
known, k = 10/(10 + 40) = 0.2.
Thus for progeny 8, its EBV can be calculated as:
ˆ
a = 0.5(aˆ + aˆ ) + k(y − b − 0.5(aˆ + aˆ ))
8 3 6 3 1 3 6
= 0.5(−0.041 + 0.177) + 0.2(5.0 − 4.358 − 0.5(−0.041 + 0.177))
= 0.183
Compared with calf 7, the proof of calf 8 is higher because it has a higher parent
average solution and higher estimate of Mendelian sampling.
In the case of an animal with records and having progeny, there is an additional
contribution from its offspring to its breeding value. Thus the breeding values of
progeny 4 and 6 using Eqn 3.8 are:

a = n (aˆ /2) + n (y − b ) + n (2(aˆ ) − aˆ )
ˆ
4 1 1 2 4 1 3 7 5
= n (0.098/2) + n (4.5 − 4.358) + n (2(−0.249) − (−0.186)) = −0.009
1 2 3
2
with n = 2a( )/4.667, n = 1/4.667 and n = 0.5a/4.667; 4.676 = the sum of the
1 3 2 3
numerators of n , n and n ; and:
1 2 3
ˆ
a = n ((aˆ + aˆ )/2) + n (y − b ) + n (2(aˆ ) − aˆ )
6 1 1 2 2 6 2 3 8 3
= n ((0.098 + −0.019)/2) + n (3.9 − 3.404) + n (2(0.183) − (−0.041))
1 2 3
= 0.177
with n = 2a , n = 1 6 and n = 05a. 6 ; 6 = the sum of the numerators of n , n and n .
2
6
1
3
3
1
2
Although contributions from parent average to both calves are similar, differences
in progeny contributions resulted in a higher breeding value for calf 6, accounting for
about 75% of the difference in the predicted breeding values between both calves.
3.3.2 Progeny (daughter) yield deviation
The yield deviation of a progeny contributes indirectly to the breeding value of its sire after
it has been combined with information from parents and the offspring of the progeny
(see Eqn 3.8). Thus progeny contribution is a regressed measure and it is not an independ-
ent measure of progeny performance as information from parents and the progeny’s off-
spring is included. VanRaden and Wiggans (1991) indicated that a more independent and
unregressed measure of progeny performance is progeny yield deviation (PYD). However,
they called it daughter yield deviation (DYD) as they were dealing with the dairy cattle
situation and records were only available for daughters of bulls. PYD or DYD can simply
be defined as a weighted average of corrected yield deviation of all progeny of a sire; the
correction is for all fixed effects and the breeding values of the mates of the sire.
DYD has been used for various purposes in dairy cattle evaluation and research.
It was used in the early 1990s for the calculation of conversion equations to convert
bull evaluations across several countries (Goddard, 1985). It was initially the variable
of choice for international evaluations of dairy bulls by Interbull, but, due to the
inability of several countries to calculate DYD, deregressed proofs were used
(Sigurdsson and Banos, 1995). In addition, Interbull methods for the validation of
genetic trends in national evaluations prior to acceptance for international evalua-
tions utilize DYDs (Boichard et al., 1995). DYDs are also commonly employed in

42 Chapter 3