Íslenskar landbúnaðarrannsóknir - 01.03.1979, Side 99

TRAITS IN ICEL. TOELTER HORSES II. 97
Exactly the same result can be obtained
by minimising the mean square deviation
between the aggregate genotype and that
predicted from the selection index; i. e. the
expression E(I —H)2 is differentiated with
respect to the b’s and the partial derivates
are equated to zero (Henderson, 1963).
The variance of the index and the co-
variance of the index and the aggregate
genotype are respectively:
(7)
<rí = b‘Pb
oth = b‘Ga = b‘Pb (8)
The equality of the variance of the index
with the covariance between index and
aggregate genotype makes Bjq . j a unity.
and therefore from equation (3)
(9)
aH = cjjí
Also as:
(10)
Cov(gi-I) = Cov(gi(b’X)) = Z bjGij
the gentic gain in individual traits can
be calculated similarily, thus for trait r:
ibjGij (H)
AHr= J----------- i
CTI
RESULTS AND DISCUSSIONS
The selection index for individual selection
The construction of the selection index
followed the general procedure of solving
simultaneous equations so as to obtain
weighing factors (bi) which will maximize
the correlation between the index value
and the aggregate genotype (Hazel, 1943;
7
Henderson, 1963; Becker, 1975). Here
the aggregate genotype is defíned as the
sum of the additive genetic merit of an
individual trait times the appropriate
multiplication factor from table 1. Then
the aggregate genotype can be expressed
as:
H = a’g = aigi + a2g2 + . . . . +
aiogio
where: gi is the additive genetic merit or
breeding value of an individual trait.
Denoting the score of the traits as Xi, X2
....Xio in the same order as in table 1,
the selection index takes the following
form:
I = 0.481X1 + 0.102X2 + 0.596X3 +
0.589X4 + 0.461Xs + 0.762Xe +
0.199X7 - 0.163X8 - 0.055X9 -
0.539Xio
The standard deviation of the index is:
o j = 0.854
and expected response in the aggregate
genotype per generation from a truncative
selection on the index is therefore:
A H = 0.854;
where i denotes the selection intensity as
defined by Falconer (1960).
The expected genetic gain per generation
in each of the traits, measured as scoring
points:
aHi AH2 aH3 AH4 AHs
0.034; 0.016; 0.062; 0.104; 0.075;
aHö AH7 aHs AH9 aHio
0.329; 0.071; 0.059; 0.034; 0.069;
Selection using the selection index above
is expected to lead to an increase in all the
traits. By far the most gain will be obtain-
ed in pace and next in the other gaits,