Íslenskar landbúnaðarrannsóknir - 01.03.1979, Síða 101

TRAITS IN ICEL. TOELTER HORSES II. 99
enough to make sampling errors neglig-
ible, and where the selection is carried out
in an infinite population (Harris, 1963).
The loss in efíiciency resulting from errors
in estimated parameters used for con-
structing a selection index of this type has
been the subject of several studies
(Harris, 1963, 1964; Pig Industry De-
VELOPMENT AuTHORITY, 1965; MAO,
1971). The overall picture from these stu-
dies indicates that the prediction of gen-
etic gain is more sensitive to error than is
the difference between a response achi-
eved with an index which uses the sample
estimates of the parameter values and the
response from the use of an optimum
index. Both Harris (1964) and Mao
(1971) conclude from their results based
on simulation exercises, that a total of
1000 observations (in half-sib analysis)
enables reasonably good estimation. Ap-
art from possible biases in this material
the calculated selection index is therefore
expected to work reasonably well, altho-
ugh expected gain may be somewhat
overestimated.
The economic weights given to the agg-
regate genotype are estimated in a subjec-
tive way. This had to be used for the pur-
pose of this study, but a thoroughly per-
formed study, aimed at objective measure
of the relative importance of the various
traits, would make the index a more eflic-
ient tool than possible at present.
A selection index for progeny tests.
The selection index for individual selecti-
on is aimed at maximizing the correlation
between an individual’s merit and its true
breeding value. Another way of estimat-
ing the individual’s breeding value is to
look at its progeny. If one can reasonably
assume that the dams are random repres-
entatives of the population, the breeding
value of a particular sire, deftned as his
additive genetic merit for the trait of
concern, is estimated as twice the mean
deviation of the progeny from the popul-
ation mean (Falconer, 1960).
The covariance between the breeding
value of a parent and its offspring’s phen-
otype equals Vg/2, where Vg denotes the
additive genetic variance of a single trait.
If the common genes are the only source of
similarity among half-sibs, the variance-
among progeny groups, consisting of n
half-sibs each, equals Vg/4 + (Vp — Vg
/4)/n. Similarly for two traits, the covar-
iance among progeny groups equals
Covg/4 + (Covp — CovG/4)/n. By mo-
difying the phenotypic matrix according
to this one could still solve the matrix
equation:
b = P-> Ga
For a given value of n the resultant bi
values of an index should maximize the
correlation between a progeny test and the
aggregate genotype of the parent tested. It
was considered feasible to calculate this
type of selection index in order to maxim-
ize the efifect of progeny tests, and to
compare the expected response in aggreg-
ate genetic merit, from selection on prog-
eny testing compared with individual sel-
ection, given the selection intensity app-
licable to each type of index selection.
Since the genotypic matrix was not chan-
ged from the calculation of the individual
selection index one can really look at it as
the correct one multiplied by a scalar 4.
Therefore the expected bi values for prog-