P. V. SUKHATME
115
are of the kind available on the farm. It does
not show how the sire would behave if the dams
are of a higher level, nor does it help a breeder
to compare the breeding value of two bulls
from different forms. The Sire Index on the
other hand, is an estimate of the breeding value
of a sire in terms of yield of milk and can tell
a breeder what and how much he can expect of
a sire when used on mates of any known level.
It follows that a breeder would prefer to
adopt a sire index rather than a progeny test,
provided the sire index gave a reliable estimate
of the breeding worth of sire. In actual fact it
is doubtful if sire index is absolutely so. The
common form of sire index, known as the
'Commercial Mount Hope Index', makes use of
the assumption that the offspring averages mid-
way between the two parents. We do not know
how far this assumption is valid, although in
a character like the milk-yield which is deter-
mined by multiple genes, it is not expected that
this assumption would be far from the truth.
Then again a sire index is relatively more
influenced by environmental differences than is
a progeny test. As against these considerations
progeny test in Fisher's 't' form, as observed
above, is of limited use to a breeder. Logically
the progeny test and sire index are not
mutually exclusive, as one is a test of signifi-
cance and the other is a problem in estimation,
and, therefore, the question of prefering one to
the other does not arise. The appropriate
course is to make a test of significance and then
construct a sire index. This, however, would
involve considerable computational work. For
the present, therefore, it is suggested that the
use of sire index alone be introduced in our
breeding farms.
It is not proposed to discuss the relative
merits of the various indices that have been
advocated for measuring the breeding worth
of a sire. The most common of these are (1)
the Daughter Average Index, which is the
average milk-yield of all daughters of a sire, and
(2) the Commercial Mount Hope Index, also
known as the Intermediate Index, which is the
difference between twice the average milk-yield
of daughters and the average milk-yield of their
mothers. The first uses information on all the
daughters of a sire, regardless of whether their
mothers were tested or not, and consequently,
is suitable for application in villages and on new
farms where the mothers' milk-yield may not
be known, whereas the second uses information
in respect of only such daughters, whose mothers
have been tested. The first is a statement of
fact independent of any assumption, whereas
the second is a hypothetical figure based on the
assumption that the offspring average midway
between the parents and is, therefore, depen-
dent for its reliability on the validity of this
assumption. Both are affected by environ-
mental errors, but the second probably is more
affected than the first. Notwithstanding these
advantages in favour of the first, the Commercial
Mount Hope Index is generally preferred
by the breeders, because it helps to predict the
performance of a sire on mates of any known
level, whereas the other, does not. Further
statistical research on Indian data on the rela-
tive efficiency of the two indices, and on the
validity of the assumption used in the const-
ruction of the second index, is clearly needed,
but in the meantime, it would appear that the
Intermediate Index would be the more useful.
The formula for the Intermendiate Index is
directly derived from the assumption that the
offspring averages midway between the sire and
the mother, and is given by
I = 2D — M
where D and M are the average milk-yields
of daughters of the sire and his mates (mothers
of daughters) respectively. The reliability of
this index is obviously dependent on the magni-
tude of the environmental and the sampling
errors. The former of these errors arise from
the difference between the environments of
mothers and daughters and the possible selec-
tion of mothers, whereas the latter, arise
principally from the sampling nature of inheri-
tance. Where it is reasonably certain that the
environmental conditions of daughters are not
distinct from those of their mothers, lest we
credit or blame the sire for something which
was due to the environment and where the
mothers have not been particuarly selected,
this index is influenced only by the errors of
sampling and can be depended upon to give a
reliable idea about the sire—provided a suffi-
ciently large number of offspring is available.
But environmental conditions usually differ not
only from farm to farm, but also between dams
and daughters on the same farm. It is, there-
fore, necessary to equalize the environmental
conditions, so far as is feasible, so as to reduce
to the minimum the environmental errors of
the index. By omitting locations which are
abnormal on account of either (1) death of calf
or still-birth, or (2) diseased condition of mother
or daughter or (3) any other abnormal factor, a
large degree of equality in the environmental
conditions can be secured. At the same time
it is also necessary to standardize other major