Íslenskar landbúnaðarrannsóknir - 01.03.1970, Qupperneq 87

COLOUR INHERITANCE IN ICELANDIC SHEEP 85
variation in table 39 B is mainly connect-
ed with twins indicates that the underly-
ing causes of the variation are different
for the two sets of data.
The preceding analysis of tlie variation
in table 39 B indicates strongly that the
variation there is due to the action of
alleles Ax and A5 in certain genotypes.
The data in table 39 C consist of such a
mixture of genotypes with so few progeny
from eacli mating that an analysis of the
combined data is unlikely to reveal clear-
cut effects of specific alleles on the varia-
tion.
H. RELATION BETWEEN SCORF.
FOR TAN COLOUR AND HOMO-
ZYGOSITY OF THE ArALLELE
As described earlier, p. 9, scores from 1 —
5 were given for the amount of tan colour
in the birth coat of otherwise white lambs.
These scores were available for altogether
366 white lambs out of parents witli known
genotype in the present study.
The matings from which these lambs
were obtained were of three types. Tlie
first type was the mating AXA^ X AjA^
(i> 1), frorn which homozygous ancl hetero-
zygous lambs are expected in the ratio 1:1,
the second type was the mating Ax Ai X
A^Aj (i, j > 1) with expected ratio of homo-
zygotes to heterozygotes of 1:2, and the
third type Ax— X A^Aj (i, j > 1), which
gives only heterozygous white lambs.
The scores given for the amount of tan
colour at birth are subjective and it is
therefore likely that some differences may
exist in scoring stanclarcls from one year
to another and also between scorers. It was
therefore decided to group the observed
scores into two classes only, class a con-
taining scores 1 and 2, and class b, con-
taining scores 3, 4 and 5. Score class a will
thus contain larnbs without tan on the
body and score class b lambs with tan
colour on the body. Table 46 shows the
observed frequencies of the white larnbs
with score for tan colour by mating groups
and score classes.
A test of the hypothesis tliat the distribu-
tion of the progeny is independent of the
mating group gives x22 = 5.111 (0.10 >P>
0.05). This indicates that there may be a
difference between homozygous and hetero-
zygous white lambs with respect to tan
colour.
In order to examine that relationship
further, two parameters were postulated, p,
the proportion of homozygotes in score
class a and q, the proportion of hetero-
zygotes in score class a. The proportion of
homozygotes in score class b was then 1 — p
and that of heterozygotes in core class b,
1 — q.
The probabilities of the individual class-
es in table 46 are shown as function of the
parameters p and q in table 47, which also
gives the expected frequencies in each class.
The maximum likelihood estimates ot'
p and q were found by the method of
maximum likelihood scoring (Bailey, 1961).
Tlie probabilities in table 47 to the power
of the corresponding frequencies in table
46 when multipliecl together formed the
likelihood, the log-likelihood was found
and was differentiated w.r.t. p and q to
find the score, and the negative expecta-
tions of the second derivatives forrned the
information matrix from which the vari-
ance-covariance matrix was obtained by
inversion.
The maximum likelihood estimates of p
and q together with their standard errors
are given in table 48.
The differences between p and q when
divided by its standarcl error gives a t-
value of 2.30 (P < 0.05).
The expectecl frequencies can now be
calculated from the relationship given in
table 47 by inserting the obtained values