Íslenskar landbúnaðarrannsóknir - 01.03.1970, Page 55

COLOUR INHERITANCE IN ICELANDIC SHEEP 53
An estimate oi p from the progeny of assuming a multinomial distribution of the
the 3 ewe groups above can be obtained colours of the progeny.
by the metliod of maximum likelihood,
The likelihood is:
eL cc (1 + p)“i (1 — 2p)n2 +”s p"4 +"7 (3 - 4p)ns;
L oc m log (1 + p) + (n2+ n8) log (1 - 2p) + (n4 + n7) log p + n5 log (3 - 4p)
dL m 2 (n2 + ns) n4 + n7 4n5
—— =-----------------------+ — — —--------, and
dp 1 + p 1 — 2p p 3 —4p
Ni Ni + 2N3 No + N3 4N2
d2L ,
-dp2 J = 1 / Var (p):
N! + 2N3 N2 + N3
2(l+p)+ 1 — 2p + p + 3-4p
The equation in p was solvecl by itera-
tion, and the rnethod of maximum likeli-
hood scoring was used for that purpose
one of its advantages being that the vari-
ance of the estimate of p is obtained as
part of the iteration procedure (Bailey,
1961).
The maximum likelihood estimate of p
and its standard error is found to be:
p = 0.f07 ± 0.032,
which gives the upper and lower 95 per
cent confidence limits of p as 0.170 and
0.044, respectively.
A mutation of A4 to A4 at the 4 cell
stage of the embryo would give p = 0.125,
a value which is within one standard
deviation from the maximum likelihood
estimate. A mutation at the 2 cell and 8
cell stages would result in expected p-
values of 0.25 and 0.0625, respectively. The
first of these is too high to be consistent
with the calculated p-value, while the latt-
er lies 1.39 standard deviations below the
maximum likelihood value. It is therefore
slightly more probable that the mutation
occurred at the 4 cell stage of the embryo
than at the 8 cell stage.
Expected numbers of progeny showing
the 3 alleles among ewe groups No. 2, 3
and 4 in table 12 can now be calculated
from the estimated value of p, and these
values compared with the observed numb-
ers by a x2-test, whicli gives:
x25 = 3.710; 0.70 > p > 0.50.
In the above x2> no allowance has been
made for expected values below 5. Four
of the 9 cells have expected values below
5.0.
The observed segregation in lines 2, 3
and 4 in table 13 thus agrees well with
exceptation under the assumption that
situation 5 on p. 51 is the correct explana-
tion of the genotype of ram No. 06043.
Two furtlier points remain to be men-
tioned. The mating of ram No. 06043 to
a grey baclgerface ewe, genotype A2 A..B,
— Sj— , resulted in a black lamb. The lamb
was born on farm No. 6. Date of mating
was 1/1/1960, date ol' lambing 23/5/1960.
One lamb, a black female. The ewe, No.
325, is of unknown ancestry. Her genotype
seems to be correctly assessed, as judged by
her lambs in other years. In this case either
the A2-allele or the A3-allele therefore
seems to have mutated to Ag.
The other point to be discussed is the
genotype of ram No. 06043 at loci B and S.
He produced 8 nonwhite lambs when mat-