Íslenskar landbúnaðarrannsóknir - 01.03.1970, Page 54

52 ÍSLENZKAR LANDBLTNAÐARRANNSÓKNIR
TABLE 13
Grouping of progeny for testing hypotheses about rnutated allele
Situation Grouped alleles Exp. with higher freq. Unaffected alleles Obs. freq. of grouped unaff. alleles X2t
1 Ai + Aö Ai A4 42 21 7.000**
2 A4 -|- A5 A4 Ai 57 6 41.286***
3 Ai + A4 Ai A5 27 36 1.286
4 a4 + A5 A5 Ai 57 6 41.286***
5 Ai + A4 a4 a5 27 36 1.286
6 Ai + As a5 A4 42 21 7.000**
** PCO.Ol
*** P< 0.001
The expected frequencies of the grouped
and unaffected alleles in table 13 are al-
ways equal, 31.5:31.5. The 6 situations
give rise to only 3 x2’s> because each situa-
tion has its reverse counterpart wliere the
only difference is that one allele is expect-
ed with higher frequency in one situation,
and the opposite allele is expected with
higher frequency in the reverse situation.
It is seen that all situation except No.
3 and 5 have to be rejected. The choice
between the two then depends on tlie ob-
servecl frequencies of the mutated allele
and its original counterpart. As seen from
table 12, the A^-allele is less frequent than
the A4-allele, so situation 5 is the only
acceptable choice out of the 6 possibilities.
The hypothesis that the genotype of the
ram was originally A4A5, and that A4
mutated to A4 is in agreement with the
observed colours among the progeny of
of ewes in group 4 in table 12. The pro-
geny of ewe groups 2 and 3 also give a
certain amount of information about the
genotype of the sire, but because of the
occurrence of the sarne alleles from sire
and dams in these groups the information
they contain can only be extracted by
estimating p, the proportion of white gam-
etes produced.
The probabilities of lambs showing the
three alleles for ewe groups 2, 3 ancl 4 are
set out below.
Ewe group Probabilities of progeny showing1) Number of progeny showing
Ai A4 A5 Ai a4 a5 Sum
AiAj (i 1 or 4) 0.5 (1+p) 0.5 (0.5 -p) 0.25 m n2 n3 Ni
a4a5 P 0.75 - p 0.25 n4 n5 n6 n2
AíAj (i, j # 1 or 4) P 0.5-p 0.5 n7 , ng n9 n3
]) Progeny not showing Ai or A4 have obtained allele A5 from the sire.