Íslenskar landbúnaðarrannsóknir - 01.03.1977, Page 75

ÍSL. LANDBÚN.
J. AGR. RES. ICEL. 1977 9, L' 73—76
Maximum likelihood estimation of sire induced
embryonic mortality in Icelandic sheep.
Stefán Aðalsteinsson
Agricultural Research Institute,
Reykjavík, lceland.
ABSTRACT
The paper describes a method by which sire-induced embryonic mortality is estimated. The estimation
is based on a comparison, between abnormal and normal sires, of ewes with twins, ewes with singles
and ewes returning on heat.
The ram is ordinarily not assumed to affect
the twinning rate of the ewes which are
mated to him. A case of marked effect of three
sires on the return rate and twinning rate
of the ewes mated to them was reported
by Adalsteinsson and Hallgrímsson
(1977). The fertility and fecundity depres-
sing effect of these rams was ascribed to ex-
cess embryonic mortality prior to embryo
implantation.
The model used for the estimation of the
cess embryonic mortality prior to embryo
implantation.
p = probability of fertilization of 2 eggs.
q = probability of fertilization of 1 egg.
r = 1 — p — q probability of fertil-
ization of 0 eggs.
(Includes both fertilization failure
and "normal” embryonic
losses = "background” loss).
s = probability of death of embryos
sired by "abnormal” sires, and
1 — s = probability of survival of embryos
sired by "abnormal” sires.
1 = probability of survival of embryos
sired by "normal” sires.
The above basic probabilities lead to the
class probabilities within individual sire
groups, which are shown in table 1.
The probabilities of a particular ewe fal-
ling into each of the three categories, T, S an
R, are shown in table 2 together with sym-
bols for the observed numbers in each ewe
group within sire group.
The likelihood equation is formed in the
ordinary way as the product of the class
probabilities in table 2 to the power of the
observed number in each class.