Agriculture Reference
In-Depth Information
in his study of the resemblance between fathers and
sons. Therefore, the narrow-sense heritability of a met-
rical character can be estimated from the regression
coefficient of offspring phenotypes on those of their
parents.
In regression analysis, one variable is regarded as
inde-
pendent
, while another is regarded as being potentially
dependent
on it. Not surprisingly, in offspring-parent
regression, the phenotype of the parent(s) corresponds
to the independent variable and that of the offspring
the dependent variable.
The narrow-sense heritability of a character in the F
2
generation is:
(the mid-parental performance) then the regression
coefficient is (given without proof ):
1
4
V
A
=
b
1
1
1
2
2
(
2
V
A
+
4
V
D
+
σ
E
)
1
2
V
A
=
1
1
2
E
2
V
A
+
4
V
D
+
σ
and since:
1
2
V
A
h
n
=
1
1
2
E
2
V
A
+
4
V
D
+
σ
1
2
V
A
h
n
=
it follows that, for the regression of offspring phenotypes
on the mean phenotypes of both their parents:
2
E
and, the regression coefficient from simple linear regres-
sion is:
1
1
2
V
A
+
4
V
D
+
σ
h
n
=
b
b
=
SP
(
x
,
y
)/
SS
(
x
)
In short, to estimate the narrow-sense heritability
it is necessary to perform a regression analysis of the
mean phenotypes of offspring on the mean phenotypes
of both their parents. The regression coefficient (
b
),
obtained by dividing the offspring-parent covariance
by the variance of the parental generation, estimates the
narrow-sense heritability directly.
Consider the following simple example. The data
below are the phenotypes of parents and their offspring
from a number of crosses in a frost tolerant winter
rapeseed breeding programme for yield (kg/ha).
Therefore, there must be some relationship between
h
n
and the regression coefficient (
b
). The regression rela-
tionship when the offspring expression is regressed onto
the expression of
one
of the parents (provided without
proof ) is:
1
4
V
A
b
=
1
1
E
2
V
A
+
4
V
D
+
σ
and since:
1
2
V
A
h
n
=
1
1
2
E
it follows that, for the regression of offspring phenotypes
on the phenotypes of one of their parents:
h
n
=
2
V
A
+
4
V
D
+
σ
Female
parent
Male
parent
Mid-parent
value
Offspring
value
995
1016
1005.5
1006
×
2
b
1004
999
1001.5
1004
In short, to estimate the narrow-sense heritability
(
h
n
)
1009
996
1002.5
1008
, it is necessary to perform a regression analysis of
the mean phenotype of the offspring of individual par-
ents on the phenotype of those parents. The regression
coefficient (
b
) is obtained by dividing the offspring-
parent covariance by the variance of the parental gener-
ation. The narrow-sense heritability is then double the
value of the regression coefficient.
When
1012
1014
1013.0
1010
1005
1014
1009.5
1013
1007
1004
1005.5
1007
1034
1014
1024.0
1024
1015
998
1006.5
1002
1017
1028
1022.5
1020
1003
1013
1008.0
1008
the
expression
of
progeny
are
regressed
onto
the
average
performance
of
both
parents
