Agriculture Reference
In-Depth Information
The total phenotypic variance of any generation is
the sum of its genetic variance plus the environmental
variance, E. So the total phenotypic variance of the F
2
generation can be written:
must be attributable exclusively to the environment.
The best estimate of the value of
2
σ
E
is therefore the mean
phenotypic variance of these two generations. Thus:
2
17.6 kg
2
σ
E
=
(
+
)/
=
16.8
18.4
2
1
2
V
A
+
1
4
V
D
+
σ
2
2
E
σ
F
2
=
and
56.9
17.6
56.9
−
2
σ
E
therefore the broad-sense
heritability of the F
2
generation is:
In terms of
V
A
,
V
D
and
h
b
=
=
0.691
In other words, 69.1% of the phenotypic variance of
the F
2
generation is estimated to be genetic in origin.
The other generation in which the phenotypic vari-
ance is also entirely attributable to environmental effects
is the F
1
. If the phenotypic variances of all three of
these genotypically invariate generations were avail-
able, the environmental component of the phenotypic
variance of the F
2
generation could be estimated as
follows:
genetic variance
total phenotypic variance
h
b
=
1
1
2
V
A
+
4
V
D
=
2
E
In order to estimate the broad-sense heritability of the
F
2
family (or indeed any other segregating family) all
that is required is an estimate of total phenotypic vari-
ation, and an estimate of environmental variation. The
former is obtained by measurements on plants within
F
2
families, while the latter is estimated from mea-
surements on families or plants that have a uniform
genotype (i.e. homozygous parental lines or F
1
families
where plants are genetically identical and any variation
between plants is due to environment).
To illustrate this, consider a simple numerical exam-
ple. A field experiment with an inbreeding crop species
was conducted which included 20 plants from Parent 1,
20 plants from Parent 2 and 100 plants from the F
2
fam-
ily derived from selfing the F
1
generation obtained by
inter-crossing the two parents. These 140 plants were
completely randomized within the experiment and at
harvest the weight of seeds from each plant recorded.
The variances in seed weight of the two parents were,
σ
1
1
2
V
A
+
4
V
D
+
σ
2
2
2
P
2
σ
P
1
+
2
σ
F
1
+
σ
σ
E
=
4
Research workers often use more elaborate formulae,
but this one will serve our purpose.
Narrow-sense heritability
Often it is of more interest, for reasons already noted,
to know what proportion of the total phenotypic vari-
ation is traceable to additive genetic effects rather than
total genetic effects. This ratio of additive genetic vari-
ance to total phenotypic variance is called narrow-sense
heritability (denoted by
h
n
)
and is calculated as:
additive genetic variance
total phenotypic variance
18.4 g
2
. The phenotypic vari-
ance (which included both genetic and environmental
variation) of the F
2
was
P
1
= 16.8 g
2
and
2
2
σ
P
2
=
h
n
=
2
F
2
= 56.9 kg
2
. Total pheno-
typic variance of the F
2
generation is
σ
2
σ
E
, what is the
narrow-sense heritability of the F
2
generation? Since:
Therefore, in terms of
V
A
,
V
D
and
2
E
and is estimated to be 56.9 k
2
(the variance of the F
2
)
1
1
2
V
A
+
4
V
D
+
σ
.
It therefore follows that the broad-sense heritability,
h
b
for these data is:
1
1
2
V
A
+
4
V
D
h
b
=
1
1
2
E
2
V
A
+
4
V
D
+
σ
2
E
−
σ
it is reasonable to suppose that:
56.9
h
b
=
56.9
The problem reduces to: what is the value of the
environmental component of the phenotypic variance,
σ
1
2
V
A
h
n
=
2
E
In order to estimate the narrow-sense heritability it is
therefore necessary to partition the genetic variance into
1
1
2
V
A
+
4
V
D
+
σ
2
E
? Since, by definition, both parents are completely
homozygous inbreds, any variance displayed by either
