Agriculture Reference
In-Depth Information
2
F 2
2
1
its two components ( V A and V D )
σ
σ
F 2 =
2 V A +
. This is done by con-
sidering the phenotypic variance of the two back cross
families (
Rearranging the equation for
(i.e.
1
2
4 V D + σ
E )
we have:
2
B 1
2
σ
σ
B 2 )
and
. Without proof the expected
2
1
4 V D σ
2
B 1
2
B 2
variances of
σ
and
σ
are:
2
2
E
V A =
σ
F 2
2 358
1
4 ×
92
155
1
4 V A +
1
4 V D
1
2 [ (
2
2
E
σ
B 1 =
a
) × (
d
) ]+ σ
=
1
4 V A +
1
4 V D +
1
2 [ (
2
E
σ
B 2 =
) × (
) ]+ σ
a
d
360 cm 2
=
1
Therefore, the narrow-sense heritability for these data is:
disappears
when the equations are added together. Therefore:
The awkward expression
2 [ (
a
) × (
d
) ]
1
2 V A
h n =
1
2 V A +
1
2 V D +
1
1
E
2
2
2
E
2 V A +
4 V D + σ
σ
B 1 + σ
B 2 =
σ
2
×
0.5
360
=
155 =
As it is also known that:
0.50
×
+
×
+
0.5
360
0.25
92
1
2 V A +
1
4 V D + σ
2
2
E
σ
F 2 =
This can be derived more simply by:
1
2
2
2
B 2
2 V A
total phenotypic variation
σ
σ
σ
Provided that numerical values for
F 2 ,
B 1 ,
and
h n =
2
σ
E can be estimated, there is sufficient information to
calculate both V A and V D , and hence the narrow-sense
heritability.
To illustrate this consider the following example.
A properly designed glasshouse experiment was car-
ried out with pea. Progeny from the F 1 ,F 2 and both
backcross families (B 1 and B 2 )
1
2 V A
σ
=
2
F 2
×
0.5
360
358
=
=
0.50
were arranged as sin-
gle plants in a completely randomized block design and
plant height recorded after flowering. The following
variances were calculated from the recorded data.
Thus, 50% of the phenotypic variation in this F 2
generation of pea is genetically additive in origin.
Heritability from offspring-parent
regression
2
358 cm 2 ;
2
285 cm 2 ;
σ
F 2 =
σ
B 1 =
2
251 cm 2 ;
2
E
155 cm 2
σ
B 2 =
σ
=
In this section we will consider one other method of
estimating the narrow-sense heritability. The option
of predicting the response to selection using heri-
tabilities will be discussed in the selection section
(Chapter 7). However, the phenomenon does suggest
another approach to measuring the heritability of a char-
acter, namely comparison of the phenotypes of offspring
with those of one or both of their parents. Close corre-
spondence in the absence of selection implies that the
heritability must be relatively high. On the other hand,
if the phenotypes appear to vary independently of one
another, this suggests that heritability must be low.
The foundations of this approach, which is termed
offspring-parent regression , were laid in the nineteenth
century by Charles Darwin's cousin Francis Galton
now:
1
2 V A +
1
2 V D +
2
2
2
2
E
σ
B 1 + σ
B 2 σ
F 2 =
σ
2
1
2 V A +
1
2 V D + σ
2
E
1
4 V D + σ
2
E
=
and
2
2
2
2
V D =
B 1 + σ
B 2 σ
F 2 σ
E )
4
=
(
+
)
4
285
251
358
155
92 cm 2
=
 
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