Agriculture Reference
In-Depth Information
σ
p
) of 19.0 kg. If we assume that from past
research it is known that the heritability (
h
2
) is equal to
0.6 and selection is to be carried out at the 10% level
(i.e.
k
σ
g
is the genetic variance component,
σ
a
is
deviation (
where
σ
p
is the phenotypic
variance. From this we can write the average perfor-
mance of a selected population after selection is:
the additive genetic variance and
=
=
1.755).
From this we have that:
σ
0.1,
i
ih
2
=
+
σ
P
X
i
=
19.0
×
1.755
=
33.34
where
X
is the average performance of the initial popu-
lation (i.e. the unselected family mean),
i
is the selection
intensity,
h
2
From this we can estimate the performance of the
selected fraction in the following year as the response to
selection would be
is the phenotypic
standard deviation between plants in the population.
This means that the very best responses from selection
are based on high family means, high selection intensity
(although limited increase in return for very high selec-
tion), heritability and the phenotypic variance. From
this breeders should be aiming to:
is the heritability and
σ
ih
2
=
20.0 kg. The mean of the selected plants would there-
fore be 560 kg
σ
×
and equal to 33.34
0.6
+
=
=
the average
performance of the top 10% selected lines in the next
year.
It should be noted that the phenotypic standard devi-
ation in the selected population must be less than the
whole (unselected) population. As it can be assumed
that the error variance remains constant, then this
must mean that the genetic variance is smaller and the
error variance is the same. From this, the heritability
between the selected population and further selection
years must be less than from the base population if the
first selection year.
Therefore, if selection continues, then there would be
decreasing response with increasing rounds of selection
(Figure 7.2).
Return now to the response equation given above,
and recall that the formula for the broad-sense and
narrow-sense heritabilities is:
σ
g
/σ
p
20 kg
580 kg
Identify highly productive families with high average
performance (i.e. high means)
•
•
Maximize heritabilities by minimizing non-genetic
errors. This can best be achieved by good exper-
imentation,
increasing plot sizes and replication
levels
•
Select as intensely as considered feasible, although
remember the efficiency will only increase as a
reciprocal beyond 20% selected
•
Choose parents which are genetically diverse for char-
acters that require improvement or change, and hence
attempt to increase the phenotypic variance
On the other hand if a plant breeding programme is
not producing the expected response, the same equation
can be used to identify possible reasons for the failure.
The close correspondence between heritability and
the proportional change in a selected character from
one generation to the next when selection is applied has
already been pointed out. Having considered estimation
of narrow-sense heritability,
h
n
in some detail earlier, it
is now appropriate to return to the issue of estimating
heritability.
A third definition of narrow-sense heritability, usu-
ally termed the realized heritability, is:
h
n
=
σ
a
/σ
p
, respectively
and
120
100
80
60
40
20
0
0
2
4 6
Generations of selection
8
10
/
R
S
Figure 7.2
Response to selection from successive rounds
of selection. The dashed line indicates the phenotypic
expression and the solid line represents the genetic gain.
Note that greatest gains are from the initial rounds of
selection and that after several rounds of selection there is
little or no gain.
where
R
is the
response to selection
(the same as described
above) and
S
is the
selection differential
. The response
to selection is the difference between the mean of the
selected genotypes for a particular character and the
mean of the population before selection was applied.
