Agriculture Reference
In-Depth Information
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of genotype
environment interactions (i.e. the dif-
ference in expression of the two alleles is large in
comparison to the variation caused by environmental
changes). For example, a potato genotype with white
flowers (a qualitatively inherited trait) will always have
white flowers in any environment in which the plants
produce flowers. Conversely, quantitatively inherited
traits are greatly influenced by environmental condi-
tions and genotype
a distribution called a
normal distribution
, and occurs
in a wide variety of aspects relating to plant growth, and
particularly to quantitative genetics.
Describing continuous variation
The normal distribution
The 11,000 potato plant weights discussed above are a
sample, albeit a large sample, of possible potato weights
from individual plants. It is possible to predict mathe-
matically the frequency distribution for the population
as a whole (i.e. every possible potato plant of that cul-
tivar grown), provided it is assumed that the sample is
representative of the population (i.e. that our sample is
an unbiased sample of all that was possible).
It is not necessary to actually draw normal distribu-
tions (which, even with the aid of computer graphics,
are difficult to do accurately). Most of the properties of
a normal distribution can be characterized by two statis-
tics, the mean or average (
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environment interactions are
common, and can be large. The greatest difficulty plant
breeders face is dealing with quantitative traits and in
particular in deciding on the better genotypes based on
their phenotypic performance. This is why it is crit-
ically important to employ appropriate experimental
design techniques to genetic experiments and also plant
breeding programmes.
A major part of quantitative genetics research related
to plant breeding has been directed towards partitioning
the variation that is observed (i.e. phenotypic varia-
tion) into its genetic and non-genetic portions. Once
achieved this can be taken further to further divide the
genetic portion into that which is additive in nature
and that which is non-additive (quite often dominance
variation). Obviously in breeding self-pollinating crops,
the additive genetic variance is of primary importance
since it is that portion of the variation due to homozy-
gous gene combinations in the population and is what
the breeder is trying to obtain. On the other hand,
variance due to dominance is related to the degree of
heterozygosity in the population and will be reduced (to
zero) over time with inbreeding as breeding lines move
towards homozygosity.
Let us now return to the potato weights as one, of
many possible examples of continuous variation. If the
frequency distribution of potato yields is inspected there
are two points to note: (1) the distribution is symmet-
rical (i.e. there are as many high yield as really low
yields); and (2) the majority of potato yield were clus-
tered around a weight in the middle. As we have taken a
class interval of 0.3 kg to produce this distribution, the
figure does not look particularly continuous. However,
we know that potato yields do not go up in increments
of 0.3 kg but show a more continuous and gradual range
of variation. If we use more class intervals in this exam-
ple we will produce a smoother histogram, and if we use
an infinity small class intervals it will result in a continu-
ous bell-shaped curve. The shape of this curve is highly
indicative of many aspects of plant science because it is
µ
) of the distribution and the
σ
standard deviation (
), a measure of the '
spread
'ofthe
distribution.
There are in fact two means, the mean of the sample
and the mean of the population from which the sample
was drawn. The latter is represented by the symbol
,
and can, in reality, seldom be known precisely. The
sam-
ple mean
is represented by
µ
x
(spoken
x
bar), and it can
be known with complete accuracy. The best estimate of
a
population mean
(
¯
) is generally the actual mean of
an unbiased sample drawn from it (
µ
x
). The population
¯
mean is thus best estimated as:
n
i
(
µ
=¯
x
=
(
x
1
+
x
2
+
x
3
+···+
x
n
)/
n
=
x
i
)/
n
where
i
(
is the sum of all
x
values from
i
=1 to
n
.
The standard deviation is an ideal statistic to examine
the variation that exists within a data set. For any nor-
mal distribution, approximately 68% of the population
sampled will be within one standard deviation from the
mean, approximately 95% will be within two standard
deviations (Figure 5.2), and approximately 99% will be
within three standard deviations of the mean.
Once again, it is necessary to distinguish between the
actual standard deviation of a population, all of whose
members have been measured, or of a particular sample,
and the estimated standard deviation of a population
based on measuring a sample of individuals from it.
The former is represented by the symbol
x
i
)
σ
(Greek letter
