Agriculture Reference
In-Depth Information
Environments can be classified into two different
forms:
by Fisher and Mackenzie, even before the formation of
the analysis of variance.
There are several conditions that are assumed when
carrying out an analysis of variance (and indeed also
some other analyses). These include: randomness; nor-
mality; additivity and homogeneity of error variance.
The latter of these is the one which usually causes
most concern when carrying out analysis of variance
of multiple location trials.
If there are only two experiments (i.e. two loca-
tions, two years, etc.) then the plant breeder can simply
perform an analysis of variance on each experiment sep-
arately and from each obtain an estimate of the error
mean square (
•
Semi-controlled environments, where they are con-
trolled by the grower or where there maybe little
change over years or seasons. For example, soil type,
seeding density, fertilizer application
•
Uncontrolled environments, where there is often no
chance of predicting conditions from one year to
another. For example, rainfall, temperature, high
winds
Obviously, even with the uncontrolled environmen-
tal conditions there can be some degree of prediction.
For example, there will always be very low temperature
in North Dakota in January and February while it will
tend to be continually warm in Death Valley, California,
during the summer months.
The early and intermediate selection have been car-
ried out at a single (or few) location and so any surviving
line should have at least been tested over more than a
single year (albeit at a common location). It is difficult
to carry out actual G
2
s can be
used as the numerator and the smaller the denomina-
tor to carry out an F-test with the appropriate degrees
of freedom. The resulting statistic can be compared to
expected values from tables to determine whether the
two
2
). The larger of the two
σ
σ
2
s values are indeed different.
In cases where more than one experiment is being
considered (i.e. an experiment carried out over three
different years), a different approach needs to be con-
sidered. The F-test can still, however, offer a simple
test where the largest
σ
×
E studies on data where a large
proportion of lines have been selected according to that
data. For example if there are three years of data avail-
able from an intermediate selection stage which begins
with 1000 lines and reduces these to 20 lines based
on phenotypic data collected over the year then all the
remaining genotypes will (by definition be those that
were selected) have high phenotypic expression in all
years.
Multiple location trials are therefore necessary for two
reasons:
2
from the experiments is
compared by dividing by the smallest
σ
2
value. How-
ever, a more accurate method is available called a
Bartlett Test
.
σ
Bartlett test
There are two forms of the Bartlett test depending on
whether the variances (
2
) to be compared all have the
same number of degrees of freedom, or whether they
have different degrees of freedom. The first of these
two situations will be considered first.
When all
σ
•
To identify particular genotypes which perform well
over a wide range of environmental conditions. These
lines are said to have
general adaptability
2
values are based on the same degrees of
freedom the Bartlett test takes the form:
σ
To identify genotypes which perform to a high degree
at specific locations or under particular conditions.
These lines are said to have
specific adaptability
•
2
=
{
(
)
−
σ
}
M
df
n
ln
S
ln
where
S
is:
2
=
σ
/
S
n
Analysis of location trials
=
+
(
+
)/(
)
C
1
n
1
3
n
d
f
Various methods have been proposed for the statis-
tical analysis of interactions in general and G
×
E
interactions in particular. The existence of interactions
between genotypes and environments was recognized
where
n
is the number of variances to be tested, df is
the degrees of freedom that
all
variances are based on,
ln refers to natural logs.
