Agriculture Reference
In-Depth Information
are, however, not commonly presented in standard
statistical tables (as for example the ones that usually
show unit normal distribution function,
t
-tables,
Table 7.12
Relative ranking of eight potato crosses (C1 to
C8) based on multivariate cross prediction (MV-rank) and
univariate cross prediction (UV-rank) of Breeder's Preference
that a genotypes chosen at random from each cross will exceed
a Breeder's Preference rating greater than 5, on the 1 to 9 scale
and the number of selected breeding lines from each cross
that was selected in the 4th, 5th and 6th selection stage in
the breeding program at the Scottish Crop Research Institute.
2
-
tables or F-tables). In addition use of the tables that
do exist can be complex and would require detailed
description.
Parameters used in multi-variate prediction are esti-
mated using the same design types (i.e. triple test
cross, F
3
prediction) that were explained previously for
univariate predictions.
When it is necessary to estimate multi-variate proba-
bilities, computers offer an easier alternative. Computer
software is available (although not commonly) which
projects a probable value, when the means, variances,
correlations and target values are entered. To our knowl-
edge there is software which can handle upto seven traits
simultaneously - how the software manages this need
not detain us here!
Similarly, it is beyond the scope of this topic to try
to explain in more detail the theory of estimating these
probabilities. It is sufficient to understand the basic con-
cept and to be aware of the usefulness of the procedure
as applied to cross prediction techniques. You should,
however, be aware that the procedure exists and that
multi-variate cross prediction can offer a powerful tool
to selection in plant breeding.
χ
Cross
MV.rank
UV.rank
Selected to stage
Four
Five
Six
C1
2
1
15
3
2
C2
2
3
9
3
2
C3
6
6
1
0
0
C4
4
4
2
0
0
C5
8
8
1
0
0
C6
5
5
11
6
1
C7
1
2
12
7
3
C8
7
7
0
0
0
preference scores were highly related to yield, num-
ber of tubers, tuber size and tuber shape. There was
also very good agreement with the predicted worth of
each cross and the number of clones which indeed show
commercial value in the advanced selection stages.
Example of multi-variate cross prediction
The eight crosses (C1
Observed number in a sample from each cross
It is possible to obtain good multi-variate probability
estimates by observing the frequency of individuals in a
small sample that exceed given target values. The diffi-
culty in using observed frequencies is related to sample
size. The accuracy of the predictions will be directly
related to the sample size examined. When the fre-
quency of desirable recombinants is low (i.e. when large
target values are used) then larger samples will need to
be examined.
Similarly, if there are low correlations between traits
of interest sample sizes will need to be relatively large to
predict effectively.
···
C8) that were evaluated for
breeders' preference (see earlier in univariate predic-
tion) also had tuber yield, tuber size and number of
tubers recorded for the 25 progeny from each cross.
Tuber shape was also visually assessed. The means and
variances of each variate were estimated along with
the correlation between traits for each cross. Based on
these statistics the probability that genotypes would
exceed target values for each character simultaneously
was estimated using a computer software package called
POTSTAT. The relative ranking of the multivarate pre-
dicted values (MV.rank) are shown in Table 7.12 along
with the ranking of the univariate cross prediction of
breeders preference (UV.rank) and the frequency of
desirable clones selected from a large sample in the
fourth, fifth and sixth round of selection.
There is good agreement between the multi-variate
predictions, based on four traits and the univariate pre-
diction based on breeders' preference. Therefore the
Use of rankings
It has been noted, above, in the univariate case that
the relative importance of the different parameters can
affect the results of prediction. In multi-variate predic-
tion three types of parameter are used, means, variances
