Agriculture Reference
In-Depth Information
in genetic variance (compare cross B and cross D) the
cross with highest mean value was always the better
choice for further breeding work, despite the high vari-
ance of cross D. However, if the target was taken to
a greater extreme, then the relationship would cease
to hold true, and extremely '
good
' genotypes is what
breeders are usually trying to identify.
If more than one trait is to be considered in cross
prediction studies it is possible to treat each indepen-
dently, carry out univariate cross prediction on each
character and examine the probabilities obtained to
make decisions on the 'best' crosses. This would of
course ignore the fact that the different traits are inter-
related (correlated) and that the relationship between
the traits is constant over all crosses involved. This may
cause problems and so it may be necessary to expand
the univariate procedure to cover several different traits
simultaneously.
Univariate cross prediction is based on evaluation
of the normal distribution function determined by the
mean and genetic variance of each cross and a chosen
target value (
T
), i.e.:
∞
Multi-variate cross prediction
Despite the usefulness of univariate cross prediction in
determining the frequency of desirable recombinants
that would transgress a given target value, its use is lim-
ited because only a single character can be evaluated.
As we noted many times already, usually a new cul-
tivar will not be successful because of high expression
in a single character, but rather it needs to express an
overall improvement in a number of morphological,
pathological and quality characters combined with high
productivity.
The problem of selecting the most desirable cross
combinations can partially be overcome by considering
a variate such as breeders' preference, which is based on
a visual assessment of several characters simultaneously
by a breeder. Indeed breeders' preference scores have
been shown to give very similar results to multi-variate
index selection schemes.
Visual inspection of several characters simultane-
ously, to result in a single overall rating for each
individual has several limitations. In potatoes this form
of assessment has been shown to have advantageous fea-
tures when used in a plant breeding selection scheme.
Breeders' preference scores in potato breeding are highly
related to actual yield, number tubers per plant, tuber
size, tuber conformity, tuber disease and absence from
defects. It has been shown that this type of evaluation
does not have such a good agreement with other impor-
tant characters such as seed size, disease resistance, yield
etc. Similarly it is not possible to combine characters
which are expressed at different times. For example it is
difficult to consider pre-harvest characters such as flow-
ering time plant height or maturity if preference scores
are recorded at harvest. In addition it is difficult to com-
bine morphological characters such as yield along with
quality characters that may be assessed in a laboratory
at a later stage. Thus it may be necessary to consider
selection for more than a single trait.
f
(
x
i
)
d
x
i
T
Suppose that two characters are to be considered. The
bi-variate normal distribution of the data from these two
traits can be described by the mean of each character
(
m
1
and
m
2
), the genetic variance of each character (
1
σ
2
) and the correlation between the characters (
and
).
Given these five parameters it is possible to estimate
the proportion of recombinants from the cross that will
transgress a given target value for character 1 (
T
1
) and
simultaneously transgress a second target value (
T
2
) for
the other trait. This probability is given by:
∞
σ
τ
∞
(
x
1
,
x
2
)
f
d
x
1
,d
x
2
T
1
T
2
where the function
f
is a bi-variate normal dis-
tribution function based on the mean of both traits,
the variance of both traits and the correlation between
traits.
It is easy to extend this to cover
n
different traits by
evaluation of the integral:
∞
(
x
1
,
x
2
)
∞
T
2
...
∞
(
...
,
x
n
)
...
f
x
1
,
x
2
,
d
x
1
,d
x
2
,
,d
x
n
T
1
T
n
is a multi-
normal distribution function based on the mean (
m
1,
n
)
of all
n
traits, the genetic variance (
In this case the function
f
(
x
1
,
x
2
,
...
,
x
n
)
2
σ
1,
n
)ofall
n
traits
τ
i
,
n
) between all
n
traits.
Given the various means, variances and correlations
it is possible to obtain bi-variate and tri-variate prob-
ability estimates from statistical tables. These tables
and the genetic correlation (
