Agriculture Reference
In-Depth Information
These can of course, sometimes be calculated more
easily by:
It should be noted here that upper and lower case
letter denoting alleles do not signify dominance as in
qualitative inheritance, but rather differentiate between
alleles. It is common to assign uppercase letters to alleles
from the parent with the greater expression of the trait,
always donated as P
1
.
There are two alleles involved. Assume that the
uppercase alleles add 60 kg/plot to the base performance
of a plant, and lowercase alleles add nothing. In this case
the base performance is equal to P
2
=
n
n
n
n
SP
(
x
,
y
)
=
x
i
y
i
−
x
i
y
i
(
n
−
1
)
=
=
=
i
1
i
1
i
1
n
2
n
n
x
i
−
SS
(
x
)
=
x
i
(
n
−
1
)
=
=
i
1
i
1
n
2
500 kg/plot.
n
n
Therefore, P
1
=
AA
=
620 kg/plant (500
+
60
+
60),
y
i
−
SS
(
y
)
=
y
i
(
n
−
1
)
P
2
=
aa
=
500 kg/plot (500
+
0
+
0), The F
1
=
=
=
i
1
i
1
Aa
0). At F
2
we have a
ratio of 1
AA
:2
Aa
:1
aa
, and we would have three
types of plants in the population:
AA
=
560 kg/plot (500
+
60
+
Correlation coefficients (
r
) range in value from
−
1to
=
620 kg/plot;
+
1 show very good positive
association between two sets of data (i.e. high values for
one variable are always associated with high values of
the other). In this case, we say that the two variables
are
positively correlated.
Values of
r
which are near to
−
1.
r
values approaching
+
Aa
500 kg/plot.
Obviously, yield in canola is not controlled by one
gene. However, let us progress gradually and assume
that two loci each with two alleles are involved. We
now have:
=
560 kg/plot and
aa
=
1 show disassociation between two sets of data (i.e. a
high value for one variate is always associated with a
low value in another). In this case we say that the two
variables are
negatively correlated
. Values of
r
that are
near to zero indicate that there is no association between
the variables. In this case a high value for one variable
can be associated with a high, medium or low value of
the other.
P
1
×
P
2
×
AABB
aabb
In this case (assuming alleles at different loci have
equal effect) each of the two uppercase alleles would
each add 30 kg/plot to the base weight. The F
1
=
AaBb
Relating quantitative genetics and the
normal distribution
560 kg/plot (the same as if only one gene was
involved). However at the F
2
we have 16 possible allele
combinations that can be grouped according to number
of uppercase alleles (or yield potential).
=
Consider two homozygous canola (
Brassica napus
) cul-
tivars (P
1
and P
2
)
. The yield potential of P
1
is
620 kg/plot, and is higher than P
2
, which has a yield
potential of 500 kg/plot. When these two cultivars were
crossed and the F
1
produced, the yield of the F
1
progeny
was exactly midway between both parents (560 kg/plot).
This would suggest that additive genetics effects rather
than dominance were present.
If yield in canola were controlled by a single locus
and two alleles (which it is not), we would have:
AAbb
AaBb
aabB
aABa
AABb
aaBb
AabB
AAbB
aAbb
aAbB
AaBB
aabb
Aabb
aaBB
aABB
AABB
500
530
560
590
620
P
1
×
P
2
Extending in the same manner one more time we see
that the frequency distribution of the phenotypic classes
in the F
2
generation when
three
genes having equal
×
AA
aa
