Agriculture Reference
In-Depth Information
Quantitative genetics models
additive effects, and which segregate independently, are:
The relationship, and importance of the normal dis-
tribution, to quantitative genetics is clear, however,
the closeness of the relationship between observed
progeny performances and theoretical distributions will
be related to
the model
on which the relationship is
based. For example, we assumed that all uppercase let-
ter alleles were of equal additive value, which of course
may not be true. It is important that an appropriate
model of inheritance is applied; otherwise other derived
statistics (i.e. heritabilities, see later in Chapter 6) which
are potentially of great value in plant breeding will be
biased, and are likely to be highly misleading.
Let us examine the basic model applied to quanti-
tative situations and see how the model can be tested
for its appropriateness to the situation or inheritance of
specific characters.
Consider again the cross between two canola culti-
vars described above. The yield of the higher yielding
parent (P
1
)
aaBbCC
aAbBcC
aAbBCc
aAbbCC
AabbCC
aabbCC AabBcC
AABBcc
aabBcC
AabBCc
AABbCc
aabBCc
AaBbcC
AABbcC
aaBbcC
AaBbCc
AAbBCc
aaBbCc
AaBBcc
AAbBcC
aaBBcc
aabBCC AAbbCC
aAbbcC
aaBBcC
AaBBCc
aAbbCc
aaBBCc
AaBBcC
aAbBcc
aABbcC AaBbCC
aabbcC
aABbcc
aABbCc AabBCC AABBcC
aabbCc AabbcC
aABBcc
aABBCc
AABBCc
aabBcc
AabbCc
AAbbcC
aABBcC AAbBCC
aaBbcc
AabBcc
AAbbCc aABbCC AABbCC
aAbbcc
AaBbcc
AAbBcc
aAbBCC aABBCC
aabbcc Aabbcc
AAbbcc
AABbcc
aaBBCC AaBBCC AABBCC
is 620 kg/plot, the yield of the lower yield-
ing parent (P
2
)
500
520
540
560
580
600
620
is 500 kg/plot, and the yield of the F
1
is
560 kg/plot. Assume a model of additive genetic effects,
where we have:
In this case each single upper case allele adds only
20 kg to the base weight of 500 kg/plot. This is
determined in the same way as for the one and two gene
models, although it is considerably more involved. You
should note, once more that the F
1
would have had a
yield potential of 560 kg/plot, exactly the same as in the
single and two gene cases.
Even with only three loci and two alleles at each locus,
it should be obvious that we are coming closer to a
shape resembling a standard normal distribution. The
frequency of different genotypes possible when four,
five and six loci are considered has 9, 11 and 12 phe-
notypic classes, respectively. It is fairly easy to visualize,
therefore, that with only a modest number of loci with
segregating alleles acting in a more or less equal additive
way, truly continuous variation in a character would
be quite closely approached. Quantitative inheritance
deals with many loci and alleles, often too many to
consider estimating, and therefore explains the ubiq-
uity of the normal distribution. Just as the mean and
variance can describe the normal distribution, many of
the important elements of the inheritance of a character
can be described and explained using progeny means
and genetic variances.
−
−
−
P
2
F
1
P
1
500
560
m
620
[
a
]
[
a
]
where the difference between the performance of the
parents is divided in half (i.e. 120
/
=
=[
]
2
60 kg
a
),
[
]
and indicates the additive effect. Note that
carries no
sign.
m
is called the mid-parent value and is midway in
value between the performance of P
1
and P
2
. Therefore:
[
a
]=
(
P
1
−
P
2
)/
a
2
=
P
2
+[
P
1
−[
]
]
m
a
or
a
P
1
=
P
2
=
+[
]
−[
]
m
a
and
m
a
is used to indicate the summation of the
additive effects over all loci involved, however many this
may be. In the example shown we assumed a completely
additive model of inheritance and the F
1
performance
was indeed equal to
m
. Therefore in the absence of dom-
inance, the mid-parent value will equal the performance
of the F
1
. Dominance will be detected in cases where
the performance of the
The term
[
a
]
F
1
is not equal to
m
.
