QUANTITATIVE INHERITANCE
Many traits, especially those that are measured in a "quantitative" manner, are affected
by many genes.
Examples include"
Height
Weight
Yield (bu/A) in crops
Growth rate in farm animals
IQ
In addition to quantitative inheritance, inheritance of these traits is often referred to as
"cumulative gene action" or "polygenic-inheritance
Genetic Analysis- contributing genes
Inheritance of quantitative traits can best be examined using simplified models.
As an example, lets consider plant height in grain sorghum (often called milo).
Wild sorghums brought from Africa are often 10' tall; those grown for grain in Texas are
more nearly 2' tall, which greatly simplifies harvest. The "combine" types are sometimes
referred to as "4-dwarf" sorghums; they are produced by the Texas Ag Exp Station
"conversion program" at the Vernon station.
The model for sorghum height is as follows:
There are 4 genes involved
Each gene has 2 alleles, one of which adds about one foot of height, the other is
"null".
The alleles that contribute to height are called "contributing alleles", and
are designated by primes, A', B' C' etc.
Non-contributing (null) alleles are designated with A, B, C etc.
(Sometimes a, b, c may be used)
A plant with no contributing alleles is 2' tall (AA, BB, CC, DD)
Each gene is equivalent and shows incomplete dominance; that is, A'A' adds 2
feet, A'A adds 1 foot and AA adds 0 feet to the base height. The same is true for
the B, C, and D gene loci.
A plant with the genotypes A'A', BB, CC, DD or AA, BB C'C', DD will be 4' tall.
A'A', BB, CC, DD (4') X AA, BB, CC, DD (2')
A'A, BB, CC, DD (3')
If we allow the 3' tall F1 progeny to self pollinate, which is normal in sorghum, we
expect to see a 1:2:1 ratio of F2 plants that are 4': 3' :2' tall, respectively. This is true
because only one gene with incomplete dominance is "segregating" (heterozygous) in
the F1 hybrid. (A'A X A'A gives 1/4th A'A' : 2/4th A'A : 1/4th AA)
One Gene Segregating
2
N
u
m 1
b
e
r
0
2'
3'
4'
Height
The same would be true if AA, B'B', CC, DD or any other 4' tall truebreeding plant
(homozygous at all 4 gene loci) was crossed to the AA, BB, CC, DD parent.
What if we cross A'A' BB, CC, DD to AA, B'B', CC, DD ? Both parents are 4' tall as is the
F1, but the F1 is heterozygous for 2 genes (A'A, B'B, CC, DD).
Now in the F2, we can predict that 1/4th of the progeny will be A'A' and that 1/4th of
these will also be B'B'; thus 1/16th of the progeny should be 6' tall! Likewise, 1/16th
should be AA, BB, CC, DD or only 2' tall having no primes.
When the range in the F2 progeny goes beyond the original parents, we see
"transgressive segregation".
Transgressive segregation implies that the parents donate contributing alleles from
different genes to the hybrid.
There should also be plants in the F2 generation that have 1 contributing allele (A'A,
BB, CC, DD or AA, B'B, CC, DD), These should represent 1/4th (1/8th + 1/8th) of the
progeny, and they will be 3' tall. The same is true for plants with 3 contributing alleles
(A'A',B'B,CC, DD and A'A, B'B', CC, DD).
Four foot tall F2s can occur several ways: A'A', BB, CC, DD; A'A, B'B, CC, DD; and AA,
B'B', CC, DD. (P= 1/16th + 1/4th + 1/16th = 6/16th).
2 Genes Segregating
6
5
N
4
u
m 3
b
e 2
r
1
0
2'
3'
4'
5'
6'
Height
On your own, make the following crosses and predict the genotype, the height of the F1
and the range of heights expected in the F2:
1) A'A', B'B', C'C', D'D' X AA, BB, CC, DD
2) A'A', B'B', CC, DD X AA, BB, C'C', D'D'
Generalized formulas can be used to calculate the number of classes expected in the F2
and the frequency of progeny that fell in the extreme classes:
If N genes are heterozygous in the F1 hybrid, there will be:
2N +1 phenotypic classes in the F2 (0, 1, 2, 3, etc. up to 2 N contributing
alleles).
The fraction of individuals falling into each of the extreme classes (0 or 2N
contributing alleles) will be 1/4th to the N power (1/4)N
Genes that contribute to quantitative traits are referred to as polygenes, or QTLs which
stands for for Quantitative Trait Loci.
The model we have used where all the genes have equal and additive effects is
simplified, but even so, there are many traits where the model applies. Examples
include wheat kernel color, ear length in rabbits, skin color and the number of
fingerprint ridges in humans, the number of rows of seeds on an ear of corn, etc.
When this model applies, the hybrid will always show a phenotype that is the average of
the parents, and there will be more variation among the F2 progeny than in either P1 or
F1 progeny. It would not be difficult to imagine cases where some genes made larger or
smaller contributions than others, or where one or more genes may be dominant. Other
than skewing the expected frequencies somewhat, neither change from the model
significantly alters the analysis of polygenic traits.
Environmental effects
Most or all quantitative traits are also influenced by environmental factors.
In the case of sorghum height, plants will not reach their genetic potential without
water, nutrients (fertilizer) and sunlight!
Environmental effects means that some differences can be seen within a purebred
parent or in an F1 population, where all of the plants have the exact same genotype.
Environmental effects will also "smooth out" the stair-step effect expected for
genotypes in the F2 that differ in the number of contributing alleles.
standard deviation
mean
The smoothing of the binomial distribution seen for segregating genes converts the
binomial distribution to a "Normal distribution", often called a "bell-curve".
The normal curve is defined by 2 parameters:
The mean or average locates the "center" of the curve
The standard deviation is a measure of breadth of the curve and is a measure of
the variation within the population. It is the square root of the variance.
If we measure height of many sorghum plants all with the genotype A'A'B'B'
CC DD, the average will be about 6' and the variation will be small;
If we measure height the F2 generation from selfing an A'A B'B C'C D'D
parent, the variation and standard deviation will be large.
Since it is not possible to "count" the number of classes in an F2 population when
environmental effects smooth away the genotypic differences, or to identify
individuals in the extremes, the number of genes that contribute to the trait cannot
be simply estimated.
Partitioning sources of variation; the concept of heritability
Normal curves can be used in other ways to analyze the contributions of genes and
environment to a trait.
The concept is to partition the sources of variation that lead to differences among
individuals in the sample, and to identify the portion of variation that results from
segregating genes.
Total variation (Vt) which is also often called phenotypic variation (Vp) arises from
differences in genotype (Vg), the environment (Ve) and may also result from
interactions (Vgxe)where some genotypes do better in one environment and others
in another.
Vt = Vp = (Vg + Ve + V gxe) In many cases, the interaction component cannot be
measured, so is ignored or handled by working within a specific environment or only
working with a specific "breed" or cross'
Heritability (H2 or broad-0sense heritability) is the fraction of variation due to
genetic differences, ie Vg. H2 = Vg/Vt
It is relatively simple to make H2 estimates in plants, since pure-breeding,
completely homozygous parents can be maintained.
Any variation within a purebreeding homozygous parent, or in the F1 progeny of a
cross between 2 purebreeding parents must result from Ve, since all plants within
each of the populations have the exact same genotype. Thus, these plants can be
used to estimate Ve.
Variation among F2 plants arises both from differences in genotype and from local
environments, so the variation in the F2 is a measure of Vt.
In the example below, two true breeding corn parents, one with an average row
number of 6 is crossed to another with an average of 14 rows.
The F1, as expected, is right between the parents, having an average of 10 rows.
Variance (V) for row number in the parents and F1 is low (arbitrarily measured as 1)
Variance in the F2 is 8. (We will not learn how to calculate variances in Gene 310)
Vt (8) = Vg + Ve (1); ignoring Vgxe since all plants were grown in the same
environment, Vg must be 7. Therefore, H2 = 7/8
Heritability for row number in maize ears from a cross
between a 6 rowed parent by a 14 rowed parent
P1
P2
V=1
V=1
6 rows
14 rows
F1
V=1
10 rows
F2
V=8
Ave = 10 rows
It is critical to realize that:
1) heritability measures are only valid for the population that was measured.
2) genetic differences will not be measured unless the parents have different
alleles
3) environment by gene interactions may be important, but are generally ignored
Plant and animal breeders are interested in heritability, because it allows them to
predict if selective breeding can be used to "improve" a trait. For example, if rate of
weight gain in nursing Hampshire pigs is highly h heritable, saving those that grow
the fastest for breeding purpose will lead to improved weight gain in future
generations. If H2 is low, changes in the diet may be more important.
Selection will make progress so long as genetic differences can be combined to make
an improved genotype;
Selection for one trait may be balanced by loss in another; for example selection for
increased egg size in Leghorns is successful, but the hens lay fewer eggs.