TOPIC FOUR: INHERITANCE OF A SINGLE GENE

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TOPIC FOUR INHERITANCE OF A SINGLE GENE
Why cant we all just get along and, say, call an
inbred line in the F6 generation simply an F6
line? Well we cannot all get along with such a
statement, because it provides no indication as
to the genetic makeup of an F6 line. Just
about the only information passed along in that
statement is the high probability one is
conversing with a plant breeder! There is no
description of the history and current genotypic
constitution of an F6 line. For example, as
you will see in this section, there is a world of
difference between an F2-derived line in the F6
and an F4-derived line in the F6, yet both could
be classified as an F6 line.
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The frequency of heterozygotes decreases by
one-half with each generation of selfing in the
absence of selection or mutation
The frequency of heterozygotes is estimated by
(1/2)G, where G is the number of generations of
selfing, i.e., F2 (1/2)1 1/2 F3 (1/2)2
1/4 F4 (1/2)3 1/8.
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Awareness of the genotypes and frequencies of
progenies resulting from self-pollination is the
key to understanding the dynamics of a breeding
nursery in the critical F2 to F8 generations that
occupy the majority of a plant breeders
efforts. It is also essential for a full
understanding of recombinant inbred techniques in
the development of mapping populations It is of
utmost importance to grasp the content of the
following three examples because the theme will
arise continuously throughout the remainder of
the course.
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1-250
251-750
751-1000
1000 F23 lines planted in 1000 rows
Like an F2
Segregation at A locus ?
Like an F3
Like an F4
Like an F5
Only aa
Fully Inbred
Mix AA aa
Only AA
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1) The frequencies of homogeneous and segregating
derived lines in the F2Y generation is the exact
same as the frequency of homozygous and
heterozygous plants, respectively, in the F2
generation (Tier 1 number).
2) The frequencies of genotypes (AA aA aa)
within the segregating derived lines in the F2Y
generation depends on the number of generations
of self-pollination undergone since the single
heterozygote plant was selected in the F2
generation (i.e., Tier 2 number minus Tier 1
number).
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1-438
439-563
564-1000
Like an F2
1000 rows
Like an F3
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I warned previously about the dire lack of
information contained in the simple designation
of an F6 line. This terminology provides no
description of the history or current genotypic
constitution of an F6 line. In both Examples 3
and 4 we have developed what could be described
as two sets of F6 lines. But the two sets of
lines, F26 and F46, are radically different in
their development and genotypic content. A much
greater percentage of random F46 lines are
homogeneous (876 versus 500) and the within
segregating line variation is much different
(0.06 versus 0.25 heterozygous plants).
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Two sets of lines with the same designation
(F46) do not necessarily have the same
genotypic frequencies between lines
Like selecting 1000 random Plants from an F3
bulk population
Like an F2
Like an F3
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Segregation at Multiple Loci with Self-Pollination
1. Unlinked Loci. In the vast majority of cases
involving cultivar development, the F2 or S0
populations will be segregating at more than one
locus. The overall effect of multilocus
segregation on genotype frequencies is to reduce
the proportion of completely homozygous
individuals relative to the case with only single
locus segregation.
AA
BB
bb
AA
aa
BB
aa
bb
In the two-locus example in Table 4.2, the
probability of homozygosity at the A or B locus
is 0.5. The probability of homozygosity at both
loci is 0.5 x 0.5 0.25. In the F3 population
the equivalent probability is 0.75 x 0.75 0.56,
and in the F4 population 0.876 x 0.876 0.77
(Appendix 4B).
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Many plant breeders prefer to wait until the F5
generation or later before making selections in
their nurseries. Two reasons are highlighted by
this example (1) the proportion of homozygous
individuals in the population is higher in later
generations and (2) if one observes a superior
genotype in later generations, its performance in
subsequent generations is more predictable based
on the low probability that its loci governing
the trait are in the heterozygous state.
Purification of lines prior to Cultivar
Release Frequently, the first generation of
expensive yield testing will involve , say, F57
lines. Obviously there will be considerable
residual heterozygosity / heterogeneity in this
material. Lines that perform well in the first
year of yield evaluation will start to undergo
purification for release based on selecting
single plants in the next season. Under this
scenario, the cultivar would be an F8-derived
line. And it is common to see them being F9-, F10
- and later generation derived lines
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Number of Potential Genotypes in a Population
Although completely inbred individuals are an aid
to efficient selection, unfortunately, one is
easily swamped with genetic variability among the
same completely inbred individuals
If the parents in a cross have contrasting
alleles at n loci, then 2n different inbred
genotypes can be derived from the cross. In the
case above where the parents differed at 20 loci,
then 220 different inbred individuals can
potentially be derived--i.e., 1,048,576.
The advantage of working with an inbred
population can be illustrated when one considers
that 320 different genotypes are possible in the
F2 generation--i.e., 3,486,784,401!
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Our bulk population plot size is about 1/220th of
an acre planted with 2500 seeds. Obviously we do
not try to grow bulk populations that contain all
potential genotypes resulting from a cross. Our
strategy is to sample a large number of different
segregating populations containing a limited
array of all potential genotypes rather than put
significant resources into a few populations with
a larger array of genotypes.
WHY? The combining ability of parents can be
unpredictable when breeding for 19 essential
traits as we do in wheat.
The unpredictable but inevitable virulence
pattern changes in fungal and insect pathogens
makes identification of the best cross
difficult
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Recovery of Progeny Superior to the Best Parent
Of great value to the breeder, however, is the
recovery of genotypes containing the superior
allele in the homozygous state at more loci than
are contained by the best parent in the cross.
For example, assume the trait in question is
governed by 20 loci. Inbred Parent 1 contains
the superior allele at loci numbers 1 to 11,
Inbred Parent 2 contains the superior allele at
loci numbers 12 to 20. Success to the breeder is
the recovery of genotypes with the superior
allele in the homozygous state at 11, 12, 13, 14,
15, ... 20 loci.
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The probability of such success can be estimated
using the Binomial Probability Formula  P(x
k) (nk)pk(1 - p)n-k  where  n number of loci
controlling the trait (independent trials),  k
number of loci homozygous for the superior
allele (successes),  p probability of fixing
the superior allele in the homozygous state in
the selfing generation Fi (i.e., 0.25 in F2
0.375 in F3 0.438 in F4), (nk) , the
binomial coefficient which estimates the number
of ways in which k successes can be chosen from
among n trials
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Number of Potential Genotypes in a Population
These probabilities likely illustrate one
mechanism for the small, but steady increase in
genetic potential for quantitatively controlled
traits brought about by a century of scientific
cultivar development. Each cycle of cultivar
development of approximately 10 to 15 years has
resulted in a steady accumulation of superior
genotypes at the loci controlling the traits.
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Linked Loci.
Linkage reduces the level of independence between
loci, it decreases the number of independent
chromosomal units (or loci). Linkage is a
conservative influence which tends to maintain
existing parental arrangements. Thus, linkage
increases the frequency of completely homozygous
individuals in a segregating population relative
to that expected if the loci were independent
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