An early dihybrid cross
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In the early 1900s, William Bateson and R. C. Punnett were studying inheritance
in the sweet pea. They studied two genes: one affecting flower color (P, purple,
and p, red) and the other affecting the shape of pollen grains (L, long, and l,
round). They crossed pure lines P/P · L/L (purple, long) × p/p · l/l (red, round),
and selfed the F1 P/p · L/l heterozygotes to obtain an F2. The following table
shows the proportions of each phenotype in the F2 plants:
Phenotype
purple, long
purple, round
red, long
red, round
Total
•
Genotype
P/- L/P/- l/l
p/p L/p/p l/l
Observed
4831
390
393
1338
6952
Expected
3910.5
1303.5
1303.5
434.5
6952
The F2 phenotypes deviated strikingly from the expected 9:3:3:1 ratio. What is
going on? This does not appear to be explainable as a modified Mendelian ratio
caused by some kind of gene interaction.
Genetica per Scienze Naturali
a.a. 03-04 prof S. Presciuttini
Testing the segregation ratios in the Bateson-Punnett cross
Null hypothesis: phenotypes in 9:3:3:1 ratio
Phenotype
Genotype
Observed Expected
purple, long
P/- L/4831
3910.5
purple, round
P/- l/l
390
1303.5
red, long
p/p L/393
1303.5
red, round
p/p l/l
1338
434.5
Total
6952
6952
P=
Null hypothesis: phenotypes in 3:1 (purple/red) ratio
Phenotype
Genotype
Observed Expected
purple
P/5221
5214.0
red
p/p
1731
1738.0
Total
6952
6952
P=
Null hypothesis: phenotypes in 3:1 (long/round) ratio
Phenotype
Genotype
Observed Expected
long
L/5224
5214.0
round
l/l
1728
1738.0
Total
6952
6952
P=
Chi-sq
216.678
640.186
635.988
1878.739
3371.591
0
Chi-sq
0.009
0.028
0.038
0.846
Chi-sq
0.019
0.058
0.077
0.782
Analysis of phenotype
proportions in F2 shows that both
traits independently follow a
typical 3:1 Mendelian ratio.
As a possible explanation for this,
Bateson and Punnett proposed
that the F1 had actually produced
more P · L and p · l gametes than
would be produced by Mendelian
independent assortment. Because
these genotypes were the gametic
types in the original pure lines,
the researchers thought that
physical coupling between the
dominant alleles P and L and
between the recessive alleles p
and l might have prevented their
independent assortment in the F1.
Genetica per Scienze Naturali
a.a. 03-04 prof S. Presciuttini
Comfirmation of coupling in Drosophila
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The confirmation of Bateson and Punnett's hypothesis had to await the
development of Drosophila as a genetic tool.
After the idea of coupling was first proposed, T. H. Morgan found a
similar deviation from Mendel's second law while studying two
autosomal genes in Drosophila.


One of these genes affects eye color (pr, purple, and pr+, red), and the other
affects wing length (vg, vestigial, and vg+, normal). The wild-type alleles of both
genes are dominant. Morgan crossed pr/pr · vg/vg flies with pr+/pr+ · vg+/vg+
and then testcrossed the doubly heterozygous F1 females: pr+/pr · vg+/vg
(female) × pr/pr · vg/vg (males).
The use of the testcross is extremely important. Because one parent (the tester)
contributes gametes carrying only recessive alleles, the phenotypes of the
offspring reveal the gametic contribution of the other, doubly heterozygous
parent. Hence, the analyst can concentrate on meiosis in one parent and forget
about the other. This contrasts with the analysis of progeny from an F1 self,
where there are two sets of meioses to consider: one in the male parent and one
in the female.
Genetica per Scienze Naturali
a.a. 03-04 prof S. Presciuttini
Results of Morgan’s experiment

Morgan's results follow; the alleles contributed by the F1 female (double
heterozygous) specify the F2 classes:

Obviously, these numbers deviate drastically from the Mendelian prediction of a
1:1:1:1 ratio, and they indicate a coupling of genes. The two largest classes are the
combinations pr+ · vg+ and pr · vg, originally introduced by the homozygous
parental flies. You can see that the testcross clarifies the situation. It directly reveals
the allelic combinations in the gametes from one sex in the F1, thus clearly showing
the coupling that could only be inferred from Bateson and Punnett's F1 self. The
testcross also reveals something new: there is approximately a 1:1 ratio not only
between the two parental types, but also between the two nonparental types.
Genetica per Scienze Naturali
a.a. 03-04 prof S. Presciuttini
Repeating the cross

Morgan then repeated the crossing experiments but changed the combinations of
alleles contributed as gametes by the homozygous parents in the first cross. In this
cross, each parent was homozygous for one dominant allele and for one recessive
allele:
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The following progeny were obtained:
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Again, these results are not even close to a 1:1:1:1 Mendelian ratio. Now, however,
the largest classes are those that have one dominant allele or the other rather than, as
before, two dominant alleles or two recessives. But notice that once again the allelic
combinations that were originally contributed to the F1 by the parental flies provide
the most frequent classes in the testcross progeny.
Genetica per Scienze Naturali
a.a. 03-04 prof S. Presciuttini
A hypothesis about coupling
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In the early work on coupling, Bateson and Punnett coined the term repulsion to
describe this situation, because it seemed to them that, in this case, the nonallelic
dominant alleles "repelled" each other the opposite of the situation in coupling,
where the dominant alleles seemed to "stick together." What is the explanation of
these two phenomena: coupling and repulsion?
Morgan suggested that the genes governing both phenotypes are located on the
same pair of homologous chromosomes. Thus, when pr and vg are introduced from
one parent, they are physically located on the same chromosome, whereas pr+ and
vg+ are on the homologous chromosome from the other parent.
This hypothesis also explains repulsion. In that case, one parental chromosome
carries pr and vg+ and the other carries pr+ and vg. Repulsion, then, is just another
case of coupling: in this case, the dominant allele of one gene is coupled with the
recessive allele of the other gene.
This hypothesis explains why allelic combinations from P remain together, but how
do we explain the appearance of nonparental combinations?
Genetica per Scienze Naturali
a.a. 03-04 prof S. Presciuttini
Crossovers

Morgan suggested that, when homologous chromosomes pair in meiosis, the
chromosomes occasionally exchange parts in a process called crossing-over. The
figure below illustrates this physical exchange of chromosome segments. The two
new combinations are called crossover products.


Data like those just presented, showing coupling and repulsion in testcrosses and in F1
selfs, are commonly encountered in genetics. Clearly, results of this kind are a departure
from independent assortment. Such exceptions, in fact, constitute a major addition to
Mendel's view of the genetic world.
The residing of genes on the same chromosome pair is termed linkage. Two genes
on the same chromosome pair are said to be linked.

It is also proper to refer to the linkage of specific alleles: for example, in one A/a · B/b
individual, A might be linked to b; a would then of necessity be linked to B.
Genetica per Scienze Naturali
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Recombination
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In modern genetic analysis, the main test for determining whether two
genes are linked is based on the concept of recombination.
Meiotic recombination is any meiotic process that generates a
haploid product with a genotype that differs from both haploid
genotypes that constituted the meiotic diploid cell.
The product of meiosis so generated is called a recombinant.
Mendelian independent assortment may be reinterpreted in terms of
recombination.


If we observe a recombinant frequency of 50 percent in a testcross, we can infer
that the two genes under study assort independently. The simplest interpretation
of such a result is that the two genes are on separate chromosome pairs.
However, genes that are far apart on the same chromosome pair
can act virtually independently and produce the same result.
Genetica per Scienze Naturali
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Recombination by crossing-over
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Recombinants arise from meioses in which nonsister chromatids cross over
between the genes under study.
For genes close together on the same chromosome pair, the physical linkage of
parental allele combinations makes independent assortment impossible and hence
produces recombinant frequencies significantly lower than 50 percent.
The recombinant frequency arising from linked genes ranges from 0 to 50 percent,
depending on their closeness. Recombinant frequencies greater than 50 percent
cannot be observed.
Note in the figure that
crossing-over generates two
reciprocal products, which
explains why the reciprocal
recombinant classes are
generally approximately
equal in frequency.
Genetica per Scienze Naturali
a.a. 03-04 prof S. Presciuttini
Recombination frequency in Morgan’s crosses
First
experiment
+
P
+
+
pr /pr · vg /vg
x
pr/pr · vg/vg
F1
pr+/pr · vg+/vg
F1 testcross
females x males
pr +/pr · vg +/vg
x
pr/pr · vg/vg
Parental (pr + · vg + )
Total F2 progeny
1339
1195
2534
151
154
305
2839
Recombination
frequency
0.107
Parental (pr · vg )
Total parental
Recombinant (pr+ · vg )
Recombinant (pr · vg+ )
Total recombinant
Second
experiment
+
+
+
pr /pr · vg /vg
x
+
pr/pr · vg /vg
+
pr+/pr · vg+/vg
F1 testcross
females x males
Parental (pr+ · vg )
Parental (pr · vg+ )
Recombinant (pr + · vg + )
Recombinant (pr · vg )
pr +/pr · vg +/vg
x
pr/pr · vg/vg
1067
965
2032
157
146
303
2335
0.130
Total
4566
608
5174
0.118
Genetica per Scienze Naturali
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Interpreting linkage data
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As Morgan studied more linked genes, he saw that the proportion of
recombinant progeny varied considerably, depending on which linked
genes were being studied, and he thought that these variations in
crossover frequency might somehow indicate the actual distances
separating genes on the chromosomes.
Morgan assigned the study of this problem to a student, Alfred
Sturtevant. Morgan asked Sturtevant to make some sense of the data
on crossing-over between different linked genes.
In one night, Sturtevant developed a method for describing relations
between genes that is still used today.

In Sturtevant's own words, "In the latter part of 1911, in conversation with
Morgan, I suddenly realized that the variations in strength of linkage, already
attributed by Morgan to differences in the spatial separation of genes, offered the
possibility of determining sequences in the linear dimension of a chromosome. I
went home and spent most of the night (to the neglect of my undergraduate
homework) in producing the first chromosome map."
Genetica per Scienze Naturali
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Sturtevant approach
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Imagine two specific genes positioned a certain fixed distance apart, and imagine
random crossing-over along the paired homologs.
Sturtevant postulated a rough proportionality: the greater the distance between the
linked genes, the greater the chance that nonsister chromatids would cross over in
the region between the genes and, hence, the greater the proportion of recombinants
that would be produced.
Thus, by determining the frequency of recombinants, we can obtain a measure of the
map distance between the genes.
Proportionality between chromosome
distance and recombinant frequency. In
every meiosis, chromatids cross over at
random along the chromosome. The two
genes T and U are farther apart on a
chromosome than V and W. Chromatids
cross over between T and U in a larger
proportion of meioses than between V and
W, so the recombinant frequency for T and
U is higher than that for V and W.
Genetica per Scienze Naturali
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The genetic map unit
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In fact, we can define one genetic map unit (m.u.) as that distance between genes for
which one product of meiosis in 100 is recombinant. Put another way, a
recombinant frequency (RF) of 0.01 (1 percent) is defined as 1 m.u
A map unit is today referred to as a centimorgan (cM) in honor of Morgan
A direct consequence of the way in which map distance is measured is that, if 5 map
units (5 cM) separate genes A and B whereas 3 m.u. separate genes A and C, then B
and C should be either 8 or 2 cM apart.
Sturtevant found this to be the case. In other words, his analysis strongly suggested
that genes are arranged in some linear order.
Because map distances are
roughly additive, calculation of
the A-B and A-C distances leaves
us with the two possibilities
shown for the B-C distance. Of
course, these two possibilities
can be discriminated by
examining the actual
recombination frequency
between B and C.
Genetica per Scienze Naturali
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Linkage groups
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The map obtained by recombination frequency analysis does not place the gene loci
at specific places on the chromosome; it simply allows us to determine the positions
of genes relative to one another (linkage groups). The small cluster of three genes
could in theory be anywhere on the actual chromosome. However, as more and more
recombination analyses are done with many more genes, the entire chromosome
becomes "fleshed out." After the genes close to each chromosome end are placed in
the map, and gene positions are determined by other techniques, can absolute
chromosome position be assigned.
Genetic analysis works in two directions. In the case of linkage analysis, we have
seen that by using RF measurements we can draw a genetic map; however, working
in the other direction, if we have the map we can predict frequencies of progeny in
different genotypic classes.

For example, if we know that the Drosophila autosomal genes Pr/pr and Vg/vg are linked
on the same chromosome 11 m.u. apart, and if we testcross a trans dihybrid Pr vg/pr Vg
to pr vg/pr vg, we can predict that there will be 11 percent recombinants. Furthermore,
there should be 5.5 percent each of Pr Vg/pr vg and pr vg/pr vg because the two
recombinant types are reciprocal products of the same type of crossover event. The
remaining 89 percent will be nonrecombinant, 44.5 percent each of Pr vg/pr vg and pr
Vg/pr vg.
Genetica per Scienze Naturali
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An example of linkage map

A genetic map of the Drosophila genome, showing how each linkage group
corresponds to one chromosome pair. Values are given in map units (cM) measured
from the gene closest to one end.
 Larger values are
calculated as sums of
shorter intervals because
the recombinant frequency
for any two loci cannot
exceed 50 percent.
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