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Griffiths AJF, Gelbart WM, Miller JH, et al. Modern Genetic Analysis. New York: W. H. Freeman; 1999.

## Modern Genetic Analysis.

Show detailsFirst, because we will now begin analyzing two or more genes in crosses, we need to introduce
more symbolism. A useful symbolism widely used by geneticists to represent two genes on
different chromosomes is to show them separated by a semicolon. Two examples from diploids are
*A/a* ; *B/b* and
*m ^{+}*

*/m*;

*p*

^{+}*/p*. Two examples from haploids are

^{+}*leu*;

^{+}*ade*and

*fr*;

^{+}*trp*.

^{+}We can illustrate the process of independent assortment with a hypothetical example, say, in
mice, involving the allele pairs *A/a* and *B/b*. We will assume
these genes are on different pairs of homologous chromosomes, a short pair and a long pair.
First we will cross two pure lines to create a **dihybrid,** or double heterozygote, in
which to study recombination. The two lines we will cross are
*A / A* ; *B / B* and
*a / a* ; *b / b:*

The F_{1} can be of only one type, as follows:

Now we can use the law of equal segregation to predict the gametic genotypes produced by the
F_{1}, and their proportions. We know that 1/2 the gametes will be *A*
and 1/2 will be *a.* We also know that 1/2 of the gametes will be
*B* and 1/2 will be *b*. These two ratios must be multiplied to
determine the overall gametic genotypes. Why? Recall that the product law (Chapter 4) states that the probability of independent
events is the product of their individual probabilities, so since the two genes in question are
acting independently, it is appropriate to multiply the gametic probabilities. The expected
gametic frequencies of 1/2 are effectively probabilities of 1/2 (or 50 percent); therefore, the
gametic array can be shown graphically as follows:

Figure 5-2 on the following page shows how this ratio is produced at the level of chromosome movements at meiosis. Basically it is because there are two different but equally frequent ways the spindle fibers can attach to the centromeres:

The general principle is known as independent
assortment of allele pairs. This principle is based on the fact that the equal
segregation of one allele pair is *independent* of the equal segregation of the
other allele pair because they are on different chromosomes.

### MESSAGE

**Allele pairs on different chromosome pairs assort independently.**

Which of the gametes are recombinants? It is simply a matter of applying the definition of
recombination: compare the meiotic input genotypes with the meiotic output genotypes. The input
genotypes were the genotypes of the parental gametes that fused to form the F_{1}, and
we know they were *A* ; *B* and
*a* ; *b*. The output is the set of gametes produced by meiosis
in the F_{1}, as shown in Figure 5-2. The
genotypes *A* ; *B* and *a* ; *b*
are the same as the parental input, so these types are not recombinant. However, the gametic
genotypes *A* ; *b* and *a* ; *B*
are not the same as the input, so by definition they are recombinants. In summary

The total **recombinant frequency (RF)** is 1/4 + 1/4 = 1/2 = 50 percent. This 50
percent RF is always observed for genes on different chromosome pairs; in fact, in a situation
in which nothing is known about the location of two genes, observing an RF value of 50 percent
in the sex cells from a dihybrid meiocyte will immediately suggest that the genes are on
different chromosome pairs. However, loci that are very far apart on the same chromosome can
also show an RF value of 50 percent, so more experimentation is needed to be sure of the exact
situation.

The analysis will be exactly the same if instead of starting with two pure-breeding strains
*A/A* ; *B/B* and *a/a* ; *b/b*, we
start with *A/A* ; *b/b* and
*a/a* ; *B/B*. Here the parental gametes are
*A* ; *b* and *a* ; *B*, so the
F_{1} is *A/a* ; *B/b* as before, and because of the law
of segregation, there will be the same types of gametes in the same proportions:

Now the recombinants will be *A* ; *B* and
*a* ; *b*, but they will still be at a frequency of 50
percent.

### MESSAGE

**In a dihybrid**
**
A/a
**

**;**

*B/b***involving two genes on two different pairs of chromosomes, the recombinant frequency will always be 50 percent.**

So far we have not addressed the problem of how to identify the genotypes of the products of
meiosis issuing from a dihybrid meiocyte. In haploid organisms this is simple (as we saw in the
*Neurospora* example above) because the products are the sexual spores (such as
ascospores in fungi), and these can easily be grown up and genotypes assigned directly. However,
in a diploid organism such as an animal the gamete genotypes cannot be observed directly, so the
individual under investigation must be crossed, to test the gametes *indirectly*.
There are two types of crosses that can be used to measure recombination in a diploid, a
testcross and a self.

## Testcross of a Dihybrid

The best way to determine the genotypes of the gametes of a dihybrid diploid is to make a
cross to a tester, an individual that carries only
recessive alleles for the genes under investigation. Such a cross is called a testcross. A tester must be fully homozygous recessive,
for example *a/a* ; *b/b.* Since the gametes of the tester carry
only recessive alleles, the genotypes of the gametes of the dihybrid will be expressed in the
phenotypes of the testcross progeny. The general nature of the testcross is illustrated in
Figure 5-3 on the following page. If the genes are on
different chromosomes, independent assortment will produce a 1:1:1:1 ratio of gametes, which in
turn will produce a 1:1:1:1 phenotypic ratio in the progeny:

The chromosomal assortment that leads to this result is summarized in Figure 5-4.

In these examples we have illustrated independent assortment with genes
*known* to be on different chromosomes. However, the standard ratios such as
the 1:1:1:1 testcross progeny ratio can be used to *infer* that genes are
assorting independently. We can illustrate this with a cross used by Mendel. Recall from Chapter 4 that Mendel deduced that the two pea color
phenotypes yellow and green were determined by two alleles of one gene, *Y*
(yellow) and *y* (green). Through other analyses he knew that two pea shape
phenotypes, round and wrinkled, were determined by alleles of another gene, with
*R* determining round and *r* wrinkled. Since in this case we
don’t know if the two genes are on separate chromosomes or on the same chromosome, we must
devise a way of representing this uncertainty symbolically. There is no universally agreed-
upon convention for this situation, but in this book we will use a *period* or
*dot* to show this uncertainty. From his cross of a pure-breeding round, yellow
plant (*R/R*.*Y/Y*) with a pure-breeding wrinkled, green one
(*r/r*.*y/y*) Mendel obtained a dihybrid F_{1} that was
(as expected) round, yellow (*R/r*.*Y/y*). When these
F_{1} individuals were testcrossed to an *r/r*.*y/y*
tester, the following progeny were produced:

Mendel saw that these numbers were very close to a 1/4:1/4 :1/4:1/4 ratio, so he deduced that
the two pairs of al-leles were assorting independently, and we now know this is because they
are located on different chromosome pairs. We would now rewrite the genotype of the dihybrid as
*R/r* ; *Y/y*.

## Self of a Dihybrid

Sometimes a tester is not available; however, independent assortment can be demonstrated in a self of a dihybrid (or a cross of identical dihybrids). As an example we can use a dihybrid system from Gregor Mendel’s work. The cross was between two dihybrid parents

We know that if the genes are on different chromosome pairs, the gametes of both parents will be in the ratio

The fusion of the male and female gametes can be represented by a 4 × 4 grid as shown in Figure 5-5.

Each of the 16 squares in the grid represents 1/16 of the total progeny outcomes, so the overall phenotypic ratio in the progeny is

This 9:3:3:1 ratio is typical of selfed dihybrids showing independent assortment. In general the progeny ratio of a self of a dihybrid for genes on separate chromosomes can be written:

A photograph of a 9:3:3:1 phenotypic ratio in corn *(Zea mays)* is shown in
Figure 5-6.

## Calculating Phenotypic and Genotypic Ratios for Independently Assorting Genes

In Chapter 4 we calculated the phenotypic ratios expected from progeny of crosses involving alleles of single genes. For example

This knowledge makes it possible to predict genotypes and phenotypes involving several genes
*if* they are assorting independently. For example in the cross
*A / a* ; *b / b*
× *A / a* ; *B / b*, we might want to calculate the expected
phenotypic ratio in the progeny. We know the progeny ratio for the first gene will be
3/4* A /* –: 1/4* a / a*, and for the second it will be
1/2* B / b*: 1/2* b / b*. Therefore, if these genes assort
*independently,* we can combine the two phenotypic ratios randomly by drawing a
device called a **branch diagram.** In the branch diagram the progeny ratios are
derived simply by multiplying the proportions according to the product law, as shown
below:

The same progeny ratio could be derived using a grid, which also portrays random
associations. Note that the axes of this grid show *phenotypic proportions.*
(Grids are very useful in genetics and can be used in numerous ways.)

In a more complex cross, say,
*A/a* ; *B/b* ; *C/c* × *a/a* ; *B/b* ; *C/c,*
we might want to predict the proportion of some specific progeny genotype required for an
experiment, perhaps the genotype
*a/a* ; *b/b* ; *c/c* for use as a tester. Since
we know the genotypic proportions for individual genes will be

If the genes assort independently, we can use the product rule simply to multiply all the
proportions of the desired *single gene* genotypes (shown in bold) to obtain the
expected proportion (probability) of
*a/a* ; *b/b* ; *c/c*; it will be 1/2 × 1/4
× 1/4 = 1/32 . Therefore if we need this genotype, we would have to screen more than 32
progeny to stand a reasonable chance of obtaining one that is
*a/a* ; *b/b* ; *c/c*.

These simple calculations based on independence can be used to predict phenotypic, genotypic,
or gametic proportions in crosses *if* it is known or assumed that the genes are
assorting independently. However, as we saw in Chapter
4 and above, genetic analysis works in two directions, so we can also use specific
progeny proportions to make deductions about the genotypes and phenotypes of the parents, if
these are not known. For example, what could we deduce if we were to self some plant with the
normal wild-type phenotype of blue, large petals and observed the following numbers of
phenotypes in the progeny:

We would note that the progeny numbers represent a very close fit to a 9:3:3:1 ratio, so we could deduce that

- 1.
The parent must have been dihybrid for two genes affecting petal color and petal size.

- 2.
Blue petal is dominant to white, and large petal is dominant to small. We could invent allele symbols

*w*= blue and^{+}*w*= white, and*s*= large and^{+}*s*= small.- 3.
The two genes are assorting independently and are most likely on different chromosome pairs; the selfed plant must have been of genotype

*w*/^{+}*w*;*s*/^{+}*s*.

- Independent Assortment - Modern Genetic AnalysisIndependent Assortment - Modern Genetic Analysis

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