Independent Assortment of Genes

Let us now consider two genes, located on different chromosomes, and see how these genes behave in a cross. This situation is a bit more complex than crosses involving a single gene existing in two forms, as we studied in chapters 2 and 3. To illustrate what happens, let us use traits that we mentioned already.

For example, let us see what genotypes of offspring a man heterozygous for sickle-cell anemia, who is also carrier of the galac-tosemia gene, can have with a woman who is also heterozygous for sickle-cell anemia and a carrier for galactosemia. Remember that both conditions are recessive so both parents are phenotypically normal. Let us call B the normal P-hemoglobin gene, and b its sickle cell counterpart. Further, let us use g for the galactosemia gene and G for the normal gene. The genotypes of both parents are thus BbGg. They will not show any sign of disease since they are heterozygous for both traits. We learned in chapter 2 that single sets of chromosomes are present in gametes. It is also known that the genes for sickle-cell anemia and galactosemia are located on different chromosomes. What kinds of gametes will these parents produce?

Each gamete has one set of chromosomes. So each gamete will have one copy of the hemoglobin gene and one copy of the "galactosemia gene," either in its normal or abnormal form. Thus we can observe gametes with the gene combinations: BG, Bg, bG, and bg. These genes follow the third law of genetics, the law of independent assortment. This law states that genes located on different chromosomes assort independently. In other words, the B gene does not preferentially associate

Figure 9.1 Independent Assortment of Two Pairs of Genes. The sixteen possible gene combinations observed in a cross involving two different pairs of genes located on separate chromosomes. A. The genotypes of the parents are shown with the genes located on separate chromosomes. Only the two pairs of chromosomes are shown for simplicity. B. The gene combinations of gametes are shown. C. A Punnett square shows all sixteen possible gene combinations of the cross.

Figure 9.1 Independent Assortment of Two Pairs of Genes. The sixteen possible gene combinations observed in a cross involving two different pairs of genes located on separate chromosomes. A. The genotypes of the parents are shown with the genes located on separate chromosomes. Only the two pairs of chromosomes are shown for simplicity. B. The gene combinations of gametes are shown. C. A Punnett square shows all sixteen possible gene combinations of the cross.

with the G gene. Rather, B can just as easily associate with g as G. In our example, the mother and the father will produce gametes having the same four chromosomal compositions; this is because they are both heterozygous for both traits. We can now build a Punnett square to see what kinds of offspring these two parents can have. In this case, since we have four possible gametes for each parent, the Punnett square will contain sixteen boxes. Remember that if only two contrasting genes are considered, the Punnett square contains only four boxes. Figure 9.1 shows that when two pairs of contrasting genes are studied, the situation becomes more complicated. Note that some gene combinations (genotypes) are represented more than once in this Punnett square. By careful counting, we see that nine different genotypes are possible (see table 9.1). Then, taking into account that B is dominant over b and that G is dominant over g, we can calculate the probability

Table 9.1 All Possible Genotype Combinations Produced by Parents with Genotype BbGg

Genotype

Number

Phenotype

Total Number of Different Phenotypes

BBGG

1

normal

BBGg

2

normal

BbGG

2

normal

BbGg

4

normal

total normal = 9

Bbgg

2

galactosemic

BBgg

1

galactosemic

total galactosemic = 3

bbGG

1

sickle cell

bbGg

2

sickle cell

total sickle cell = 3

bbgg

1

sickle cell & galactosemic

total both = 1

of individuals with various phenotypes. The individuals who are BBGG, BBGg, BbGG and BbGg will have the same phenotype: no symptoms of sickle-cell anemia and no symptoms of galactosemia. Next, the individuals who are BBgg and Bbgg will show no signs of sickle-cell anemia, but will be galactosemic. Then, those who are bbGG and bbGg will have sickle-cell anemia, but no galactosemia. Finally, the individuals with the bbgg genotype will unfortunately suffer from both diseases. Thus, crosses involving two pairs of contrasting genes produce nine different genotypic categories and four different phenotypic categories.

By carefully counting the boxes in the Punnett square that contain different genotypes, we realize that the four phenotypic categories come in a 9:3:3:1 ratio. Nine out of sixteen boxes (-56 percent) represent the probability of being phenotypically normal for both traits. Three out of sixteen boxes (-19 percent) fall in the category where the first phenotype is normal (no sickle-cell anemia) but the other is not (galactosemia is present). Next, three out of sixteen boxes (-19 percent) represent the probability for an offspring to have sickle-cell anemia but not galactosemia. Finally, there is a 1 in 16 probability (-6 percent) that double heterozygous parents will have an offspring with both sickle-cell anemia and galactosemia.

This is different from a cross involving single genes (existing in two forms), where only three possible genotypes and two phenotypic categories are observed (see chapter 2). There, remember that the phenotypic ratio is 3:1. As you can well imagine, things get even more complicated if three pairs of genes are considered. In this case, the

Punnett square contains sixty-four boxes, and there are eight possible phenotypic classes. In the human case, forty-six chromosomes (twenty-three pairs) segregate and assort independently during meiosis. This means that 223 possible phenotypic classes are potentially generated from each offspring, simply from the independent assortment of chromosomes into the gametes! You can now understand why each human is unique. Identical twins are an exception to this rule because they originate from the splitting of a single fertilized egg. For an example of independent assortment, see the "Try This at Home" at the end of this chapter.

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