Question

How many different types of gametes can be formed by individuals of the following genotypes: (a) \(A a B b\) (b) \(A a B B\) (c) \(A a B b C c\) (d) \(A a B B c c\) (e) \(A a B b c c,\) and (f) \(A a B b C c D d E e ?\) What are the gametes in each case?

Short answer

Question: For each of the following genotypes, determine the number of different types of gametes that can be formed. (a) AaBb, (b) AaBB, (c) AaBbCc, (d) AaBBcc, (e) AaBbcc, (f) AaBbCcDdEe. Answer: (a) 4, (b) 2, (c) 8, (d) 4, (e) 4, (f) 32.

Step-by-step solution

(a) Genotype: \(A a B b\)

There are two alleles for each gene, A and a, and B and b. Each gamete will have one allele for each gene. The possible combinations for each gene are: - \(A\): and \(a\) - \(B\): and \(b\) By applying the principle of independent assortment, the different types of gametes formed can be calculated: 2 (possible alleles for A) x 2 (possible alleles for B) = 4 The gametes formed are: \(Ab\), \(aB\), \(AB\), and \(ab\).

(b) Genotype: \(A a B B\)

The possible combinations for each gene are: - \(A\): and \(a\) - \(B\): (only one allele B) By applying the principle of independent assortment, the different types of gametes formed can be calculated: 2 (possible alleles for A) x 1 (possible allele for B) = 2 The gametes formed are: \(AB\) and \(aB\).

(c) Genotype: \(A a B b C c\)

The possible combinations for each gene are: - \(A\): and \(a\) - \(B\): and \(b\) - \(C\): and \(c\) By applying the principle of independent assortment, the different types of gametes formed can be calculated: 2 x 2 x 2 = 8 The gametes formed are: \(ABC\), \(ABc\), \(AbC\), \(Abc\), \(aBC\), \(aBc\), \(abC\), and \(abc\).

(d) Genotype: \(A a B B c c\)

The possible combinations for each gene are: - \(A\): and \(a\) - \(B\): (only one allele B) - \(C\): and \(c\) By applying the principle of independent assortment, the different types of gametes formed can be calculated: 2 x 1 x 2 = 4 The gametes formed are: \(ABc\), \(Abc\), \(aBc\), and \(abc\).

(e) Genotype: \(A a B b c c\)

The possible combinations for each gene are: - \(A\): and \(a\) - \(B\): and \(b\) - \(C\): (only one allele c) By applying the principle of independent assortment, the different types of gametes formed can be calculated: 2 x 2 x 1 = 4 The gametes formed are: \(Abc\), \(aBc\), \(ABc\), and \(abC\).

(f) Genotype: \(A a B b C c D d E e\)

The possible combinations for each gene are: - \(A\): and \(a\) - \(B\): and \(b\) - \(C\): and \(c\) - \(D\): and \(d\) - \(E\): and \(e\) By applying the principle of independent assortment, the different types of gametes formed can be calculated: 2 x 2 x 2 x 2 x 2 = 32 In this case, there will be 32 different types of gametes formed. We could enumerate them all, but it's not necessary for this exercise.

Key concepts

Independent Assortment

The principle of independent assortment is a key concept in understanding how genetic diversity arises through sexual reproduction. It describes how alleles, which are different versions of a gene, segregate independently from each other during the formation of gametes. This means that the allele a parent passes on for one gene does not affect the allele passed on for another gene.

For example, consider a plant with a genotype of AaBb, which has two genes, one with alleles A and a, and another with alleles B and b. The principle of independent assortment states that the allele inherited for the A gene (either A or a) does not influence the inheritance of the allele for the B gene. The result is a combination of gametes where all possible combinations of alleles are equally likely, leading to four gamete types: Ab, aB, AB, and ab.

This concept, discovered by Gregor Mendel in the 19th century, reveals that the gametes (sperm or eggs) produced by an organism contain a random mix of the parent's chromosomes, thereby contributing to genetic variation in offspring. This randomness is due to the way chromosomes line up independently before separating during meiosis, a type of cell division specific to gamete formation.

Genotype to Gamete Calculation

When predicting the types of gametes an organism can produce, we must understand how the genotype leads to different potential gametes. The genotype represents an organism's genetic makeup for a particular set of genes, with alleles (variant forms of a gene) denoted by letters such as A and a. To calculate the possible gametes, tally the number of alleles for each gene and then use the multiplication rule from probability theory.

Let's illustrate this with a simple genotype, AaBb. For each gene, there are two possible alleles that can be passed on to the gametes. Applying the multiplication rule, we take the number of possibilities for the first gene (2) and multiply by the possibilities for the second gene, also (2). Therefore, for this genotype, there are 2x2=4 possible types of gametes. This method can be extended to more complex genotypes with multiple genes, such as AaBbCcDdEe, by multiplying the number of possibilities for each gene: 2x2x2x2x2, resulting in 32 possible gametes.

Mendelian Genetics

Mendelian genetics is the foundation of classical genetics and offers a simple way of understanding how traits are inherited. The core principles put forward by Gregor Mendel, based on his work with pea plants, include the law of segregation and the law of independent assortment.

The law of segregation states that every individual has two alleles for each gene, and these alleles separate during gamete formation, ensuring that each gamete carries only one allele for a gene. Due to the independent assortment, each allele pairs independently or randomly, which leads to the formation of gametes with all possible combinations of alleles.

Illustrative Example

For instance, if we take the genotype AaBbCc, where each pair of letters represents different genes with two alleles, Mendelian genetics helps us predict that allele A will separate from allele a, and each will independently assort with B or b, and C or c. This ultimately results in a diversity of gametes, each with a unique combination of alleles. These fundamental principles explain how genetic traits are transferred from parents to offspring, highlighting the probabilistic nature of inheritance and the variety seen within species.