Question

What are the possible gametes that can be formed from the following genotypes, assuming all the gene pairs segregate independently? What are the gamete frequencies? (a) \(\mathrm{A} \mathrm{aBBCc}\) (b) DdEEffGg (c) \(\mathrm{MmNnOo}\)

Short answer

For the given genotypes: (a) AaBBCc Possible gametes: ABC, ABc, aBC, aBc Gamete frequencies: \(1/4\) for each gamete. (b) DdEEffGg Possible gametes: DEFg, DEF, dEfG, dEf Gamete frequencies: \(1/4\) for each gamete. (c) MmNnOo Possible gametes: MNO, MNo, MnO, Mno, mNO, mNo, mnO, mno Gamete frequencies: \(1/8\) for each gamete.

Step-by-step solution

Determine possible alleles for each gene pair:

The first gene pair is \(\mathrm{Aa}\) with alleles \(\mathrm{A}\) and \(\mathrm{a}\), the second one is \(\mathrm{BB}\) with only one allele \(\mathrm{B}\) being possible (since it's homozygous) and finally, \(\mathrm{Cc}\) with alleles \(\mathrm{C}\) and \(\mathrm{c}\).

Create possible gamete combinations:

By combining the possible alleles, we get the following gametes: \(\mathrm{ABC}\), \(\mathrm{ABc}\), \(\mathrm{aBC}\), and \(\mathrm{aBc}\).

Calculating gamete frequencies:

All the four gametes have an equal probability of forming, so the frequencies are: \(\frac{1}{4}\) for \(\mathrm{ABC}\), \(\frac{1}{4}\) for \(\mathrm{ABc}\), \(\frac{1}{4}\) for \(\mathrm{aBC}\), and \(\frac{1}{4}\) for \(\mathrm{aBc}\). #b) DdEEffGg

Determine possible alleles for each gene pair:

The gene pairs are \(\mathrm{Dd}\) with alleles \(\mathrm{D}\) and \(\mathrm{d}\), \(\mathrm{EE}\) with only one possible allele \(\mathrm{E}\), \(\mathrm{ff}\) with the only possible allele \(\mathrm{f}\), and \(\mathrm{Gg}\) with alleles \(\mathrm{G}\) and \(\mathrm{g}\).

Create possible gamete combinations:

By combining the possible alleles, we get the following gametes: \(\mathrm{DEFg}\), \(\mathrm{DEF}\), \(\mathrm{dEfG}\), and \(\mathrm{dEf}\).

Calculating gamete frequencies:

All the four gametes have an equal probability of forming, so the frequencies are: \(\frac{1}{4}\) for \(\mathrm{DEFg}\), \(\frac{1}{4}\) for \(\mathrm{DEF}\), \(\frac{1}{4}\) for \(\mathrm{dEfG}\), and \(\frac{1}{4}\) for \(\mathrm{dEf}\). #c) \(\mathrm{MmNnOo}\)

Determine possible alleles for each gene pair:

The gene pairs are \(\mathrm{Mm}\) with alleles \(\mathrm{M}\) and \(\mathrm{m}\), \(\mathrm{Nn}\) with alleles \(\mathrm{N}\) and \(\mathrm{n}\), and \(\mathrm{Oo}\) with alleles \(\mathrm{O}\) and \(\mathrm{o}\).

Create possible gamete combinations:

By combining the possible alleles, we get the following gametes: \(\mathrm{MNO}\), \(\mathrm{MNo}\), \(\mathrm{MnO}\), \(\mathrm{Mno}\), \(\mathrm{mNO}\), \(\mathrm{mNo}\), \(\mathrm{mnO}\), and \(\mathrm{mno}\).

Calculating gamete frequencies:

All the eight gametes have an equal probability of forming, so the frequencies are: \(\frac{1}{8}\) for each of the eight gametes (\(\mathrm{MNO}\), \(\mathrm{MNo}\), \(\mathrm{MnO}\), \(\mathrm{Mno}\), \(\mathrm{mNO}\), \(\mathrm{mNo}\), \(\mathrm{mnO}\), and \(\mathrm{mno}\)).

Key concepts

Genetic Segregation

Genetic segregation is a key concept in understanding how gametes are formed and how traits are passed from parents to offspring. This principle, first outlined by Gregor Mendel, describes how pairs of gene variants (alleles) are separated during the formation of reproductive cells (gametes), ensuring that each gamete receives only one allele from each pair.

In the given exercise example with genotype (a), we consider the Aa, BB, and Cc gene pairs. The alleles A and a segregate into separate gametes, as do C and c, while B is homozygous and therefore all gametes will have the B allele. The process of creating gametes is similar to shuffling a deck of cards: each card (allele) is distributed independently, giving rise to diverse combinations in the resulting gametes, such as ABC and aBc. This genetic mixture is the foundation of genetic diversity, an essential component of natural selection and evolution.

Alleles

Alleles are the different forms of a gene that determine distinct traits which can be passed from parents to their offspring. Each individual possesses two alleles for each gene, one inherited from each parent. These alleles can be either dominant or recessive; dominant alleles express their traits even when paired with a different allele, while recessive alleles only express traits when paired with another recessive allele.

In gamete formation, as seen in genotypes (b) and (c), alleles are sorted into gametes such that each gamete carries only one allele of a particular gene. For instance, in genotype (c) \(\mathrm{MmNnOo}\), the Mm pair has two different alleles, M (dominant) and m (recessive). During the formation of gametes, each gamete will receive either M or m, but not both, contributing to the genetic variation observed in the offspring.

Mendelian Inheritance

Mendelian inheritance refers to the patterns of inheritance that are characteristic of organisms with sexual reproduction. It encompasses laws derived from the work of Gregor Mendel in the 19th century. His experiments on pea plants established the principles that govern inheritance, such as the law of segregation and the law of independent assortment.

The law of segregation is illustrated in our problem, where different genotypes like \(\mathrm{AaBBCc}\) produce gametes that have one allele from each gene pair, embodying the concept that allele pairs separate or 'segregate' during gamete formation. Mendelian inheritance forms the basis of classical genetics and helps explain the distribution of heritable traits from parents to their offspring.

Gamete Frequency

Gamete frequency refers to the likelihood of the formation of specific gametes from a parent genotype. It is imperative in predicting the ratios of offspring genotypes. In a genotype with multiple heterozygous genes, each unique gamete has an equal chance of being formed when all genes assort independently, according to Mendel's law of independent assortment.

In the exercise solutions, as seen in all three genotypes (a), (b), and (c), each gamete combination has an equal frequency of formation because the alleles assort independently. For example, in genotype (c), there are eight possible gamete combinations (e.g., MNO, MNo, MnO, etc.), each with a frequency of \(1/8\), assuming there are no linkage or other genetic interactions that would alter these probabilities. Understanding gamete frequencies is essential for predicting the outcome of genetic crosses and the genetic makeup of future generations.