Question

In a plant, a tall variety was crossed with a dwarf variety. All \(\mathrm{F}_{1}\) plants were tall. When \(\mathrm{F}_{1} \times \mathrm{F}_{1}\) plants were interbred, \(9 / 16\) of the \(\mathrm{F}_{2}\) were tall and \(7 / 16\) were dwarf. (a) Explain the inheritance of height by indicating the number of gene pairs involved and by designating which genotypes yield tall and which yield dwarf. (Use dashes where appropriate.) (b) What proportion of the \(F_{2}\) plants will be true breeding if self- fertilized? List these genotypes.

Short answer

Answer: There are two gene pairs involved in the inheritance of height. The genotypes that yield tall plants are T-T-, T-tt, and ttT-, while the dwarf plants have the genotype tttt. The proportion of F2 plants that will be true-breeding when self-fertilized is 1/8. The true-breeding genotypes in the F2 generation are T-T- (tall) and tttt (dwarf).

Step-by-step solution

(Step 1: Determine the genotype of the F1 generation)

As the problem states that all F1 plants are tall, we can represent the dominant allele (tall) with the letter T and the recessive allele (dwarf) with the letter t. Since all F1 plants are tall, their genotype must be heterozygous for the trait (Tt).

(Step 2: Analyze the F2 generation ratios)

The given ratio is \(9/16\) tall and \(7/16\) dwarf. This ratio indicates that there are two gene pairs involved in the inheritance of height, and we can deduce that plant height exhibits a dihybrid inheritance pattern (9:3:3:1 ratio).

(Step 3: Deduce genotypes that correspond to phenotypes)

Based on the dihybrid inheritance pattern, we know the genotypes that yield tall plants are T-T-, (9 tall plants), T-tt (3 tall plants), and ttT- (3 tall plants). The dwarf plants have the genotype tttt (1 dwarf plant).

(Step 4: Calculate proportions of true-breeding plants in F2 generation)

True-breeding plants must have homozygous genotypes for both gene pairs. From our analysis in Step 3, there are two true-breeding plants out of the 16: T-T- (tall) and tttt (dwarf). The proportion of true-breeding plants in the F2 generation is thus \(2/16 = 1/8\).

(Step 5: List true-breeding genotypes)

The true-breeding genotypes in the F2 generation are T-T- (tall) and tttt (dwarf).

Key concepts

Genetics

Genetics is the study of how traits are passed from parents to offspring through genes. Each organism has its own set of genetic instructions, which are composed of DNA. These instructions are divided into units called genes, which are responsible for the various characteristics or traits seen in an organism, like the color of a flower or the height of a plant.

In a classical genetics framework, genes exist in different forms called alleles. For instance, a gene that determines plant height might have two alleles: one for tall plants and one for dwarf plants. The combination of alleles that an individual carries defines its genotype, which in turn affects its phenotype—the observable traits.

Mendelian Inheritance

Mendelian inheritance refers to the patterns of inheritance that are characteristic of organisms that reproduce sexually. It was first described by Gregor Mendel in the 19th century, through his experiments on pea plants. Mendel identified that traits are inherited as discrete units (genes), and these units are passed on from generation to generation in predictable ratios.

A key concept in Mendelian inheritance is the distinction between dominant and recessive alleles. Dominant alleles are expressed even if only one copy is present (heterozygous condition), whereas recessive alleles are expressed only when both copies are present (homozygous condition). Mendel's Law of Segregation states that during the formation of gametes (sperm or eggs), the two alleles for a gene separate from each other so that each gamete carries only one allele for each gene.

Phenotypic Ratios

Phenotypic ratios are the relative numbers of organisms showing a particular trait or combination of traits in a cross. These ratios are a representation of the underlying genetic makeup or genotype of the organisms. In a dihybrid cross, which involves two gene pairs, the expected phenotypic ratio if both genes are assorting independently according to Mendelian principles is 9:3:3:1.

This means that in a large number of offspring, 9 would show both dominant traits, 3 would show the dominant trait for the first gene and the recessive trait for the second, another 3 would show the recessive trait for the first gene and the dominant trait for the second, and 1 would show both recessive traits. This ratio arises from the combination of two independent monohybrid crosses (each with a 3:1 phenotypic ratio). Understanding these ratios is crucial for predicting the outcome of genetic crosses and for understanding how traits are inherited.

True-breeding Genotypes

True-breeding genotypes are those that, when self-fertilized or mated with another of the same genotype, produce offspring that are uniform and identical to the parent for the trait in question. For organisms to be considered true-breeding, they must have a homozygous genotype for the trait(s), meaning they carry two of the same allele, either dominant (such as TT) or recessive (such as tt).

The significance of true-breeding genotypes lies in their predictability: they are essential for establishing stable traits within a population and serve as a foundation for studying inheritance patterns. In the context of a dihybrid cross resulting in the F2 generation, the proportion of true-breeding individuals can be determined by identifying homozygous genotypes for both traits investigated.