An inbred strain of plants has a mean height of 24 cm. A second strain of the same species from a different geographic region also has a mean height of 24 cm. When plants from the two strains are crossed together, the F₁ plants are the same height as the parent plants. However, the F₂ generation shows a wide range of heights; the majority are like the P₁ and F₁ plants, but approximately 4 of 1000 are only 12 cm high and about 4 of 1000 are 36 cm high.

How many gene pairs are involved?

Verified step by step guidance

1. Identify the phenotypic extremes in the F₂ generation, which are 12 cm and 36 cm.
2. Recognize that the parental and F₁ generation plants have a mean height of 24 cm, indicating that the trait is likely controlled by multiple genes with additive effects.
3. Use the formula for polygenic inheritance: \( (1/4)^n = \text{frequency of extreme phenotypes} \), where \( n \) is the number of gene pairs.
4. Given that approximately 4 out of 1000 plants are at the extreme phenotypes, calculate the frequency: \( 4/1000 = 0.004 \).
5. Solve for \( n \) in the equation \( (1/4)^n = 0.004 \) to determine the number of gene pairs involved.

Key Concepts

Inbreeding and Genetic Variation

Inbreeding refers to the mating of closely related individuals, which can lead to a reduction in genetic diversity. In the context of the question, the inbred strains of plants have similar mean heights due to limited genetic variation. However, crossing these strains can reveal hidden genetic diversity in the offspring, particularly in the F₂ generation, where a wider range of phenotypes is observed.

Phenotypic Ratios and Polygenic Inheritance

Polygenic inheritance involves multiple gene pairs contributing to a single trait, resulting in a continuous range of phenotypes. The F₂ generation's height variation suggests that several gene pairs influence plant height, leading to a phenotypic ratio that can be analyzed to estimate the number of genes involved. The presence of extreme heights (12 cm and 36 cm) indicates that multiple alleles are interacting.

Quantitative Trait Loci (QTL)

Quantitative Trait Loci (QTL) are specific regions of the genome that correlate with variation in a quantitative trait, such as plant height. The wide range of heights in the F₂ generation suggests that multiple QTLs are involved, each contributing to the overall phenotype. By analyzing the distribution of heights, one can infer the number of gene pairs affecting the trait, which in this case can be estimated based on the observed phenotypic extremes.