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.
Indicate three possible genotypes that could account for F₂ plants that are 18 cm high and three that account for F₂ plants that are 33 cm high.

Verified step by step guidance

1. Step 1: Understand the genetic context. The problem involves two inbred strains with the same mean height (24 cm), their F₁ offspring also have 24 cm height, and the F₂ generation shows variation including extreme heights (12 cm and 36 cm). This suggests that height is controlled by multiple genes (polygenic inheritance) with additive effects.
2. Step 2: Define the genetic model. Assume that each gene contributes additively to the height. For example, each gene has two alleles: a 'plus' allele (+) that adds a certain amount to height and a 'minus' allele (-) that adds less or subtracts. The parental strains are homozygous but differ in alleles, so crossing them produces heterozygous F₁ with intermediate height.
3. Step 3: Determine the genotypes for extreme phenotypes. The shortest plants (12 cm) likely have all 'minus' alleles (e.g., all --), and the tallest plants (36 cm) have all 'plus' alleles (e.g., all ++). The F₁ plants are heterozygous at all loci (e.g., all +-), resulting in the intermediate height (24 cm).
4. Step 4: Calculate intermediate heights (18 cm and 33 cm). Since height is additive, plants with genotypes having fewer 'plus' alleles than F₁ but more than the shortest will have intermediate heights. For 18 cm, identify genotypes with one fewer 'plus' allele than F₁; for 33 cm, genotypes with one more 'plus' allele than F₁ but fewer than the tallest.
5. Step 5: List three possible genotypes for each intermediate height. For 18 cm, genotypes could be those with one locus homozygous 'minus' and others heterozygous (e.g., -- + - + -), or heterozygous at all loci except one homozygous 'minus'. For 33 cm, genotypes could be those with one locus homozygous 'plus' and others heterozygous (e.g., ++ + - + -), or heterozygous at all loci except one homozygous 'plus'.

Key Concepts

Quantitative Trait Inheritance

Quantitative traits, like plant height, are controlled by multiple genes (polygenes) and show continuous variation. The F₂ generation often displays a range of phenotypes due to the combination of alleles from both parents, resulting in intermediate and extreme trait values.

Genotype-Phenotype Relationship in Polygenic Traits

In polygenic inheritance, each gene contributes additively to the phenotype. Different combinations of alleles produce a spectrum of phenotypes, where specific genotypes correspond to particular trait values, such as intermediate or extreme heights in the F₂ plants.

Segregation and Recombination in F₂ Generation

During the formation of the F₂ generation, alleles segregate and recombine independently, creating new genotype combinations. This leads to phenotypic variation, including rare extreme phenotypes and intermediate heights, reflecting the underlying genetic diversity.