A dark-red strain and a white strain of wheat are crossed and produce an intermediate, medium-red F₁. When the F₁ plants are interbred, an F₂ generation is produced in a ratio of 1 dark-red: 4 medium-dark-red: 6 medium-red: 4 light-red: 1 white. Further crosses reveal that the dark-red and white F₂ plants are true breeding
How many additive alleles are needed to produce each possible phenotype?

Verified step by step guidance

1. Step 1: Understand the inheritance pattern described. The F₁ generation shows an intermediate phenotype (medium-red) between the two parent strains (dark-red and white), indicating incomplete dominance or additive gene action rather than simple dominance.
2. Step 2: Analyze the F₂ phenotypic ratio given: 1 dark-red : 4 medium-dark-red : 6 medium-red : 4 light-red : 1 white. Notice this ratio resembles the expansion of a binomial or multinomial expression, suggesting multiple alleles contribute additively to the phenotype.
3. Step 3: Recognize that the ratio 1:4:6:4:1 corresponds to the coefficients of the expansion of \((a + b)^4\), which implies there are 4 loci (or 4 additive alleles) involved, each contributing equally and additively to the color intensity.
4. Step 4: Assign the number of additive alleles to each phenotype based on the number of dominant alleles present. For example, the white phenotype has 0 dominant alleles, dark-red has 4 dominant alleles, and the intermediate phenotypes have 1, 2, or 3 dominant alleles respectively.
5. Step 5: Summarize that the number of additive alleles needed to produce each phenotype corresponds to the number of dominant alleles inherited, ranging from 0 (white) to 4 (dark-red), with intermediate phenotypes having intermediate numbers of dominant alleles.

Key Concepts

Incomplete Dominance and Additive Gene Action

Incomplete dominance occurs when heterozygotes show an intermediate phenotype between two homozygotes. In additive gene action, multiple alleles contribute quantitatively to the phenotype, with each allele adding a certain effect. This explains the intermediate colors seen in the wheat strains, where the phenotype depends on the cumulative effect of alleles.

Genotypic Ratios and Phenotypic Classes in F2 Generation

The F2 generation phenotypic ratio reflects the segregation and combination of alleles from the F1 hybrids. The given 1:4:6:4:1 ratio suggests multiple alleles or loci contributing additively, producing a range of phenotypes. Understanding how these ratios arise helps determine the number of additive alleles influencing the trait.

True Breeding and Homozygosity

True breeding plants produce offspring identical to themselves, indicating homozygosity for the trait alleles. The fact that dark-red and white F2 plants are true breeding means these phenotypes correspond to homozygous genotypes with either all additive alleles present or none, helping to define the allele contribution to each phenotype.