Suppose a polygenic system for producing color in kernels of a grain is controlled by three additive genes, G, M, and T. There are two alleles of each gene, G₁ and G₂, M₁, and M₂, and T₁ and T₂. The phenotypic effects of the three genotypes of the G gene are G₁G₁ = 6 units of color, G₁G₂ = 3 units of color, and G₂G₂ = 1 unit of color. The phenotypic effects for genes M and T are similar, giving the phenotype of a plant with the genotype G₁G₁M₁M₁T₁T₁ a total of 18 units of color and a plant with the genotype G₂G₂M₂M₂T₂T₂ a total of 3 units of color. Suppose that instead of an additive genetic system, kernel-color determination in this organism is a threshold system. The appearance of color in kernels requires nine or more units of color; otherwise, kernels have no color and appear white. In other words, plants whose phenotypes contain eight or fewer units of color are white. Based on the threshold model, what proportion of the F₂ progeny produced by the trihybrid cross in part (b) will be white? Explain your answer.

Verified step by step guidance

1. Identify the genotypes for each gene (G, M, T) and their corresponding phenotypic color units: G₁G₁ = 6, G₁G₂ = 3, G₂G₂ = 1; similarly for M and T.
2. Calculate the total color units for each possible genotype combination in the F₂ generation by adding the units from G, M, and T.
3. Determine which genotype combinations result in a total of 8 or fewer color units, as these will be white according to the threshold model.
4. Calculate the probability of each genotype combination occurring in the F₂ generation using Mendelian inheritance ratios (e.g., 1:2:1 for each gene).
5. Sum the probabilities of all genotype combinations that result in 8 or fewer color units to find the proportion of white kernels in the F₂ progeny.

Key Concepts

Polygenic Inheritance

Polygenic inheritance refers to the phenomenon where multiple genes contribute to a single trait, resulting in a continuous range of phenotypes. In this case, three additive genes (G, M, and T) influence kernel color, with each gene having two alleles that contribute varying amounts to the overall phenotype. Understanding this concept is crucial for analyzing how different combinations of alleles can lead to diverse color outcomes in the progeny.

Additive Effects of Alleles

Additive effects occur when the contributions of different alleles combine to produce a cumulative effect on the phenotype. For example, in the given scenario, the G gene has specific phenotypic values associated with its genotypes, which add up with the contributions from the M and T genes. This concept is essential for calculating the total units of color produced by various genotypes and determining which combinations meet the threshold for color expression.

Threshold Trait

A threshold trait is a type of trait where a certain level of genetic contribution must be reached before a specific phenotype is expressed. In this case, a kernel must accumulate at least nine units of color to appear colored; otherwise, it appears white. Understanding this concept helps in predicting the proportion of progeny that will exhibit the white phenotype based on the genetic combinations derived from the trihybrid cross.