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. Step 1: Understand the genetic system described in the problem. The kernel color is determined by three additive genes (G, M, and T), each with two alleles. The phenotypic effects of the genotypes for each gene are additive, and the total color units are calculated by summing the contributions from all three genes.
2. Step 2: Recognize the threshold system. In this model, kernels require nine or more units of color to appear colored. Kernels with eight or fewer units of color will appear white. This threshold system changes the interpretation of the phenotypic effects.
3. Step 3: Determine the possible genotypes and their corresponding phenotypic effects for each gene. For example, G₁G₁ contributes 6 units, G₁G₂ contributes 3 units, and G₂G₂ contributes 1 unit. Similarly, calculate the contributions for M and T genes. Combine these contributions to find the total color units for each genotype combination.
4. Step 4: Perform a trihybrid cross (G₁G₂M₁M₂T₁T₂ × G₁G₂M₁M₂T₁T₂) and use a Punnett square to determine the genotypic combinations of the F₂ progeny. For each combination, calculate the total color units by summing the contributions from the G, M, and T genes.
5. Step 5: Identify the proportion of F₂ progeny with total color units less than or equal to 8 (white kernels). Count the number of genotypic combinations that result in white kernels and divide by the total number of progeny to find the proportion. This step involves analyzing the Punnett square and applying the threshold model.

Key Concepts

Polygenic Inheritance

Polygenic inheritance refers to the control of a trait by multiple genes, each contributing to the phenotype in an additive manner. In this case, three genes (G, M, and T) influence kernel color, with each gene having two alleles that contribute different amounts of color. The cumulative effect of these genes results in a continuous range of phenotypes, rather than discrete categories.

Threshold Trait

A threshold trait is a type of genetic trait where a certain level of phenotypic expression must be reached for the trait to be visibly expressed. In this scenario, kernel color only appears if the total color units from the contributing genes reach nine or more. If the total is below this threshold, the kernels will not show color and will appear white, illustrating how environmental and genetic factors can interact in trait expression.

F₂ Generation and Progeny Ratios

The F₂ generation is the second filial generation resulting from a cross between two F₁ individuals. In a trihybrid cross involving multiple genes, the expected phenotypic ratios can be calculated using the principles of Mendelian genetics. Understanding how to derive these ratios is essential for predicting the proportion of offspring that will exhibit a specific phenotype, such as the proportion of white kernels in this threshold model.