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.
Two trihybrid plants are mated. What is the expected proportion of progeny plants displaying 9 units of color? Explain your answer.

Verified step by step guidance

1. Step 1: Understand the problem. This is a polygenic inheritance problem involving three additive genes (G, M, and T), each with two alleles. The phenotypic effects of the genotypes for each gene are additive, meaning the total color units are the sum of contributions from all three genes. The goal is to determine the proportion of progeny plants displaying 9 units of color when two trihybrid plants are mated.
2. Step 2: Determine the possible genotypes for each gene. Each gene (G, M, T) has three possible genotypes: homozygous dominant (e.g., G₁G₁), heterozygous (e.g., G₁G₂), and homozygous recessive (e.g., G₂G₂). The phenotypic contributions for each genotype are given as follows: G₁G₁ = 6 units, G₁G₂ = 3 units, G₂G₂ = 1 unit. The same applies to M and T genes.
3. Step 3: Calculate the combinations of genotypes that result in 9 units of color. Since the phenotypic effects are additive, we need to find all combinations of genotypes across the three genes (G, M, T) that sum to 9 units. For example, one combination could be G₁G₂ (3 units), M₁M₂ (3 units), and T₁T₂ (3 units). Repeat this process for all possible combinations.
4. Step 4: Determine the probability of each genotype combination. For each gene, the trihybrid parents (G₁G₂M₁M₂T₁T₂) produce gametes with equal probabilities for each allele (e.g., 1/2 for G₁ and 1/2 for G₂). Use the Punnett square to calculate the probabilities of each genotype for G, M, and T. Multiply these probabilities to find the overall probability of each genotype combination that results in 9 units of color.
5. Step 5: Sum the probabilities of all genotype combinations that result in 9 units of color. Add the probabilities calculated in Step 4 for all combinations that produce 9 units of color. This sum represents the expected proportion of progeny plants displaying 9 units of color.

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, the color of the grain kernels is influenced by three additive genes (G, M, and T), each with two alleles. The cumulative effect of these genes leads to various phenotypic expressions, making it essential to understand how these genes interact to predict the outcome of crosses.

Additive Gene Effects

Additive gene effects occur when the contributions of different alleles combine to produce a phenotype. For example, in the G gene, the genotypes G₁G₁, G₁G₂, and G₂G₂ contribute 6, 3, and 1 unit of color, respectively. This additive nature allows for the calculation of total phenotypic values based on the combination of alleles from both parents, which is crucial for determining the expected color in progeny.

Punnett Square and Progeny Ratios

A Punnett square is a tool used to predict the genetic makeup of offspring from a cross between two parents. By analyzing the combinations of alleles from the parents, one can determine the expected ratios of different phenotypes in the progeny. In this scenario, calculating the expected proportion of progeny displaying 9 units of color involves identifying the specific allele combinations that yield this phenotype and their respective probabilities.