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. Assuming the threshold model applies to this kernel-color system, what proportion of the progeny of the cross G₁G₂M₁M₂T₂T₂xG₁G₂M₁M₂T₁T₂ do you expect to display colored kernels?
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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, and the total color is determined by summing the contributions of all three genes. The goal is to calculate the proportion of progeny that display colored kernels based on the threshold model.
Step 2: Determine the parental genotypes and their contributions. The parental genotypes are G₁G₂M₁M₂T₂T₂ and G₁G₂M₁M₂T₁T₂. Each parent contributes one allele for each gene to the progeny. The phenotypic contributions of the alleles are: G₁ = 3 units, G₂ = 1 unit, M₁ = 3 units, M₂ = 1 unit, T₁ = 3 units, and T₂ = 1 unit.
Step 3: Calculate the possible genotypes of the progeny. For each gene, the progeny can inherit one allele from each parent. For the G gene, the possible genotypes are G₁G₁, G₁G₂, and G₂G₂. For the M gene, the possible genotypes are M₁M₁, M₁M₂, and M₂M₂. For the T gene, the possible genotypes are T₁T₁, T₁T₂, and T₂T₂. Combine these to determine all possible genotypes of the progeny.
Step 4: Calculate the phenotypic contribution of each possible progeny genotype. For each genotype, sum the contributions of the alleles for the G, M, and T genes. For example, the genotype G₁G₁M₁M₁T₁T₁ contributes 6 + 6 + 6 = 18 units of color, while G₂G₂M₂M₂T₂T₂ contributes 1 + 1 + 1 = 3 units of color. Repeat this for all possible genotypes.
Step 5: Apply the threshold model to determine the proportion of progeny with colored kernels. Define the threshold for 'colored kernels' (e.g., a minimum number of color units). Count the number of progeny genotypes that meet or exceed this threshold and divide by the total number of possible progeny genotypes to calculate the proportion.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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 to the overall phenotype. This complexity leads to a variety of color expressions based on the combination of alleles inherited from the parents.
Additive gene 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 different phenotypic effects based on its genotype, with G₁G₁ contributing the most color units. Understanding how these additive effects work is crucial for predicting the overall phenotype resulting from specific genotypes in a polygenic system.
The threshold model in genetics suggests that a certain level of genetic contribution is required to express a particular phenotype. In the context of the kernel-color system, this model implies that only progeny with a combined genetic contribution above a certain threshold will display colored kernels. This concept is essential for determining the expected proportion of colored kernels in the progeny from the specified cross.