Suppose a polygenic system for producing color in kernels of a gr...

Question

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.

Accepted Answer

Hey, everyone. Let's take a look at this question together. A flower petal color is determined by three genes. R G and B with two alleles. Each. The R gene has three genotypes. Homozygous dominant R which has five color units. Heterozygous R which has three color units and homozygous recessive R which has one color unit. The G and B genes have similar effects. A plant with the genotype homozygous dominant R G and B has 15 color units. While the genotype homozygous recessive R G and B has three colors units, two tri hybrid plants which are heterozygous four R G and B are mated. What is the expected proportion of progeny plants displaying units of color? Is it answer choice? A one out of 64 answer choice B four out of 64 answer choice C 16 out of 64 or answer choice D 32 out of 64. Let's work this problem out together to try to figure out what the expected proportion of progeny plants displaying 15 units of color is. So from the question, we know we have three genes that have two alleles each, which means that we have two to the power of three, since we have those two alleles, and we have three genes, which is equal to eight, which is the number of possible gammy combinations that can be formed from those three unlinked genes. And since we have eight possible gammy combinations in a tri Hibri cross, that means that we have 64 boxes in our punt square. And since we want to determine of those 64 possible genotypes, what is the expected proportion that would display 15 units of color, which we note that 15 units of color comes from three genes that are displaying five units of color. And we note that those five units of color come from the homozygous dominant genotypes. And since we have three of them, that means that we need three homozygous dominant genotypes. So we have the homozygous dominant r homozygous dominant G and homozygous dominant B. And we know that in this cross of the two tri hybrid plants with that heterozygous genotype for each gene, we have a one out of four possible outcome to get that homozygous dominant genotype for each of the genes. And so we want to determine the possibility of the homozygous dominant for all three genes, which means we multiply one out of four by one out of four by one out of four to get our total of one out of 64. Since four multiplied by four, multiplied by four is equal to 64 which means that the expected proportion of progeny plants displaying 15 units of color is one out of 64 which is answer choice. A the correct answer since a cross between two tri hybrid plants results in 64 possible genotypes of which the only one displaying those 15 units of color is the genotype that is homozygous dominant for all three genes which shows up in one out of 64 of the possible genotypes. So answer choice A is the correct answer. I hope you found this video to be helpful. Thank you and goodbye.

Key Concepts

Polygenic Inheritance

Additive Gene Effects

Expected Proportions in Genetic Crosses

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