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Ch. 19 - Genetic Analysis of Quantitative Traits
Sanders - Genetic Analysis: An Integrated Approach 3rd Edition
Sanders3rd EditionGenetic Analysis: An Integrated ApproachISBN: 9780135564172Not the one you use?Change textbook
Chapter 19, Problem 23a

New Zealand lamb breeders measure the following variance values for their herd.
Table showing variance values for body mass, fat, and length in lambs: phenotypic, genetic, and additive variances.
Calculate the broad sense heritability (H²) and the narrow sense heritability (h²) for each trait in this lamb herd.

Verified step by step guidance
1
Identify the variance components given for each trait: phenotypic variance (VP), genotypic variance (VG), and additive genetic variance (VA).
Recall the formulas for heritability: Broad sense heritability (H²) is calculated as H² = VG / VP, which represents the proportion of phenotypic variance due to all genetic factors.
Narrow sense heritability (h²) is calculated as h² = VA / VP, representing the proportion of phenotypic variance due to additive genetic effects only.
For each trait (Body mass, Body fat, Body length), substitute the given values into the formulas: calculate H² by dividing VG by VP, and calculate h² by dividing VA by VP.
Interpret the heritability values to understand the genetic contribution to each trait's variation, which can inform selective breeding decisions.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Phenotypic Variance (VP)

Phenotypic variance represents the total observed variation in a trait within a population, combining both genetic and environmental influences. It is the sum of genetic variance (VG) and environmental variance (VE). Understanding VP is essential because heritability calculations use it as the denominator to express the proportion of variance due to genetics.
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Analyzing Trait Variance

Broad Sense Heritability (H²)

Broad sense heritability is the proportion of total phenotypic variance attributable to all genetic variance (VG), including additive, dominance, and epistatic effects. It is calculated as H² = VG / VP. This measure indicates the overall genetic contribution to trait variation but does not distinguish the type of genetic effects.
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Calculating Heritability

Narrow Sense Heritability (h²)

Narrow sense heritability quantifies the proportion of phenotypic variance due specifically to additive genetic variance (VA), which is the genetic component passed from parents to offspring. It is calculated as h² = VA / VP and is crucial for predicting response to selection in breeding programs.
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Related Practice
Textbook 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.

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Textbook 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. 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.

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Textbook 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.

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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Textbook Question

New Zealand lamb breeders measure the following variance values for their herd.

How would you characterize the potential response to selection (R) for each trait?

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Textbook Question

Cattle breeders would like to improve the protein content and butterfat content of milk produced by a herd of cows. Narrow sense heritability values are 0.60 for protein content and 0.80 for butterfat content. The average percentages of these traits in the herd and the percentages of the traits in cows selected for breeding are as follows. Trait Herd Average Selected Cows Protein content 20.2% 22.7% Butterfat content  6.5%  7.4% Determine the selection differential (S) for each trait in this herd.

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Textbook Question

Cattle breeders would like to improve the protein content and butterfat content of milk produced by a herd of cows. Narrow sense heritability values are 0.60 for protein content and 0.80 for butterfat content. The average percentages of these traits in the herd and the percentages of the traits in cows selected for breeding are as follows. Trait Herd Average Selected Cows Protein content 20.2% 22.7% Butterfat content  6.5%  7.4% Which trait is likely to be the most responsive to artificial selection applied by the cattle breeders through selection of cows for mating?

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