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Ch. 25 - Quantitative Genetics and Multifactorial Traits
Klug - Concepts of Genetics  12th Edition
Klug12th EditionConcepts of Genetics ISBN: 9780135564776Not the one you use?Change textbook
Chapter 25, Problem 12a

The following variances were calculated for two traits in a herd of hogs.
Table showing phenotypic, genetic, and additive variances for back fat and body length traits in a hog herd.
Calculate broad-sense () and narrow-sense () heritabilities for each trait in this herd.

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1
Identify the variances given for each trait: phenotypic variance (\(V_P\)), genetic variance (\(V_G\)), and additive genetic variance (\(V_A\)). These are provided in the table for back fat and body length.
Recall the formula for broad-sense heritability (\(H^2\)), which is the proportion of phenotypic variance due to total genetic variance: \(H^2 = \frac{V_G}{V_P}\)
Recall the formula for narrow-sense heritability (\(h^2\)), which is the proportion of phenotypic variance due to additive genetic variance: \(h^2 = \frac{V_A}{V_P}\)
For each trait (back fat and body length), substitute the values from the table into the formulas for \(H^2\) and \(h^2\) to set up the calculations.
Interpret the heritability values to understand the genetic contribution to the traits: higher values indicate a greater genetic influence on the phenotypic variation.

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Key Concepts

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

Phenotypic Variance (V_P)

Phenotypic variance represents the total variation observed in a trait within a population. It includes genetic variance, environmental variance, and their interactions. Understanding V_P is essential because it forms the denominator in heritability calculations, reflecting all sources of trait variation.
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Analyzing Trait Variance

Genetic Variance (V_G) and Additive Genetic Variance (V_A)

Genetic variance (V_G) is the portion of phenotypic variance due to genetic differences among individuals. Additive genetic variance (V_A) is the part of V_G attributable to the additive effects of alleles, which predictably pass from parents to offspring. V_A is crucial for narrow-sense heritability, while V_G is used for broad-sense heritability.
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Broad-sense (H²) and Narrow-sense (h²) Heritability

Broad-sense heritability (H²) is the ratio of total genetic variance (V_G) to phenotypic variance (V_P), indicating the proportion of trait variation due to all genetic factors. Narrow-sense heritability (h²) is the ratio of additive genetic variance (V_A) to V_P, reflecting the proportion of variation that can be passed to offspring and is key for predicting response to selection.
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Related Practice
Textbook Question

What kind of heritability estimates (broad sense or narrow sense) are obtained from human twin studies?

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Textbook Question

List as many human traits as you can that are likely to be under the control of a polygenic mode of inheritance.

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Textbook Question

Corn plants from a test plot are measured, and the distribution of heights at 10-cm intervals is recorded in the following table: 

 Height (cm)   Plants (no.)    

100          20    

110          60    

120          90    

130         130    

140         180   

 150         120    

160          70    

170         50    

180         40 

Calculate 

(a) the mean height, 

(b) the variance, 

(c) the standard deviation, and 

(d) the standard error of the mean. 

Plot a rough graph of plant height against frequency. Do the values represent a normal distribution? Based on your calculations, how would you assess the variation within this population?

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Textbook Question

The following variances were calculated for two traits in a herd of hogs.

Which of the two traits will respond best to selection by a breeder? Why?

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Textbook Question

The mean and variance of plant height of two highly inbred strains (P₁ and P₂) and their progeny (F₁ and F₂) are shown here.


  Strain  Mean (cm)  Variance 

   P₁     34.2        4.2

   P₂     55.3        3.8

   F₁     44.2        5.6

   F₂     46.3       10.3


Calculate the broad-sense heritability () of plant height in this species.

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Textbook Question

A hypothetical study investigated the vitamin A content and the cholesterol content of eggs from a large population of chickens. The following variances (V) were calculated.

Calculate the narrow-sense heritability () for both traits.

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