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Ch. 25 - Quantitative Genetics and Multifactorial Traits
Klug - Concepts of Genetics 12th Edition
Klug12th EditionConcepts of GeneticsISBN: 9780135564776Non è quello che usi tu?Cambia libro di testo
Capitolo 25, Problema 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 (H²) and narrow-sense (h²) heritabilities for each trait in this herd.

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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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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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Traits and Variance

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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Calculating Heritability
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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


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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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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 

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(b) the variance, 

(c) the standard deviation, and 

(d) the standard error of the mean. 

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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 (h²) for both traits.

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