Textbook Question
The following variances were calculated for two traits in a herd of hogs.
Calculate broad-sense (H²) and narrow-sense (h²) heritabilities for each trait in this herd.
Ch. 20 - Quantitative Genetics and Multifactorial Traits
Klug10th EditionEssentials of GeneticsISBN: 9780135588789
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Table of contents
- Ch. 1 - Introduction to Genetics16
- Ch. 2 - Mitosis and Meiosis28
- Ch. 3 - Mendelian Genetics37
- Ch. 4 - Modification of Mendelian Ratios53
- Ch. 5 - Sex Determination and Sex Chromosomes32
- Ch. 6 - Chromosome Mutations: Variation in Number and Arrangement37
- Ch. 7 - Linkage and Chromosome Mapping in Eukaryotes36
- Ch. 8 - Genetic Analysis and Mapping in Bacteria and Bacteriophages24
- Ch. 9 - DNA Structure and Analysis38
- Ch. 10 - DNA Replication29
- Ch. 11 - Chromosome Structure and DNA Sequence Organization22
- Ch. 12 - The Genetic Code and Transcription36
- Ch. 13 - Translation and Proteins27
- Ch. 14 - Gene Mutation, DNA Repair, and Transposition34
- Ch. 15 - Regulation of Gene Expression in Bacteria22
- Ch. 16 - Regulation of Gene Expression in Eukaryotes37
- Ch. 17 - Recombinant DNA Technology27
- Ch. 18 - Genomics, Bioinformatics, and Proteomics30
- Ch. 19 - The Genetics of Cancer21
- Ch. 20 - Quantitative Genetics and Multifactorial Traits37
- Ch. 21 - Population and Evolutionary Genetics45
Chapter 20, Problem 14
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 (H²) of plant height in this species.
Verified step by step guidance1
Identify the components needed to calculate broad-sense heritability (H²). Broad-sense heritability is defined as the proportion of total phenotypic variance that is due to genetic variance. Mathematically, it is expressed as \(H^{2} = \frac{V_{G}}{V_{P}}\), where \(V_{G}\) is the genetic variance and \(V_{P}\) is the total phenotypic variance.
Estimate the environmental variance (\(V_{E}\)) using the variance of the parental strains (P₁ and P₂). Since these strains are highly inbred and genetically uniform, their variance mainly reflects environmental variance. Calculate \(V_{E}\) as the average of the variances of P₁ and P₂: \(V_{E} = \frac{4.2 + 3.8}{2}\).
Determine the total phenotypic variance (\(V_{P}\)) in the F₂ generation, which is given as 10.3. This variance includes both genetic and environmental components.
Calculate the genetic variance (\(V_{G}\)) in the F₂ generation by subtracting the environmental variance from the total phenotypic variance: \(V_{G} = V_{P} - V_{E}\).
Finally, compute the broad-sense heritability using the formula \(H^{2} = \frac{V_{G}}{V_{P}}\) by substituting the values of \(V_{G}\) and \(V_{P}\) obtained in the previous steps.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Broad-Sense Heritability (H²)
Broad-sense heritability (H²) measures the proportion of total phenotypic variance in a trait that is due to genetic variance. It is calculated as the ratio of genetic variance to total phenotypic variance, indicating how much of the observed variation is inherited. H² helps predict the response to selection in breeding programs.
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07:04
Calculating Heritability
Phenotypic Variance and Genetic Variance
Phenotypic variance (Vp) is the total variation observed in a trait, arising from both genetic and environmental factors. Genetic variance (Vg) is the portion of phenotypic variance attributable to genetic differences among individuals. In inbred strains, environmental variance can be estimated from within-strain variance, aiding in separating genetic effects.
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08:34Analyzing Trait Variance
Use of Inbred Strains and Progeny Variance in Heritability Estimation
Highly inbred parental strains have minimal genetic variation within themselves, so their variance mainly reflects environmental effects. The increased variance in F₂ progeny compared to parents reflects genetic segregation and recombination. Comparing variances of parents and progeny allows estimation of genetic variance and thus broad-sense heritability.
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Related Practice
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.
Which trait, if either, is likely to respond to selection?
Textbook Question
In a herd of dairy cows the narrow-sense heritability for milk protein content is 0.76, and for milk butterfat it is 0.82. The correlation coefficient between milk protein content and butterfat is 0.91. If the farmer selects for cows producing more butterfat in their milk, what will be the most likely effect on milk protein content in the next generation?
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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?
1
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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
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.