Ch. 20 - Quantitative Genetics and Multifactorial Traits

Klug - Essentials of Genetics 10th Edition

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Klug 10th Edition

Ch. 20 - Quantitative Genetics and Multifactorial Traits

Problem 11

Chapter 20, Problem 11

In a cross between a strain of large guinea pigs and a strain of small guinea pigs, the F₁ are phenotypically uniform, with an average size about intermediate between that of the two parental strains. Among 1014 F₂ individuals, 3 are about the same size as the small parental strain and 5 are about the same size as the large parental strain. How many gene pairs are involved in the inheritance of size in these strains of guinea pigs?

Verified step by step guidance

Recognize that the problem describes incomplete dominance or additive gene action, where the F₁ phenotype is intermediate between the two parental phenotypes, and the F₂ shows a range of phenotypes including parental types and intermediates.

Identify that the number of gene pairs (n) involved can be estimated by analyzing the proportion of F₂ individuals that resemble the parental phenotypes, which correspond to the homozygous genotypes at all loci.

Recall that for n gene pairs with additive effects, the proportion of F₂ individuals showing the parental phenotype is given by the formula \(\left(\frac{1}{4}\right)^n\) for each parental type, because each gene pair segregates independently and the parental phenotype requires homozygosity at all loci.

Calculate the observed frequency of each parental phenotype in the F₂ generation by dividing the number of individuals with that phenotype by the total number of F₂ individuals (e.g., for the small phenotype, frequency = \(\frac{3}{1014}\)).

Set up the equation \(\left(\frac{1}{4}\right)^n = \text{observed frequency}\) and solve for n by taking the logarithm of both sides: \(n = \frac{\log(\text{observed frequency})}{\log(\frac{1}{4})}\). This will give the number of gene pairs involved.

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Key Concepts

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

Incomplete Dominance and Intermediate Phenotypes

Incomplete dominance occurs when the heterozygote phenotype is intermediate between the two homozygotes, as seen in the F₁ guinea pigs with sizes between large and small parents. This suggests that neither allele is completely dominant, resulting in blending traits rather than a dominant-recessive pattern.

Polygenic Inheritance

Polygenic inheritance involves multiple gene pairs contributing additively to a single trait, such as size. The continuous variation and intermediate phenotypes in the F₂ generation indicate that size is controlled by several genes, each with small effects, rather than a single gene.

Segregation Ratios and Estimating Number of Gene Pairs

The number of gene pairs can be estimated by analyzing the frequency of parental phenotypes in the F₂ generation. The proportion of individuals resembling parental extremes follows a (1/4)^n pattern, where n is the number of gene pairs, allowing calculation of n from observed counts of extreme phenotypes.

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In the following table, average differences of height, weight, and fingerprint ridge count between monozygotic twins (reared together and apart), dizygotic twins, and nontwin siblings are compared:

Based on the data in this table, which of these quantitative traits has the highest heritability values?

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

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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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What advantages do cDNA libraries provide over genomic DNA libraries? Describe cloning applications where the use of a genomic library is necessary to provide information that a cDNA library cannot.

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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,

(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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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.

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