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Chapter 20: Problem 11

In a cross between a strain of large guinea pigs and a strain of small guinea pigs, the \(F_{1}\) are phenotypically uniform, with an average size about intermediate between that of the two parental strains. Among $1014 \mathrm{F}_{2}$ 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?

Short Answer

Expert verified
Approximately 2 gene pairs are involved in the inheritance of size in these strains of guinea pigs.

Step by step solution

01

Identify the total number of phenotypes in the F2 generation

From the given data, we know that there are \(\text{3 small}\), \(\text{5 large}\), and \((1014-3-5) = 1006\) intermediate individuals in the \(F_2\) generation.
02

Calculate the fraction of extreme phenotypes in the F2 generation

Since there are \(3\) small and \(5\) large-sized individuals, the fraction of extreme phenotypes in the \(F_2\) generation is: $$ \frac{3+5}{1014} = \frac{8}{1014} \approx 0.0079 $$
03

Determine the number of gene pairs

To find the number of gene pairs involved in the variation of size in these guinea pigs, we can use the following formula: $$ \frac{1}{4^{n}} = \text{fraction of extreme phenotypes} $$ where \(n = \) the number of gene pairs. In this case, the fraction of extreme phenotypes is \(0.0079\). We can calculate the number of gene pairs as follows: $$ \frac{1}{4^{n}} = 0.0079 $$ Taking the logarithm of both sides: $$ \log_{4}\left(\frac{1}{4^{n}}\right) = \log_{4}(0.0079) \\ -n = \log_{4}(0.0079) \\ n = -\log_{4}(0.0079) \\ n\approx 2 $$
04

Answer the question

Based on our calculations, there are approximately \(2\) gene pairs involved in the inheritance of size in these strains of guinea pigs.

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Most popular questions from this chapter

A dark-red strain and a white strain of wheat are crossed and produce an intermediate, medium-red \(\mathrm{F}_{1}\). When the \(\mathrm{F}_{1}\) plants are interbred, an \(\mathrm{F}_{2}\) generation is produced in a ratio of 1 dark-red: 4 medium-dark-red: 6 medium-red: 4 light-red: 1 white, Further crosses reveal that the dark-red and white \(\mathrm{F}_{2}\) plants are true breeding. (a) Based on the ratios in the \(\mathrm{F}_{2}\) population, how many genes are involved in the production of color? (b) How many additive alleles are needed to produce each possible phenotype? (c) Assign symhols to these alleles and list pnssible genotypes that give rise to the medium-red and light-red phenotypes. (d) Predict the outcome of the \(F_{1}\) and \(F_{2}\) generations in a cross between a true-breeding medium-red plant and a white plant.

While most quantitative traits display continuous variation, there are others referred to as "threshold traits" that are distin- guished by having a small number of discrete phenotypic classes. For example, Type 2 diabetes (adult-onset diabetes) is considered to be a polygenic trait, but demonstrates only two phenotypic classes: individuals who develop the disease and those who do not. Theorize how a threshold trait such as Type 2 diabetes may be under the control of many polygenes, but express a limited number of phenotypes.

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

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

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 cor- relation 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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