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Chapter 23: Problem 24

In a series of crosses between two true-breeding strains of peaches, the \(F_{1}\) generation was uniform, producing 30 -g peaches. The \(\mathrm{F}_{2}\) fruit mass ranges from 38 to \(22 \mathrm{g}\) at intervals of \(2 \mathrm{g}\) (a) Using these data, determine the number of polygenic loci involved in the inheritance of peach mass. (b) Using gene symbols of your choice, give the genotypes of the parents and the \(\mathrm{F}_{1}\).

Short Answer

Expert verified
Answer: There are 2 polygenic loci involved in the inheritance of peach mass. The parent genotypes are AABB (with alleles contributing to the larger phenotype) and aabb (with alleles contributing to the smaller phenotype). In the F1 generation, all individuals have the genotype AaBb.

Step by step solution

01

Identify the phenotypic range of F2 generation

In the exercise, we are given that the F2 fruit mass ranges from 38 g to 22 g at intervals of 2 g. We would use this information to identify the number of distinct phenotypes within the range.
02

Calculate the number of polygenic loci

To determine the number of polygenic loci involved in the inheritance of peach mass, count the number of distinct phenotypes within the F2 range (subtract the lowest mass from the highest mass, divide by the interval, and add one). Then take the square root of this number and compare it to the standard 1:2:1 ratio for a single polygenic locus. Based on the calculated ratio, we can then identify the number of polygenic loci involved in the inheritance of peach mass.
03

Calculate the genotypes of the parents and F1 generation

After identifying the number of polygenic loci involved in the inheritance of peach mass, we can determine the genotypes of the parents and F1 generation by giving gene symbols of our choice.
04

Identify the phenotypic range of F2 generation

The F2 fruit mass ranges from 38 g to 22 g at intervals of 2 g. Subtract the lowest mass from the highest mass and divide by the interval: (38-22)/2 = 16/2 = 8. Add one to the result, and we have a total of 9 distinct phenotypes in the F2 generation.
05

Calculate the number of polygenic loci

Now, we need to compare the number of distinct phenotypes in the F2 generation to the standard 1:2:1 ratio for a single polygenic locus. The ratio 1:2:1 has three distinct phenotypes: 3^n, where n is the number of polygenic loci. We take the square root of the number of distinct phenotypes (9) to calculate the number of loci: n = \(\sqrt{9} = 3\). Therefore, there are 2 polygenic loci involved in the inheritance of peach mass.
06

Calculate the genotypes of the parents and F1 generation

We choose two gene symbols, A and B, to represent the two polygenic loci involved in the inheritance of peach mass. Since both parent strains are true-breeding, one parent strain would be AABB (with alleles contributing to the larger phenotype) and the other parent strain would be aabb (with alleles contributing to the smaller phenotype). In the F1 generation, all individuals are heterozygotes and will have the genotype AaBb.

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Most popular questions from this chapter

An inbred strain of plants has a mean height of \(24 \mathrm{cm} .\) A second strain of the same species from a different geographical region also has a mean height of \(24 \mathrm{cm} .\) When plants from the two strains are crossed together, the \(\mathrm{F}_{1}\) plants are the same height as the parent plants. However, the \(\mathrm{F}_{2}\) generation shows a wide range of heights; the majority are like the \(P_{1}\) and \(F_{1}\) plants, but approximately 4 of 1000 are only \(12 \mathrm{cm}\) high and about 4 of 1000 are \(36 \mathrm{cm}\) high. (a) What mode of inheritance is occurring here? (b) How many gene pairs are involved? (c) How much does each gene contribute to plant height? (d) Indicate one possible set of genotypes for the original \(P_{1}\) parents and the \(\mathrm{F}_{1}\) plants that could account for these results. (e) Indicate three possible genotypes that could account for \(\mathrm{F}_{2}\) plants that are \(18 \mathrm{cm}\) high and three that account for \(\mathrm{F}_{2}\) plants that are \(33 \mathrm{cm}\) high.

Erma and Harvey were a compatible barnyard pair, but a curious sight. Harvey's tail was only \(6 \mathrm{cm}\) long, while Erma's was \(30 \mathrm{cm} .\) Their \(\mathrm{F}_{1}\) piglet offspring all grew tails that were \(18 \mathrm{cm}\) When inbred, an \(\mathrm{F}_{2}\) generation resulted in many piglets (Erma and Harvey's grandpigs), whose tails ranged in \(4-\mathrm{cm}\) intervals from 6 to \(30 \mathrm{cm}(6,10,14,18,22,26, \text { and } 30) .\) Most had \(18-\mathrm{cm}\) tails, while \(1 / 64\) had \(6-\mathrm{cm}\) tails and \(1 / 64\) had \(30-\mathrm{cm}\) tails. (a) Explain how these tail lengths were inherited by describing the mode of inheritance, indicating how many gene pairs were at work, and designating the genotypes of Harvey, Erma, and their 18 -cm-tail offspring. (b) If one of the \(18-\mathrm{cm} \mathrm{F}_{1}\) pigs is mated with one of the \(6-\mathrm{cm}\) \(\mathrm{F}_{2}\) pigs, what phenotypic ratio will be predicted if many offspring resulted? Diagram the cross.

In this chapter, we focused on a mode of inheritance referred to as quantitative genetics, as well as many of the statistical parameters utilized to study quantitative traits. Along the way, we found opportunities to consider the methods and reasoning by which geneticists acquired much of their understanding of quantitative genetics. From the explanations given in the chapter, what answers would you propose to the following fundamental questions: (a) How do we know that threshold traits are actually polygenic even though they may have as few as two discrete phenotypic classes? (b) How can we ascertain the number of polygenes involved in the inheritance of a quantitative trait?

Describe the value of using twins in the study of questions relating to the relative impact of heredity versus environment.

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 darkred: 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 symbols to these alleles and list possible 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.
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