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Chapter 3: Problem 12

Two organisms, \(A A B B C C D D E E\) and aabbccddee, are mated to produce an \(\mathrm{F}_{1}\) that is self-fertilized. If the capital letters represent dominant, independently assorting alleles: (a) How many different genotypes will occur in the \(\mathrm{F}_{2}\) ? (b) What proportion of the \(\mathrm{F}_{2}\) genotypes will be recessive for all five loci? (c) Would you change your answers to (a) and/or (b) if the initial cross occurred between \(A A b b C C d d e e \times a a B B c c D D E E\) parents? (d) Would you change your answers to (a) and/or (b) if the initial cross occurred between \(A A B B C C D D E E \times\)aabbccddEE parents?

Short Answer

Expert verified
Answer: The proportion of F2 genotypes that are recessive for all five loci when organism 1 (\(A A B B C C D D E E\)) mates with organism 2 (\(a a B B c c D D E E\)) is \(\frac{1}{1024}\).

Step by step solution

01

Determine the F1 genotype

From the given information, we can determine the genotype of the F1 offspring when Organism 1 (\(A A B B C C D D E E\)) mates with Organism 2 (aabbccddee). Since capital letters represent dominant alleles, the genotypes of the F1 offspring will be \(AaBbCcDdEe\).
02

Determine the possible gametes for the F1 offspring

For the F1 offspring with genotype \(AaBbCcDdEe\), we need to find all the possible gametes they can produce. There are two possibilities for each gene, resulting in \(2^5=32\) different gametes.
03

Calculate the number of different genotypes in the F2 generation (Part a)

When the F1 offspring self-fertilizes, it will produce the F2 generation with 32 possible genotypes. Since each F1 gamete can pair with any of the other 32 gametes, there will be \(32 \times 32 = 1024\) possible genotypes in the F2 generation.
04

Calculate the proportion of F2 genotypes that are recessive for all five loci (Part b)

To find the proportion of F2 genotypes that are recessive for all five loci, we need to find the probability for each individual gene to be recessive and then multiply these probabilities together. For each gene separately, the probability of homozygous recessive is \((\frac{1}{2})^2=\frac{1}{4}\). Therefore, the probability of being recessive for all five loci is \((\frac{1}{4})^5=\frac{1}{1024}\).
05

Analyze the effect of changing initial cross (Part c)

The new initial cross is between \(A A b b C C d d e e\) and \(a a B B c c D D E E\). The F1 offspring will have the same genotype as before, \(AaBbCcDdEe\). Therefore, the answers to parts (a) and (b) will not change, as the number of F2 genotypes and the proportion of recessive genotypes will remain the same.
06

Analyze the effect of changing initial cross (Part d)

The new initial cross is between \(A A B B C C D D E E\) and \(aabbccddEE\). The F1 offspring will now have the genotype \(AaBbCcDdEE\). Since the E gene is now homozygous dominant in the F1 offspring, there will be no recessive genotype for the E gene in the F2 generation. Therefore, the answers to parts (a) and (b) would change, as the number of F2 genotypes will be different, and the proportion of completely recessive genotypes will be 0.

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Most popular questions from this chapter

In this chapter, we focused on the Mendelian postulates, probability, and pedigree analysis. We also considered some of the methods and reasoning by which these ideas, concepts, and techniques were developed. On the basis of these discussions, what answers would you propose to the following questions: (a) How was Mendel able to derive postulates concerning the behavior of "unit factors" during gamete formation, when he could not directly observe them? (b) How do we know whether an organism expressing a dominant trait is homozygous or heterozygous? (c) In analyzing genetic data, how do we know whether deviation from the expected ratio is due to chance rather than to another, independent factor? (d) since experimental crosses are not performed in humans, how do we know how traits are inherited?

Consider three independently assorting gene pairs, \(A / a, B / b,\) and \(C / c,\) where each demonstrates typical dominance \((A-, B-, C-)\) and recessiveness \((a a, b b, c c) .\) What is the probability of obtaining an offspring that is \(A A B b C c\) from parents that are \(A a B b C C\) and \(A A B b C c ?\)

Albinism, lack of pigmentation in humans, results from an autosomal recessive gene (a). Two parents with normal pigmentation have an albino child. (a) What is the probability that their next child will be albino? (b) What is the probability that their next child will be an albino girl? (c) What is the probability that their next three children will be albino?

Mendel crossed peas with round, green seeds with peas having wrinkled, yellow seeds. All \(\mathrm{F}_{1}\) plants had seeds that were round and yellow. Predict the results of testcrossing these \(F_{1}\) plants.

Mendel crossed peas having round seeds and yellow cotyledons with peas having wrinkled seeds and green cotyledons. All the \(\mathrm{F}_{1}\) plants had round seeds with yellow cotyledons. Diagram this cross through the \(\mathrm{F}_{2}\) generation, using both the Punnett square and forked-line methods.
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