Question

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

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

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 \(AaBbCcDdEe\).

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.

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.

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 \((\frac{1}{4})^5=\frac{1}{1024}\).

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.

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.