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 \(A A b b C C\)ddee\(\times\)aaBBccDDEE 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: There are 162 different genotypes in the F2 generation for this initial cross.

Step-by-step solution

a. Different genotypes in F2 generation

To find the number of different genotypes that will occur in the F2 generation, we have to evaluate the self-fertilization of an F1 organism. The F1 organism genotype is AaBbCcDdEe as it is the product of the given initial mating. To solve this, we have to consider all 5 loci individually and then combine the results. Each allele has 3 combinations: 1. Homozygous dominant (AA, BB, CC, DD, EE) 2. Homozygous recessive (aa, bb, cc, dd, ee) 3. Heterozygous (Aa, Bb, Cc, Dd, Ee) Now, combining all 5 loci we have \(3^5 = 243\) possible different genotypes in the F2 generation.

b. Proportion of F2 genotypes recessive for all five loci

To find the proportion of F2 genotypes that are recessive for all five loci, we can use the probability rules. The probability of each recessive allele combination occurring is \(\frac{1}{4}\), as we should only consider the homozygous recessive genotype from each loci: 1. aa (1/4) 2. bb (1/4) 3. cc (1/4) 4. dd (1/4) 5. ee (1/4) To find the probability of all five occurring together, we multiply their individual probabilities: \((\frac{1}{4})^5 = \frac{1}{1024}\). So, the proportion of F2 genotypes that are recessive for all five loci is \(\frac{1}{1024}\).

c. Initial cross between AAbbCCddee and aaBBccDDEE parents

a. The number of different genotypes that will occur in the F2 generation will not change if the initial cross occurs between AAbbCCddee and aaBBccDDEE parents. The resulting F1 genotype will still be AaBbCcDdEe, and the total number of possibilities in F2 will still be \(3^5 = 243\) different genotypes. b. The proportion of F2 genotypes that are recessive for all five loci will not change either. The F1 organism still has the same genotype, so the probability of getting the recessive phenotype for all loci remains \(\frac{1}{1024}\).

d. Initial cross between AABBCCDDEE and aabbccddEE parents

a. The number of different genotypes that will occur in the F2 generation will change if the initial cross occurs between AABBCCDDEE and aabbccddEE parents. The F1 offspring genotype is AaBbCcDdEE. We still have three allelic combinations for the first four loci but only two for the last one (EE and Ee). Hence, we have \(3^4\times2 = 162\) different genotypes for the F2 generation. b. The proportion of F2 genotypes that are recessive for all five loci will also change because all offspring from the initial cross are EE and therefore no offspring will have the homozygous recessive genotype ee. So, for the F2 generation, there will be no genotypes recessive for all five loci, making the proportion \(0\).

Key concepts

Mendelian Inheritance

Mendelian inheritance, established through the pioneering work of Gregor Mendel, is a foundational principle of genetics that describes how traits are passed down from parents to offspring. Through his experiments with pea plants, Mendel discovered that organisms inherit two copies of each gene, one from each parent. These genes come in different variants, known as alleles, which can be dominant or recessive.

Dominant alleles are expressed even if only one copy is present, while recessive alleles require two copies to be expressed. In our textbook exercise example, alleles represented by capital letters (A, B, C, D, E) are dominant while lowercase letters (a, b, c, d, e) denote recessive alleles. Through Mendel's laws of segregation and independent assortment, the exercise explores the offspring genotypes resulting from the mating of two organisms with opposing alleles.

Specifically, Mendel's law of independent assortment states that alleles for different genes assort independently during the formation of gametes. This is assuming that the genes are not linked on the same chromosome, which is a condition satisfied in the provided exercise.

Independent Assortment

The concept of independent assortment is further explored as the exercise estimates the various genotypic combinations in the F2 generation. Each trait is inherited independently because different genes are located on different chromosomes, allowing for a greater genetic variation. For instance, the Aa genotype from one gene assorting independently of the Bb genotype from another gene results in diverse combinations.

In our example, when an organism with an AaBbCcDdEe genotype self-fertilizes, the alleles for each of the five genes can segregate and recombine in numerous ways, creating a multitude of genotypic variations. This is why calculations in the exercise consider each gene locus separately and then use combinatory logic to deduce the total number of genotypes possible in the F2 population.

Genotypic Variation

Genotypic variation is essential for the survival and evolution of species, as it provides a genetic reservoir that can help populations adapt to changing environments. Discussing genotypic differences within a population as seen in our exercise, involves understanding the likelihood of certain genotypes appearing in a generation. The textbook scenario specifically inquires about the proportion of recessive genotypes across all five loci in the \( F_2 \) generation.

In this context, understanding the probabilities associated with Mendelian inheritance helps us predict that the likelihood of an individual being recessive for all five traits is relatively low. This is because the individual would need to inherit the recessive allele from both parents for each trait. The exercise demonstrates this through a probability calculation, a useful technique that reflects the rare occurrence of such genotype. Genetic variation, influenced by Mendelian mechanisms, is what ultimately leads to a diverse pool of genotypes in any given population.