Question

The gene \(\mathrm{r}\), for rosy eyes, is 12 map units away from the gene \(k\), for kidney-shaped eyes. Both of these genes are recessive to their wild-type alleles. If a heterozygous wild-type fly, resulting from a cross between a homozygous wild-type fly and a fly with rosy, kidney-shaped eyes, is crossed to a fly with rosy, kidney-shaped eyes, what will be the types of gametes and the frequencies of each?

Short answer

The gametes produced by each parent fly and their frequencies are as follows: - Heterozygous wild-type fly (RrKk): RK (0.44), Rk (0.06), rK (0.06), and rk (0.44) - Fly with rosy, kidney-shaped eyes (rrkk): rk (1.00)

Step-by-step solution

Determine the phenotypes of each parent fly

Initially, we are given the genotypes of two parent flies: a heterozygous wild-type fly and a fly with rosy, kidney-shaped eyes. The wild-type alleles of these genes are dominant, meaning that if a fly carries at least one wild-type allele for each gene, it will exhibit the wild-type (normal) phenotype for that trait. Since the wild-type fly is also heterozygous, this means it carries one recessive allele for each gene. Therefore, the wild-type fly's phenotype will be normal eyes and normal eye shape. The fly with rosy, kidney-shaped eyes carries two recessive alleles for each gene. Therefore, this fly's phenotype will be rosy eyes and kidney-shaped eyes.

Determine the genotypes of each parent fly

Now, let's assign letters to the alleles. Let's use R and r for the eye color gene, with R representing the wild-type (dominant) allele and r representing the rosy eye (recessive) allele. Similarly, let's use K and k for the eye shape gene, with K representing the wild-type (dominant) allele and k representing the kidney-shaped eye (recessive) allele. The heterozygous wild-type fly carries one wild-type allele and one recessive allele for both genes. Therefore, its genotype is RrKk. The fly with rosy, kidney-shaped eyes carries two recessive alleles for both genes. Therefore, its genotype is rrkk.

Determine the possible gametes that can be produced by each parent fly

Each parent fly will produce gametes containing one allele of each gene. Using the rules of segregation and independent assortment, we can determine the possible combinations of alleles that can appear in the gametes. The heterozygous wild-type fly (RrKk) can produce gametes with the following combinations: RK, Rk, rK, and rk. The fly with rosy, kidney-shaped eyes (rrkk) can only produce gametes with the following combination: rk.

Determine the frequencies of each gamete

To calculate the frequency of each gamete, we need to consider the possibility of crossing over between the two genes. Since the genes are 12 map units apart, there is a 12% chance of crossing over occurring between them during gamete formation. Since crossing over produces recombinant gametes, we will calculate the frequency of recombinant (Rk and rK) and parental (RK and rk) gametes separately. For the heterozygous wild-type fly (RrKk): - Frequency of recombinant gametes (Rk and rK): 12% (0.12) / 2 = 6% (0.06) each - Frequency of parental gametes (RK and rk): 100% - 12% = 88% (0.88) / 2 = 44% (0.44) each For the fly with rosy, kidney-shaped eyes (rrkk), there is only one possible gamete (rk). Therefore, the frequency of this gamete is 100% (1.00). So, the frequencies for the gametes produced by each parent fly are as follows: - Heterozygous wild-type fly (RrKk): RK (0.44), Rk (0.06), rK (0.06), and rk (0.44) - Fly with rosy, kidney-shaped eyes (rrkk): rk (1.00)

Key concepts

Map Units in Genetics

Understanding map units in genetics is akin to learning how to measure distances on a roadmap. Just as you'd measure the distance between two cities in miles or kilometers, geneticists measure the distance between genes on a chromosome in map units. A map unit, also known as a centimorgan, represents the frequency of recombination between two genes during the process of crossing over in meiosis. If two genes are 1 map unit apart, it implies that they have a 1% chance of being separated onto different chromosomes due to crossing over in a single generation.
The exercise illustrates this by discussing two genes that are 12 map units apart, which means there is a 12% chance of recombination occurring between them. This relatively short distance indicates that these genes are fairly close to one another on the chromosome and thus have a higher likelihood of being inherited together unless crossing over splits them apart. Consequently, when calculating the types and frequencies of gametes in genetic crosses, map unit distances are crucial for determining the proportion of recombinant and parental gametes produced.

Alleles and Genotypes

When delving into the diverse world of genetics, we encounter terms like 'alleles' and 'genotypes', which are fundamental in understanding heredity. Alleles are different versions of a gene. In every individual organism, genes come in pairs, and thus, so do alleles. Alleles can be dominant or recessive; dominant alleles mask the expression of recessive alleles when they are together in a heterozygous pair.
In the given exercise, the alleles 'R' and 'K' for eye color and shape, respectively, are dominant, while 'r' and 'k' are their recessive counterparts. The genotype is the set of alleles an individual carries. For instance, 'RrKk' is the genotype of a heterozygous wild-type fly, indicating it has both dominant and recessive alleles for eye color and shape. Genotypes are crucial because they determine phenotypes—the observable characteristics. When generating the types of gametes for genetic crosses, researchers look at the genotype to predict potential genetic outcomes, like the gametes 'RK', 'Rk', 'rK', and 'rk' derived in the steps of the exercise.

Segregation and Independent Assortment

Segregation and independent assortment are key principles put forth by Gregor Mendel, known as the father of genetics, and they are essential for understanding how alleles are distributed in gametes. Segregation refers to the separation of allele pairs during gamete formation, ensuring that each gamete carries only one allele for each gene. In the exercise, this would mean the separation of 'R' from 'r' and 'K' from 'k' during the formation of gametes in the wild-type fly.

Independent Assortment

Mendel's law of independent assortment states that the alleles of different genes are distributed independently of one another from the parental organisms into the gametes. This is as long as the genes are not on the same chromosome or are far apart on the same chromosome. The 12 map units distance in the exercise suggests a relatively low, but significant, probability of recombination due to crossing over. The wild-type fly, with the genotype 'RrKk', can produce gametes with 'RK', 'Rk', 'rK', and 'rk', showcasing that these alleles can indeed sort independently. However, because the genes are not infinitely far apart, the parental combinations 'RK' and 'rk' are more frequent than the recombinant 'Rk' and 'rK' due to the 12% recombination frequency.