Question

Given the following testcross data for corn in which the genes for fine stripe (f), bronze aleurone (bz) and knotted leaf \((\mathrm{Kn})\) are involved: Phenotype \(\mathrm{Kn}++\) \(\mathrm{Kn} \mathrm{f}+\) \(+++\) \(+\mathrm{fbz}\) \(\mathrm{Kn}+\mathrm{bz}\) \(++\mathrm{bz}\) \(+\mathrm{f}+\) \(\mathrm{Kn} \mathrm{f} \mathrm{bz}\) Total $$ \begin{gathered} \text { Number } \\ 451 \\ 134 \\ 97 \\ 436 \\ 18 \\ 119 \\ 24 \\ 86 \\ \hline 1,365 \end{gathered} $$ (a) Determine the sequence of the three genes. (b) Calculate the amount of recombination that occurred between each pair of loci. (c) Calculate the coefficient of coincidence.

Short answer

The sequence of the three genes is \(\textit{bz}\)-\(\textit{f}\)-\(\textit{Kn}\). The recombination frequency between \(\textit{bz}\) and \(\textit{f}\) is approximately \(0.0889\), whereas the recombination frequency between \(\textit{f}\) and \(\textit{Kn}\) is approximately \(0.4181\). The coefficient of coincidence is approximately \(2.695\).

Step-by-step solution

Identify the Parent Generation Genotypes

From the given phenotypic data, we can infer the genotypes of the parent generation that participated in the testcross. Let + denote the dominant alleles (e.g., wild type) and lowercase letters denote the recessive alleles. The parent genotypes are as follows: 1. \(\mathrm{Kn}++\): \(\textit{Kn}\) is dominant, while \(\textit{f}\) and \(\textit{bz}\) are recessive. 2. \(\mathrm{Kn} \mathrm{f}+\): \(\textit{Kn}\) and \(\textit{f}\) are dominant, while \(\textit{bz}\) is recessive. 3. \(+++\): All three dominant alleles are present. 4. \(+\mathrm{fbz}\): \(\textit{f}\) and \(\textit{bz}\) are dominant and \(\textit{Kn}\) is recessive. 5. \(\mathrm{Kn}+\mathrm{bz}\): \(\textit{Kn}\) and \(\textit{bz}\) are dominant and \(\textit{f}\) is recessive. 6. \(++\mathrm{bz}\): \(\textit{bz}\) is dominant and \(\textit{Kn}\) and \(\textit{f}\) are recessive. 7. \(+\mathrm{f}+\): \(\textit{f}\) is dominant and \(\textit{Kn}\) and \(\textit{bz}\) are recessive. 8. \(\mathrm{Kn} \mathrm{f} \mathrm{bz}\): All three recessive alleles are present.

Determine the Gene Sequence

Notice that in the parent generation phenotypes, one gene is always associated with the highest frequency among the total number of offspring (1519). This suggests that this gene is the least likely to undergo recombination and, therefore, can be considered to be in the middle of the other two genes. From the data, \(\textit{f}\) is the highest-frequency gene (1519), so the gene sequence is \(\textit{bz}\) - \(\textit{f}\) - \(\textit{Kn}\).

Calculate Recombination Frequencies

To calculate the recombination frequencies between the pairs of loci, we first need to identify the single and double crossover phenotypes. Single crossovers occur between either \(\textit{bz}\) and \(\textit{f}\) or \(\textit{f}\) and \(\textit{Kn}\), while double crossovers involve all three genes. Single crossovers between \(\textit{bz}\) and \(\textit{f}\): \(\mathrm{Kn} \mathrm{f} \mathrm{bz}\) \(+\mathrm{f}+\) Single crossovers between \(\textit{f}\) and \(\textit{Kn}\): \(\mathrm{Kn} \mathrm{f}+\) \(+\mathrm{fbz}\) Double crossovers: \(\mathrm{Kn}+\mathrm{bz}\) \(++\mathrm{bz}\) Now, we can calculate the recombination frequencies: Recombination frequency between \(\textit{bz}\) and \(\textit{f}\): \(\frac{\text{Total Crossovers}}{\text{Total Offspring}} = \frac{97 + 24} {1365} \approx 0.0889\) Recombination frequency between \(\textit{f}\) and \(\textit{Kn}\): \(\frac{\text{Total Crossovers}}{\text{Total Offspring}} = \frac{134 + 436} {1365} \approx 0.4181\)

Calculate the Coefficient of Coincidence

The coefficient of coincidence is the ratio of observed double crossovers to the expected double crossovers. Expected double crossovers = \(\text{Recombination between} \ \textit{bz \ and \ f} \times \text{Recombination between} \ \textit{f \ and \ Kn} \times \text{Total Offspring} = 0.0889 \times 0.4181 \times 1365 \approx 50.84\) Observed double crossovers = \(\mathrm{Kn}+\mathrm{bz} \text{ and } ++\mathrm{bz}\) (18 and 119) = 137 Coefficient of Coincidence = \(\frac{\text{Observed Double Crossovers}}{\text{Expected Double Crossovers}} = \frac{137}{50.84} \approx 2.695\)

Key concepts

Gene Sequence Determination

Determining the sequence of genes on a chromosome is a fundamental concept in genetics. This process, known as gene mapping, plays a critical role in understanding how traits are passed down through generations.

Within a given set of testcross data, phenotypic ratios can reveal the likelihood of recombination events between alleles. The less likely a recombination event is, the closer together the involved genes are on a chromosome. In our example with corn, by identifying the parent phenotypes and the number of offspring, we inferred that the gene sequence is bz - f - Kn, which means the f gene is located between bz and Kn on the chromosome. This position was deduced from the high frequency of the f allele, implying it is less prone to recombination and thus likely situated centrally among the three genes.

Exercise Improvement Advice

When approaching problems of gene sequence determination, carefully assess parental and offspring phenotypes. Closely inspect the data to determine which gene is consistently passed down to the offspring, as this will point to its central position in the sequence. Additionally, understanding that genes physically closer on a chromosome have lower recombination frequencies can help in deducing their sequence.

Recombination Frequency Calculation

Recombination frequency is a measure of genetic linkage and is used to map the distance between genes. The calculation is based on the proportion of offspring that are recombinants – individuals showing a new combination of traits not seen in the parents – resulting from crossing over during meiosis.

The frequency of recombination can be calculated by dividing the number of recombinant offspring by the total number of offspring. In our corn testcross example, we calculated the recombination frequencies between bz and f, and between f and Kn. These calculations gave us frequencies of 0.0889 and 0.4181, respectively. A higher recombination frequency between two genes suggests they are farther apart on the chromosome, which can be crucial for mapping gene locations.

Exercise Improvement Advice

To improve accuracy in these calculations, be mindful of the phenotypes that represent single and double crossover events. It's necessary to correctly identify which offspring categories result from each type of crossover, as this impacts the recombination frequency values obtained. Taking this step thoughtfully will lead to more precise gene mapping.

Coefficient of Coincidence

The coefficient of coincidence is a metric used by geneticists to quantify the degree of interference in the crossing over of genes. Interference occurs when the occurrence of a crossover in one region of a chromosome inhibits the occurrence of another crossover nearby.

In our exercise, we compared the observed double crossovers with the expected double crossovers, the latter being a product of the individual recombination frequencies of gene pairs. The result of about 2.695 indicates significant interference, as the actual occurrence of double crossovers is far from what was expected. A coefficient of coincidence of 1 means no interference; a value less than 1 suggests positive interference (fewer double crossovers than expected), while a value greater than 1 indicates negative interference (more double crossovers than expected).

Exercise Improvement Advice

When calculating the coefficient of coincidence, ensure that you are working from accurate recombination frequency calculations. Also, remember that while the coefficient gives insights into the crossover behavior, it does not modify the sequence or distances previously determined—it helps explain the crossover dynamics that occurred during gamete formation. Understanding the implication of the coefficient in genetic mapping is essential for interpreting genetic data accurately.