Question

A cross is made between a heterozygote, \(+++/ \mathrm{rmc}\), and a recessive homozygote, rmc/rmc. 1,280 progeny were analyzed, giving the results below. Determine the order of the three genes \(\mathrm{r}, \mathrm{m}\), and \(\mathrm{c} .\) Calculate the coincidence and the interference.

Short answer

The gene order is r - m - c. The recombination frequencies between r and m is 45.31%, between r and c is 46.09%, and between m and c is 41.4%. The coincidence is 0.1869 and the interference is 0.8131.

Step-by-step solution

Analyze the progeny

Given the progeny data, we need to separate the parental and recombinant progeny by comparing their phenotypes. When comparing, we are looking for the phenotype combinations where only a single gene has changed. To separate the progeny, write down their phenotypes: Parental: +++/rmc and rmc/rmc Recombinant: ++-/rmc, +m+/rmc, r++/rmc, and rm+/rmc Now, we are going to analyze the recombinant progeny to find the gene order.

Determine the gene order

We are going to assign the genes to each phenotypic class and see which order generates two pair of recombinant phenotypes that only differ by one gene. Let's consider the following order: r - m - c Assigning the genes for each recombinant phenotype: 1. r-+/rmc 2. +-m/rmc 3. +-/rc+ 4. ++c/rm+ Here we can see that recombinant phenotypes 1 and 2 differ by one gene. In the same way, the recombinant phenotypes 3 and 4 also differ by one gene. Thus, r - m - c is the correct gene order.

Determine the recombination frequencies

Now that the correct order of the genes has been found, we can calculate the recombination frequencies for each pair of genes: rm/rm+ and ++c/++c represent recombinants involving r and m: 530 + 50 = 580 rm+/++c (no recombination between r and m) : 600 + 40 = 640 Recombination frequency (RF) between r and m: \( \frac{580}{1280} \cdot 100 = 45.31 \% \) rc/rc+ and ++m/++m represent recombinants involving r and c: 550 + 40 = 590 rc+/++m (no recombination between r and c) : 610 + 50 = 660 Recombination frequency (RF) between r and c: \( \frac{590}{1280} \cdot 100 = 46.09 \% \) mc/mc+ (double crossovers): 50 RF between m and c can be found by adding the RF between r and m and the RF between r and c, then subtracting the RF between r and m and r and c: 45.31% + 46.09% - 50 = 41.4%

Calculate the coincidence

Coincidence is the ratio of observed double crossovers to expected double crossovers. Expected double crossovers: (RF between r and m) * (RF between r and c) * total progeny = 0.4531 * 0.4609 * 1280 = 267.42 Observed double crossovers: 50 Coincidence: \( \frac{50}{267.42} = 0.1869 \)

Calculate the interference

Interference is a measure of how much the occurrence of one crossover event prevents the occurrence of another crossover event in the same region and can be calculated as: Interference = 1 - Coincidence = 1 - 0.1869 = 0.8131 Now, we have determined the gene order (r - m - c), calculated the recombination frequencies, coincidence (0.1869), and interference (0.8131) for the given progeny.

Key concepts

Recombination Frequencies

Recombination frequencies are a key concept in genetics used to map the position of genes on a chromosome. They provide a way to estimate the physical distance between two genes based on the likelihood that they will be separated during recombination. In the context of gene mapping, recombination frequency is calculated by observing the progeny of a genetic cross and identifying recombinant versus parental types.

When genes are close together on the same chromosome, the chance of crossing over happening between them is low, leading to a lower recombination frequency. Conversely, genes that are far apart are more likely to experience recombination, presenting a higher recombination frequency. This value is often expressed as a percentage, indicating the proportion of recombinants among the total offspring.

• To calculate the recombination frequency, divide the number of recombinant offspring by the total number of offspring and multiply by 100.
• A recombination frequency of less than 50% suggests linkage between the genes.

Using recombination frequencies, researchers can construct genetic maps giving the relative positions of genes on a chromosome, essential for understanding gene interaction and heritability.

Gene Order Determination

Determining gene order involves analyzing genetic linkage data to arrange genes in the correct sequence on a chromosome. This is done using recombination frequency data from genetic crosses, where the goal is to find the order that best explains the observed progeny phenotypes.

In genetic mapping, the gene order is inferred based on the fact that double crossovers are less frequent than single crossovers. By examining the phenotypes of recombinant offspring, geneticists can identify which pair of genes is the middle gene based on recombination events.

• The gene order is hypothesized by finding which configuration of genes results in the least number of genes differing among recombinant phenotypes.
• Each recombination event between gene pairs helps guide the determination of the order.

Ultimately, correct gene order determination allows for more accurate prediction of genetic outcomes and identification of gene interactions, which is crucial for advancing genetic research and breeding programs.

Genetic Interference

Genetic interference is the phenomenon where the occurrence of a crossover in one region of a chromosome affects the probability of a crossover happening in a nearby region. It is an important concept in genetic mapping because it helps explain patterns of genetic variation that cannot be accounted for by recombination frequencies alone.

Interference is measured by comparing the observed number of double crossovers to the expected number, which is calculated from the product of individual recombination frequencies for two intervals. An interference value of 1 indicates complete interference, where no double crossovers occur, whereas an interference value of 0 suggests no interference, meaning events occur independently.

• Calculate expected double crossovers by multiplying recombination frequencies of adjacent gene pairs and scaling to the total number of progeny.
• The interference is then calculated as: Interference = 1 - Coincidence.

This interference can provide insights into the physical constraints on chromosome structure and the mechanics of recombination, adding depth to genetic map interpretation and enhancing our understanding of genome organization.