In a diploid plant species, an F₁ with the genotype Gg Ll Tt is test-crossed to a pure-breeding recessive plant with the genotype gg ll tt. The offspring genotypes are as follows:
Why is the recombination frequency for the outside pair of genes not equal to the sum of recombination frequencies between the adjacent gene pairs?

Question

In a diploid plant species, an F₁ with the genotype Gg Ll Tt is test-crossed to a pure-breeding recessive plant with the genotype gg ll tt. The offspring genotypes are as follows:

Table displaying offspring genotypes and their frequencies from a genetic cross in a diploid plant species.

Why is the recombination frequency for the outside pair of genes not equal to the sum of recombination frequencies between the adjacent gene pairs?

Accepted Answer

Hi, everyone. Welcome back. Let's look at our next problem. It says intra Sophal CPA I gene S E curled wings, gene C U and ebony body gene E are encoded by recessive genes found on chromosome three. A researcher crosses S E C U E slash plus plus plus females with S E C U E slash S E C U E males and obtains the following progeny data. And we have a table with the left side being the genotype of the offspring and the right side being the number of offspring with that genotype. Uh However, when I read the genotype out, I'm not going to read the entire genotype. We know that one of the parents is homozygous recessive for all of those genes. And therefore the offspring will all have one set of recessive alleles. That's the same for all of them. So I will only read the genotype of the, all they inherited from the heterozygous parent since that's what varies here. So our table has the genotype S E C U E 340 plus plus plus S E C U plus 60 S E plus plus 110 plus C U E 84 plus plus E S E plus E 10 N plus C U plus 16. Then our question says, determine the coefficient of coincidence across this region. When the frequency of crossing over is 22% for genes S E and C U and 16.6% for gene C U and E. The answer choices are a zero, B 0.36, C 0.67 and D 0.71. So let's start with recalling what a coefficient of coincidence is. And that is a measure of the interference and formation of chromosomal crossing over. And what that means is that sometimes when you have one crossover occurring that interferes with the likelihood of a second crossover occurring. So they're not occurring independently of each other but can interfere with the possibility of other crossing over occurring. And there's actually a formula to calculate to what degree this interference occurs. And that formula gives us the coefficient of coincidence and it equals the observed number of offspring with two crossovers divided by the expected number of offspring with two crossovers. So that's what we need to find out to calculate our coefficient of coincidence. Well, the observed number of offspring with two crossovers is fairly easy to obtain. We have a chart of offspring with different genotypes. So we merely look for the number of offspring that have two crossovers. Well, we can sit and look at the genotypes and see where the crossing over will occur. But there is a quicker method, which is that when you have a chart like this, uh where one or two crossovers can occur, the two lowest numbers will reflect the incidences of two crossovers since that's the least likely to happen. So when we look at our table, our two lowest numbers are at the bottom of 10 for genotype S E plus E and 16 for genotype plus C U plus. So that gives us 26 observed offspring with two crossovers. And we can double check those genotypes against our list of genes given to us and see that yes, the way those genes are do reflect two crossing over incidences occurring. So now we just need to figure out what our expected number of offspring with two crossovers would have been. Well, to calculate our expected number, we would need to multiply the frequency expected of two crossovers by the total number of offspring. Well, how do we calculate what our expected frequency of the two crossovers is? But we recall on probability, the probability of two independent events occurring is the product of the probability of each individual event occurring. So that means that the frequency expected frequency of two crossovers is calculated by multiplying the crossover frequency of one crossover. So the S E C U crossover by the crossover frequency, uh the second crossover. So the C U E crossover, so those two frequencies multiplied by each other, give us the expected frequency of two crossovers occurring. And again, all that will be multiplied by the total number of offspring. Well, we have all of these values given to us in the problem. So our crossover frequency of S E N C U is given to us as 22% or 0.22, the crossover frequency between C between C U and E is given to us as 16.6% or 0.166. So that gives us our two crossover frequencies. And then to get the total number of offspring, we simply add up all of the numbers of offspring given to us in our table. So when we add them all together, we get 1000 total offspring. So our final number in this formula is 1000. So we have 0.22, multiplied by 0.166, multiplied by 1000. And when we do that calculation, we're going to get 36.52 as our expected number of offspring with double crossovers. So now we have both of the numbers we need and we go down to our formula for coefficient of coincidence. So our observed number of offspring with two crossovers is 26. We got from our table and we're going to divide that by our expected number of offspring with two crossovers, which we calculated as 36.52. And when we do that division, our coefficient of coincidence is going to equal 0.71. So then we just go over to our answers and we see that choice D is indeed 0.71. And therefore our coefficient of coincidence here in this region, when our frequency of crossing over is 22% for genes S E N C U and 16.6% for gene C UN E is choice D 0.71. See you in the next video.

Verified video answer for a similar problem:

Key Concepts

Linkage and Recombination

Test Cross

Chi-Square Analysis