# Map Distances from F2 Data

In our previous cross (Table 4), the F1 dihybrid sW/Sw was crossed to a sw/sw (Shrunken, Waxy) plant. If the Shrunken Waxy line was not available, the geneticist could still obtain information to determine map distance by selfing the F1 to produce F2 progeny (Table 5). Here is the procedure.

Table 5. Offspring data after selfing the sW/Sw F1's.

 Phenotype Number of progeny Plump, Normal 254 Plump, Waxy 122 Shrunken, Normal 120 Shrunken, Waxy 4 Total F2s: 500

## Step one: Identify the double recessive.

How do we obtain recombinant gamete frequencies from this F2 phenotype information? The first thing to remember is that this is a self-cross rather than a test cross and a different Punnett square is needed to depict how gametes produced these F2s (Fig. 13). From the Punnett square we can see that four kinds of gametes are made in both the male and female in this cross. Therefore, the Plump, Normal seeds can be made nine different ways in our diagram and will consist of five different genotypes (SW/SW, SW/sW, sW/SW, sW/Sw and SW/sw). We cannot tell by observing the phenotype of the Plump, Normal seeds which genotype it has. The Plump, Waxy and Shrunken, Normal F2 seeds will each consist of two different genotypes (Sw/sw and Sw/Sw are Plump, Waxy. sW/sw and sW/sW are Shrunken, Normal). The only F2 phenotypes that consist of a single genotype are the Shrunken, Waxy. They are all ssww (sw/sw). By focusing on how this phenotype was produced in the F2, we can estimate the frequency of recombinant gametes made by the selfed parent.

## Step two: Calculate the double recessive phenotype frequency.

Look at the Punnett square and think about how the Shrunken, Waxy seeds were made (Fig. 13). First, a sw gamete in the male part of the plant and a sw gamete in the female needed to be made. The parent had the genotype sW/Sw that means that these would be recombinant gametes in both the male and female. Once these gametes were made, they needed to come together at random during pollination to produce the seed. Mathematically, we can say that the frequency of the Shrunken, Waxy seeds is the frequency of the sw gamete made in the male multiplied by the frequency of the sw gamete made in the female. If we assume that crossovers occur in the pollen forming cells at the same frequency as the egg forming cells, then the frequency of the Shrunken, Waxy seeds is the square of the frequency of sw. Check your understanding of what this means by looking at Figure 13 before reading the next step. The sw/sw blue cell is created by an sw from the female and the sw from the male coming together.

## Step three: Calculate the gamete frequency using the square root mathematical function.

Now we can use our seed phenotype frequency to estimate gamete frequency in the selfed parent. Four of the 500 seeds produced were Shrunken, Waxy. That would give our square in the lower right a frequency of 0.008 (4/500). This frequency should be the sw gamete frequency squared (sw2). If we want to know the frequency of sw, we can take the square root of 0.008 and get about 0.09. Now we have an estimate of the frequency of one sw gamete. This would be the same for both the male and female gametes, where 9% of all gametes produced by the sW/Sw parent will be sw. As it turns out, we can calculate the frequency of the other three gametes from this information if we think about how the gametes were made in meiosis.

## Step four: Double the frequency, decide if parental or recombinant.

In our continuing example the sw gamete was made when a crossover occurred in the sW/Sw parent. Crossovers are a reciprocal exchange between non-sister chromatids so every time a sw gamete was made, a SW gamete was also made. Therefore, if the sw frequency is 0.09 then the SW frequency is also 0.09. These are our recombinant gametes so the frequency of recombinant gametes is 2 X 0.09 or 0.18. We can tell from this frequency that these are the recombinant gametes since they are less frequently made than the parental gametes. The parental gametes would total 82% of the gametes, each parental gamete making up half (41%) of that total. Thus, 18 map units between the S,s and W,w loci is our map distance estimate from the data. Because we use only a subset of the information in this procedure (only the double recessive numbers) this estimate is more subject to chance than the test cross data. We can use more complex math to estimate gamete frequencies from all the F2 data, but this square root method is a quick way to detect linkage and estimate map distance. In cases where geneticists cannot perform a testcross, working with F2 data is a necessary part of gene mapping. Can you think of some instances where this would be true?