How many genes govern resistance to each race?

Steps to Solve

1. Identify Given Data

From the problem, we have the following segregation in the F2 generation:

• Resistant to both races: 128 plants
• Susceptible to both races: 14 plants
• Resistant to race 1 and susceptible to race 2: 39 plants
• Susceptible to race 1 and resistant to race 2: 44 plants

2. Determine Phenotypic Ratios

We can add the counts to find the total number of plants observed:

$$ \text{Total} = 128 + 14 + 39 + 44 = 225 $$

Now, we can express the segregation data as a ratio:

• Resistant to both races (RR): 128
• Susceptible to both races (rr): 14
• Resistant to race 1 only (Rr, rr): 39
• Resistant to race 2 only (Rr, rr): 44

3. Analyze Ratios for Each Race

Next, let's focus on the counts for each race to understand the inheritance pattern.

• For Race 1:

  • Resistant (R): 128 (RR) + 39 (Rr) = 167
  • Susceptible (r): 14

• For Race 2:

  • Resistant (R): 128 (RR) + 44 (Rr) = 172
  • Susceptible (r): 14

4. Determine Gene Count for Resistance

Using the observed segregation ratios, we apply the concept of simple Mendelian inheritance.

For each race, we can count the number of dominant and recessive phenotypes that have been observed.

If we assume a single gene governs resistance for each race, the ratio should ideally be 3:1 for dominant (resistant) to recessive (susceptible):

• Race 1 ratio (3:1): $$ 3x + 1x = 225 \implies 4x = 225 \implies x = 56.25 $$
• Since x must be whole, this suggests two genes may be involved given excess of 3:1 ratio indicates more complex interaction.

5. Conclusion on Gene Number

Given that we observe a skewed ratio, at least two genes govern resistance for each race due to the complex interaction of dominant and recessive factors.