How many genes govern resistance to each race?

Steps to Solve

1. Identify the total number of plants Add up all the observed plant categories to find the total.

• $128 + 14 + 39 + 44 = 225$ total plants.

2. Determine the observed segregation ratios The segregation ratios can help to identify the inheritance pattern.

• The observed counts are:
  • Resistant to both: 128
  • Susceptible to both: 14
  • Resistant to race 1, susceptible to race 2: 39
  • Susceptible to race 1, resistant to race 2: 44

3. Calculate the expected ratios for 2 genes From the number of types of resistance, we expect a ratio resembling $9:3:3:1$ if two genes are independently assorting.

• This implies a total of 16 parts in the ratio, where:
  • 9 are resistant to both,
  • 3 are resistant to one and susceptible to the other,
  • 3 are the opposite,
  • 1 is susceptible to both.

4. Check compatibility with observed numbers Verify the counts against the expected ratio.

• Total ratio contributions:
  • Resistant to both: $9x$
  • Resistant to race 1 and susceptible to race 2: $3x$
  • Susceptible to race 1 and resistant to race 2: $3x$
  • Susceptible to both: $1x$

This leads to:

• $9x + 3x + 3x + 1x = 16x$, which should equal the total count of plants (225).

5. Solve for x Calculate $x$ to find the individual ratio contributions.

• Setting $16x = 225$ gives: $$x \approx \frac{225}{16} \approx 14.0625$$

6. Conclude with the number of genes From the observed segregation ratios (like $9:3:3:1$), we infer there are likely two genes controlling resistance:

• Each gene independently influences resistance to the viral races, confirming the presence of 2 genes.