Question

When pink sweet peas were self-pollinated and the seeds were collected and sown, the following flower colors were obtained: Red 34 Pink 76 White 40 Use a chi-squared test to determine whether these results are consistent with the hypothesis that pink flowers are heterozygous for a single pair of color alleles, showing incomplete dominance. If this is indeed a case of incomplete dominance, what ratio of red: pink: white flowers should we predict for our null hypothesis?a. 9:3:4b. 3:1:0c. 1:2:1 d. 1:4:1

Answer 1

Answer:

c. 1:2:1

The results are consistent with incomplete dominance for this trait, with pink flowers being heterozygous.

Explanation:

If flower color were determined by a gene showing incomplete dominance, the possible genotypes and phenotypes are as follows:

• RR- red
• ww - white
• Rw - pink

If pink sweet peas are self-pollinated, then a cross between two heterozygous individuals is done (Rw x Rw).

From this cross the expected ratios are:

• 1/4 RR (red)
• 2/4 Rw (pink)
• 1/4 ww (white)

So the null hypothesis is that the observed results exhibit a 1:2:1 ratio.

Chi square test

$X^{2} = \sum \frac{(Observed - Expected)^2}{Expected}$

The observed frequencies were:

• 34 Red
• 76 Pink
• 40 White

Total 150

The expected frequencies for our null hypothesis are:

• 1/4 x 150 = 37.5 Red
• 2/4 x 150 = 75 Pink
• 1/4 x 150 = 37.5 white

$X^{2} = \frac{(34- 37.5)^2}{37.5} + \frac{(76- 75)^2}{75} + \frac{(40- 37.5)^2}{37.5}$

$X^2=0.5067$

The degrees of freedom (DF) are calculated as number of phenotypes - 1; in this case DF = 3-1 = 2.

If we look at the Chi square table, for 2 DF and a probability of p0.05, the critical value is 5.991

Our X^2 value of 0.5067 is less than the critical value, so we do not reject the null hypothesis. The results are consistent with incomplete dominance for this trait, with pink flowers being heterozygous.