By the way, my homework is due Wednesday, November 13th at 4:10 pm. I would appreciate it if you could please walk me through all of the steps to solve all parts of this problem. In the garden pea, orange pods (g) are recessive to green pods (G), and sensitivity to pea mosaic virus (m) is recessive to resistance to the virus (M). A true-breeding plant with orange pods and sensitivity to the virus was crossed to a true-breeding plant with green pods and resistance to the virus. The F1 plants were then testcrossed to plants homozygous recessive for both traits. The F2 progeny counts are as follows: 160 have an orange pod color and are sensitive to the virus, 140 have a green pod color and are resistant to the virus, 107 have an orange pod color and are resistant to the virus, and 113 have a green pod color and are sensitive to the virus.
a. Are these genes linked? Give the chi squared value to test this hypothesis.
b. Given your chi squared value and the degrees of freedom, should we reject the null hypothesis?
To solve this problem, we will go step by step:
Step 1: Understand the problem.
The problem involves two traits in garden peas: pod color (orange or green) and sensitivity to pea mosaic virus (sensitive or resistant). We need to determine if these traits are linked and perform a chi-squared test to test this hypothesis.
Step 2: Understand the genetics involved.
In the given problem, orange pods (g) are recessive to green pods (G), and sensitivity to the virus (m) is recessive to resistance to the virus (M). "True-breeding" means that the plants are homozygous for the respective traits.
Step 3: Set up the cross.
In the cross, a true-breeding plant with orange pods (ggmm) and sensitivity to the virus is crossed with a true-breeding plant with green pods (GGMM) and resistance to the virus.
Step 4: Determine the F1 generation.
The F1 generation results from crossing these two parents. Since the orange pod color and sensitivity to the virus are both recessive traits, the F1 generation would have green pods (Gg) and resistance to the virus (Mm).
Step 5: Perform the testcross.
The F1 generation is testcrossed to plants that are homozygous recessive for both traits (ggmm). This testcross will allow us to determine the linkage of the two traits.
Step 6: Analyze the F2 progeny counts.
The F2 progeny counts are as follows:
- 160 have an orange pod color and are sensitive to the virus
- 140 have a green pod color and are resistant to the virus
- 107 have an orange pod color and are resistant to the virus
- 113 have a green pod color and are sensitive to the virus
Step 7: Calculate the expected numbers.
To determine if the genes are linked, we need to compare the observed counts with the expected counts. The expected counts can be calculated using a Punnett square.
Using a Punnett square, we can determine that half of the offspring are expected to have linked traits, while the other half are expected to have unlinked traits. Thus, we can estimate the expected counts as follows:
- 150 (1/4 of total) have an orange pod color, and are sensitive to the virus (linked)
- 150 (1/4 of total) have a green pod color, and are resistant to the virus (linked)
- 150 (1/4 of total) have an orange pod color, and are resistant to the virus (unlinked)
- 150 (1/4 of total) have a green pod color, and are sensitive to the virus (unlinked)
Step 8: Perform the chi-squared test.
The chi-squared test is used to determine if the observed counts significantly deviate from the expected counts.
Step 9: Calculate the chi-squared value.
To calculate the chi-squared value, we use the formula: χ² = Σ((Observed - Expected)² / Expected)
Using the observed and expected counts from Step 6 and Step 7, respectively, we can calculate the chi-squared value.
Step 10: Calculate the degrees of freedom.
The degrees of freedom (df) can be determined by subtracting 1 from the number of traits being analyzed. In this case, since we are analyzing two traits (pod color and virus sensitivity), the df is 2-1 = 1.
Step 11: Compare the chi-squared value to the critical value.
Using the chi-squared distribution table or a calculator, we can find the critical value for the given significance level (usually 0.05). For the df = 1, the critical value is 3.84.
Step 12: Determine if we should reject the null hypothesis.
If the chi-squared value is greater than the critical value, we reject the null hypothesis (genes are linked). If the chi-squared value is less than the critical value, we fail to reject the null hypothesis (genes are not linked).
In this case, if the calculated chi-squared value is greater than 3.84, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
By following these steps, you will be able to solve the problem, calculate the chi-squared value, and determine whether the genes are linked or not.