13. A plant with red fruit is crossed to a plant with white fruit. The F1 progeny had red fruits. On selfing the F1 two kinds of progeny were observed, plants with red fruits and those with white fruits. To test whether it was a case of recessive epistatic interactions a chi-square test was performed. A value of 1.062 was obtained (chi- square value of Poos=3.841 for Degree of freedom=1).
The following statements were made:
A. The null hypothesis was that plant with red and white fruits will occur in a 9:7 ratio
B. The null hypothesis was that plant with red and white fruits will occur in a ratio
C. Based on the chi square value, it is a case of recessive epistatic interactions
D. Based on the chi square value, it is not a case of recessive epistatic interactions
Which of the combination of above statements is correct?
(1) A and C (2) A and D
(3) Band C (4) B and D
Here is a detailed solution and explanation of the question on recessive epistatic interactions tested by chi-square, followed by an SEO-friendly article.
Detailed Solution and Explanation
In this question:
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A red fruit plant is crossed with a white fruit plant.
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F1 progeny all have red fruits.
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On selfing F1, two types of fruit colors appear: red and white.
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A chi-square test was done for the hypothesis of recessive epistasis showing expected ratio 9:7.
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Obtained chi-square value = 1.062 with critical chi-square (degree of freedom=1) = 3.841.
Step 1: Understanding the Hypotheses
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Statement A: The null hypothesis is red:white = 9:7 (expected ratio in duplicate recessive epistasis).
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Statement B: The null hypothesis is red:white = 1:1 (wrong for recessive epistasis in this case).
The correct null hypothesis for testing recessive epistasis in duplicate recessive epistasis cases is usually 9:7, not 1:1.
Step 2: Interpreting the Chi-square test result
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Calculated chi-square = 1.062
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Critical value at P0.05 (df=1) = 3.841
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Since 1.062 < 3.841, we fail to reject the null hypothesis.
This means the observed data fit well with the expected 9:7 ratio, supporting recessive epistasis.
Step 3: Assessing Statements C and D
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Statement C: Based on chi-square value, it is a case of recessive epistatic interactions. This is true as the observed ratio fits expected 9:7.
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Statement D: Based on chi-square value, it is not a case of recessive epistatic interactions. This is false.
Correct combination of statements:
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A (null hypothesis 9:7)
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C (fit supports recessive epistasis)
So, correct answer is (1) A and C.
Explanation of Each Option
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Option A: Correct null hypothesis for recessive epistasis duplicate interaction is 9:7. (True)
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Option B: Wrong null hypothesis for this epistasis study; 1:1 ratio would not reveal recessive interactions here. (False)
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Option C: Since chi-square value is less than the critical value, null hypothesis (epistasis 9:7 ratio) is accepted, indicating recessive epistatic interaction. (True)
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Option D: Since null hypothesis isn’t rejected, this statement is false.
Introduction
Recessive epistasis is a genetic interaction where the recessive alleles of one gene mask the expression of alleles at another gene, affecting traits like fruit color. In genetics, the chi-square test helps confirm if observed progeny ratios fit expected ratios such as 9:7 for recessive epistasis. This article explains how to interpret such data with examples and hypothesis testing.
Explanation of Null Hypothesis in Chi-square Test
In a genetic cross involving recessive epistasis, the expected phenotypic ratio often differs from classic Mendelian ratios. For duplicate recessive epistasis, the typical expected ratio of phenotypes is 9:7 (dominant to recessive traits). This ratio forms the null hypothesis—the assumption that observed data should match this ratio unless proved otherwise by statistical testing.
Interpreting the Chi-square Test Result
The chi-square (χ²) test measures how much observed data deviate from expected ratios. A calculated chi-square value less than the critical value (from chi-square distribution tables at a set significance level) means failing to reject the null hypothesis. This indicates that the data fit the predicted ratio well, supporting the hypothesis of recessive epistasis.
Practical Application: Fruit Color Inheritance
For example, crossing plants with red fruit and white fruit may yield F1 all red. Selfing F1 showing a progeny ratio of red:white that fits the 9:7 ratio, and a chi-square value of 1.062 (less than 3.841 critical value), confirms recessive epistatic interaction. The color inheritance pattern here is best explained by duplicate recessive genes affecting the fruit color phenotype.
Conclusion
Geneticists use chi-square tests effectively to understand complex gene interactions like recessive epistasis. Knowing how to set the correct null hypothesis and interpret the chi-square values helps confirm genetic phenomena such as the 9:7 phenotypic ratio, important in plant breeding and molecular genetics research.
This comprehensive explanation clarifies the question and related concepts in recessive epistasis and chi-square test analysis.
If you want, I can also prepare a detailed stepwise calculation or quiz-style explanation. Just let me know!
