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Ch. 3 - Mendelian Genetics
Klug - Concepts of Genetics 12th Edition
Klug12th EditionConcepts of GeneticsISBN: 9780135564776Non è quello che usi tu?Cambia libro di testo
Capitolo 3, Problema 18

The following are F₂ results of two of Mendel's monohybrid crosses.
Data table showing results of Mendel's monohybrid crosses for pod and flower traits with counts for each phenotype.
For each cross, state a null hypothesis to be tested using x² analysis. Calculate the x² value and determine the p value for both. Interpret the p-values. Can the deviation in each case be attributed to chance or not? Which of the two crosses shows a greater amount of deviation?

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Step 1: State the null hypothesis for each cross. For Mendel's monohybrid crosses, the null hypothesis typically states that the observed phenotypic ratios follow the expected Mendelian ratio of 3:1 (dominant to recessive phenotype). So, for both crosses, the null hypothesis is: "The observed phenotypic ratios fit a 3:1 ratio."
Step 2: Calculate the expected numbers for each phenotype based on the total observed individuals and the expected 3:1 ratio. For each cross, sum the observed counts to get the total number of individuals (N). Then calculate expected counts as follows: \(Expected_{dominant} = \frac{3}{4} \times N\) and \(Expected_{recessive} = \frac{1}{4} \times N\).
Step 3: Use the chi-square formula to calculate the chi-square (\(\chi^2\)) value for each cross: \(\chi^2 = \sum \frac{(Observed - Expected)^2}{Expected}\) Calculate this separately for each phenotype and then sum the values to get the total \(\chi^2\) for each cross.
Step 4: Determine the degrees of freedom (df) for the test. Since there are two phenotypic categories (dominant and recessive), the degrees of freedom is \(df = number\ of\ categories - 1 = 2 - 1 = 1\). Use the chi-square distribution table to find the p-value corresponding to the calculated \(\chi^2\) value and 1 degree of freedom.
Step 5: Interpret the p-values for each cross. If the p-value is greater than 0.05, the deviation from the expected ratio can be attributed to chance, and we fail to reject the null hypothesis. If the p-value is less than 0.05, the deviation is statistically significant, and we reject the null hypothesis. Compare the \(\chi^2\) values to determine which cross shows a greater amount of deviation from the expected ratio.

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Mendelian Monohybrid Cross and Expected Ratios

A monohybrid cross involves one gene with two alleles, typically showing a 3:1 phenotypic ratio in the F2 generation if one allele is dominant. Mendel's experiments established these expected ratios, which serve as a baseline for testing genetic hypotheses. Understanding these ratios is essential for comparing observed data to expected outcomes.
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Monohybrid Cross

Chi-Square (χ²) Test for Goodness of Fit

The chi-square test evaluates whether observed data deviate significantly from expected ratios due to chance. It calculates a χ² value by summing the squared differences between observed and expected counts, divided by expected counts. This test helps determine if deviations are statistically significant or likely due to random variation.
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Chi Square Analysis

Interpreting p-Values and Hypothesis Testing

The p-value derived from the χ² test indicates the probability that observed deviations occurred by chance under the null hypothesis. A high p-value (usually >0.05) suggests no significant deviation, supporting the null hypothesis, while a low p-value indicates significant deviation. This interpretation guides conclusions about genetic inheritance patterns.
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Chi Square and Linkage
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