T. H. Morgan's data on eye color and wing form genetic linkage between the two genes. Test the genetic linkage (shown in the figure below) data with chi-square analysis, and show that the results are significantly different from the expectation under the assumption of independent assortment.

Verified step by step guidance

1. Step 1: Understand the hypothesis and data. The null hypothesis assumes that the two genes (eye color and wing form) assort independently, meaning the observed phenotypic ratios should follow Mendel's independent assortment. The alternative hypothesis is that the genes are linked, so the observed ratios will deviate from expected independent assortment ratios.
2. Step 2: Determine the expected phenotypic ratios under independent assortment. For two genes with two alleles each, the expected phenotypic ratio is typically 9:3:3:1 for a dihybrid cross, or 1:1:1:1 for a test cross, depending on the experimental design. Identify which ratio applies based on Morgan's experimental setup.
3. Step 3: Calculate the expected number of offspring for each phenotypic class by multiplying the total number of offspring by the expected proportion for each class under independent assortment.
4. Step 4: Use the chi-square formula $\chi ^2={\sum }_{}^{}$in(O_i-E_i)2E_i, where $O$_i is the observed count and $E$_i is the expected count for each phenotypic class. Calculate this value by summing over all classes.
5. Step 5: Determine the degrees of freedom, which is the number of phenotypic classes minus 1, and compare the calculated chi-square value to the critical value from the chi-square distribution table at an appropriate significance level (usually 0.05). If the calculated value exceeds the critical value, reject the null hypothesis, indicating significant genetic linkage.

Key Concepts

Genetic Linkage

Genetic linkage occurs when two genes are located close together on the same chromosome and tend to be inherited together, rather than assorting independently. This linkage affects the expected ratios of offspring phenotypes, deviating from Mendel’s law of independent assortment.

Chi-Square Test for Independence

The chi-square test is a statistical method used to compare observed data with expected data under a specific hypothesis, such as independent assortment. It calculates a value that helps determine if deviations from expected ratios are due to chance or indicate a significant difference.

Mendelian Independent Assortment

Mendel’s law of independent assortment states that alleles of different genes segregate independently during gamete formation, leading to predictable phenotypic ratios. Testing this assumption helps identify whether genes are linked or assort independently.