How is the chi-squared test used in genetic studies to analyze frequency distributions?

Sourav PanNovember 9, 2024

Answered step-by-step

The chi-squared test is a statistical tool widely used in genetic studies to analyze frequency distributions and determine whether observed data deviate significantly from expected outcomes based on specific hypotheses. Here’s how the chi-squared test is applied in genetics:

Purpose of the Chi-Squared Test in Genetics

1. Testing Mendelian Ratios: The chi-squared test is often employed to evaluate whether the observed frequencies of phenotypes in offspring conform to expected Mendelian ratios (e.g., 3:1 for a monohybrid cross or 9:3:3:1 for a dihybrid cross). By comparing observed data to expected ratios, researchers can assess the validity of Mendelian inheritance patterns.
2. Assessing Gene Linkage: The test can also be used to determine if two genes are linked or assort independently. If genes are unlinked, the expected phenotype combinations will reflect independent assortment. Conversely, if the observed frequencies differ significantly from expectations, it may suggest that the genes are linked.

Steps in Performing a Chi-Squared Test

1. Formulate Hypotheses:
   • Null Hypothesis (H0): Assumes that there is no significant difference between observed and expected frequencies (e.g., the genes assort independently).
   • Alternative Hypothesis (Ha): Assumes that there is a significant difference, indicating potential linkage between genes.
2. Collect Data:
   • Gather observed frequencies of phenotypes from genetic crosses. For example, in a dihybrid cross of pea plants, you might observe counts for different combinations of traits.
3. Calculate Expected Frequencies:
   • Based on Mendelian ratios or other theoretical expectations, calculate the expected frequencies for each phenotype category.
4. Compute Chi-Squared Statistic:
   • Use the formula:
   χ2=∑(O−E)2/Eχ2​

   where $O$ is the observed frequency and $E$ is the expected frequency. This calculation quantifies how much the observed data deviate from what was expected.
5. Determine Degrees of Freedom:
   • Calculate degrees of freedom (df), typically determined by the number of categories minus one (df = k – 1).
6. Compare to Critical Value:
   • Use a chi-squared distribution table to find the critical value for your calculated degrees of freedom at a chosen significance level (commonly α = 0.05).
7. Make a Decision:
   • If the calculated chi-squared value exceeds the critical value, reject the null hypothesis, suggesting that there is a significant difference between observed and expected frequencies.

Example Application

In a study involving pea plants where you want to determine if two traits (e.g., seed shape and color) assort independently, you would:

• Conduct a dihybrid cross and record the phenotypes of offspring.
• Calculate expected ratios based on Mendelian inheritance.
• Use the chi-squared test to compare observed counts with expected counts.
• Determine if any significant deviation indicates linkage between traits.