A Drosophila experiment examining potential genetic linkage of X-linked genes studies a recessive eye mutant (echinus), a recessive wing-vein mutation (crossveinless), and a recessive bristle mutation (scute). The wild-type phenotypes are dominant. Trihybrid wild-type females (all have the same genotype) are crossed to hemizygous males displaying the three recessive phenotypes. Among the 20,765 progeny produced from these crosses are the phenotypes and numbers listed in the table. Any phenotype not given is wild type.

Use chi-square analysis to demonstrate that the data in this experiment are not the result of independent assortment.

Verified step by step guidance

1. Step 1: Understand the problem and identify the hypothesis. The null hypothesis (H₀) in this case is that the genes are assorting independently. To test this, we will use a chi-square analysis to compare the observed phenotypic frequencies with the expected frequencies under independent assortment.
2. Step 2: Calculate the expected frequencies for each phenotype under the assumption of independent assortment. First, determine the total number of progeny (20,765) and the proportions expected for each phenotype based on Mendelian inheritance. For three genes, independent assortment predicts a 1:1:1:1 ratio for each combination of phenotypes. Use this ratio to calculate the expected frequency for each phenotype.
3. Step 3: Apply the chi-square formula for each phenotype. The formula is: χ² = Σ((Oᵢ - Eᵢ)² / Eᵢ), where Oᵢ is the observed frequency and Eᵢ is the expected frequency for each phenotype. Substitute the observed and expected values for each phenotype into the formula.
4. Step 4: Sum the chi-square values for all phenotypes to obtain the total chi-square statistic. This value will represent the overall deviation of the observed data from the expected data under the null hypothesis.
5. Step 5: Compare the calculated chi-square statistic to the critical value from a chi-square distribution table. Use the degrees of freedom (df), which is calculated as the number of phenotypic categories minus 1. If the chi-square statistic exceeds the critical value at a chosen significance level (e.g., 0.05), reject the null hypothesis and conclude that the genes are not assorting independently.

Key Concepts

Genetic Linkage

Genetic linkage refers to the tendency of genes located close to each other on the same chromosome to be inherited together during meiosis. This phenomenon contrasts with independent assortment, where genes segregate independently. In the context of the Drosophila experiment, analyzing the inheritance patterns of the X-linked genes can reveal whether they are linked or assorting independently based on the observed progeny ratios.

Chi-Square Analysis

Chi-square analysis is a statistical method used to determine if there is a significant difference between observed and expected frequencies in categorical data. In genetics, it helps assess whether the distribution of phenotypes in progeny aligns with expected ratios under the assumption of independent assortment. A significant chi-square value indicates that the observed data deviates from what would be expected if the genes assorted independently, suggesting linkage.

Phenotypic Ratios

Phenotypic ratios represent the relative frequencies of different phenotypes observed in the offspring of a genetic cross. In this experiment, the ratios of the various phenotypes, including recessive mutants and wild types, provide insight into the genetic relationships between the traits. By comparing these ratios to expected ratios under independent assortment, researchers can infer whether the genes are linked or assorting independently.