Dr. Ara B. Dopsis and Dr. C. Ellie Gans are performing genetic crosses on daisy plants. They self-fertilize a blue-flowered daisy and grow 100 progeny plants that consist of 55 blue-flowered plants, 22 purple-flowered plants, and 23 white-flowered plants. Dr. Dopsis believes this is the result of segregation of two alleles at one locus and that the progeny ratio is 1:2:1. Dr. Gans thinks the progeny phenotypes are the result of two epistatic genes and that the ratio is 9:3:4.
The two scientists ask you to resolve their conflict by performing chi-square analysis on the data for both proposed genetic mechanisms. For each proposed mechanism, fill in the values requested on the form the researchers have provided for your analysis.
Use the form below to calculate chi-square for the 9:3:4 hypothesis of Dr. Gans.

Verified step by step guidance

1. Step 1: Understand the problem. The goal is to perform a chi-square analysis to test the hypothesis proposed by Dr. Gans, which suggests a 9:3:4 phenotypic ratio resulting from two epistatic genes. The observed data consists of 55 blue-flowered plants, 22 purple-flowered plants, and 23 white-flowered plants, totaling 100 progeny.
2. Step 2: Calculate the expected numbers for each phenotype based on the 9:3:4 ratio. First, determine the proportion of each phenotype in the ratio: 9/16 for blue, 3/16 for purple, and 4/16 for white. Multiply these proportions by the total number of progeny (100) to get the expected counts for each phenotype.
3. Step 3: Use the chi-square formula to calculate the chi-square value for the 9:3:4 hypothesis. The formula is: χ² = Σ((O - E)² / E), where O is the observed count, E is the expected count, and the summation is over all phenotypic categories. For each phenotype (blue, purple, white), calculate the difference between observed and expected counts, square the difference, divide by the expected count, and sum these values.
4. Step 4: Determine the degrees of freedom (df) for the chi-square test. The formula for degrees of freedom is df = (number of phenotypic categories - 1). In this case, there are three phenotypic categories (blue, purple, white), so df = 3 - 1 = 2.
5. Step 5: Compare the calculated chi-square value to the critical value from a chi-square distribution table at the appropriate degrees of freedom (df = 2) and significance level (commonly 0.05). If the calculated value is greater than the critical value, the 9:3:4 hypothesis is rejected; otherwise, it is not rejected.

Key Concepts

Alleles and Loci

Alleles are different versions of a gene that can exist at a specific locus, or position, on a chromosome. In the context of the daisy plants, the blue, purple, and white flower colors are determined by different alleles at a single locus. Understanding how alleles segregate during reproduction is crucial for predicting the phenotypic ratios of offspring.

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 this case, it will help assess whether the observed flower color ratios in the progeny fit the expected ratios proposed by Dr. Dopsis (1:2:1) or Dr. Gans (9:3:4). This analysis is essential for validating or refuting the genetic hypotheses.

Epistasis

Epistasis refers to the interaction between genes, where the expression of one gene can mask or modify the expression of another gene. In Dr. Gans's hypothesis, two epistatic genes are proposed to explain the 9:3:4 ratio of flower colors. Understanding epistasis is important for interpreting complex inheritance patterns and phenotypic outcomes in genetic crosses.