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.

What is your conclusion regarding these two genetic hypotheses: the 1:2:1 hypothesis and the 9:3:4 hypothesis?

Question

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.

What is your conclusion regarding these two genetic hypotheses: the 1:2:1 hypothesis and the 9:3:4 hypothesis?

Accepted Answer

Hi, everyone. Let's take a look at this practice problem together. A di hybrid cross is made between two genes exhibiting epitasis. The F2 generation produces 68 individuals with the dominant phenotype and 28 individuals with the recessive phenotype. If the expected ratio is 9-3-4, what is the Chi Square value for this set of data? The answer options are a 11. B 16. c 22.3 and D 28.4. Now, in order to solve for the chi square value, we must know what the chi square formula is and that formula is on the screen. The formula is chi square equals Sigma symbol, open parentheses, O minus E close parentheses squared divided by E where O is the observed values and E is the expected values. Recall that the Sigma symbol means to sum up. So we will sum all together the calculations for each outcome the observed values are given to us in the question and the expected values we will solve for. So on the screen is going to be a table that we will use to organize our information. The first column is class, the second is the observed value. The third is the expected values. And the fourth column is the chi square calculation for a epitasis dy hybrid cross. There are three possible phenotypes. So each one of those is a class. If we fill in the table for each phenotype in a separate row, there is dominant, intermediate and recessive. The observed values given in the question was for the dominant and 28 for the recessive. So let's fill those into the table 68 for the dominant 28 for the recessive. And that means zero observed values for the intermediate. Now we are told the phenotypic expected phenotypic ratio is 9-3-4. We can use this ratio to determine the expected number of offspring for each phenotype to do this. We need to know the total number of offspring Which is the 68 plus the 28, plus 28 equals 96 total offspring. Now to calculate each of the expected values for column three, we will take the expected number for that phenotype from the ratio and divide that by the total number of outcomes in the ratio and multiply that by the total number of offspring. let's do the calculations together to see how that works. So for our expected values, we begin with the dominant phenotype That is calculated by nine Dominant, divided by 16 possible outcomes in the ratio multiplied by 96 total offspring equals 54. Now we just repeat that process for the intermediate and recessive phenotypes. So the intermediate Equals three, this time Divided by 16, multiplied by 96 equals 18. And lastly recessive phenotype equals four, Divided by 16, multiplied by 96 equals 24. So these are the expected values. And let's fill in the table 54 for dominant 18 for intermediate and 24 for it. The recessive, the next step is to do the chi square calculation for each of the phenotypes and fill in this fourth column. Recall that the equation is open parentheses. O minus E closed parentheses squared divided by E. So let's do those calculations together. The chi square values we begin with the dominant Is calculated open parentheses. The observed value is 68 Minour expected value 54 close parentheses squared Divided by expected value, Equals 3. for the intermediate phenotype. The chi square value is calculated by open parentheses, observed value zero minus expected value 18, close parentheses squared Divided by expected value 18 And that equals 18. Lastly, the recessive chi square value is calculated open parentheses observed value 28 minus expected value 24 close parentheses squared Divided by 24 expect which is the expected value and that equals 0.667. Now we can enter those values into the table 3.630 for dominant 18 for intermediate and 0.667 for the recessive. The last step is to sum up each of the high score values for each of the class. So our total sum is 3.630 plus plus 0. equals 22.297, Which equals 22.3. Therefore, the correct answer is option C 22.3. All right, everyone. I hope you found this helpful and I'll see you soon for the next practice problem.

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Key Concepts

Mendelian Inheritance and Genotypic Ratios

Epistasis and Modified Phenotypic Ratios

Chi-Square Test for Genetic Hypothesis Testing