Sepia Eyes and Curved Wings

You will now investigate some of the possiblities when more than one trait is investigated at the same time. Mendel did this and discovered his principle of independent assortment. As the crosses get more complicated, it also gets harder and harder to know whether the observed ratios are really the same as what you expected. To deal with this, we need to use a statistical test called the chi-square test.

Specific learning objectives for this assignment:

Scientific Method Learning Goals

  • Propose reasonable hypotheses to explain experimentally derived data
  • Devise experiments to test the hypothesis
  • Evaluate the results of the experimental test and determine whether the hypothesis is supported or not, using statistical methods when appropriate
  • Revise hypotheses to incorporate new results
  • Write a succinct conclusion describing the experimental evidence supporting the most likely hypothesis

Mendelian genetics

  • Diagram the experimental sequence whereby it can be shown that discrete alternative phenotypes are determined by the alleles of a single gene.
  • Use the principle of equal segregation to predict progeny of crosses of known genotypes for a single gene.
  • Use the principles of independent assortment and equal segregation, and the product and sum rules of probability to predict progeny ratios from independent genes.
  • From progeny ratios, deduce parental genotypes.
  • Demonstrate the use of branch diagrams and Punnett squares in predicting progeny genotypes and phenotypes.
  • Use a chi-square test to evaluate whether data from a cross is close enough to the expected ratio.
  • Deduce sex linkage from inheritance data in experimental organisms.
  • Predict outcomes of crosses involving sex-linked genes.
  • Draw a diagram showing the organization of sex-linked and pseudo-autosomal genes on the X and Y chromosomes.
  • Deduce lethality from inheritance data in experimental organisms.
  • Infer dominance/recessiveness from cross data.
  • Infer the type of gene interaction implied by 9:7 and 9:4:3 ratios in F2.
  • Predict phenotypic ratios from given modes of gene interaction.
  • Design and interpret crosses of unknown traits and be able to determine genotypes and make predictions about crosses when the inheritance may be autosomal, sex-linked, lethal, multiple genes, dominant/recessive, or include epistatic interactions.

Analyze the following traits using the FlyLab. For this cross you will be analyzing two traits at the same time. Thus in addition to determining the inheritance pattern of each trait individually you need to explain the inheritance patterns that occur when both mutations are involved in the same cross (a dihybrid cross). In addition, you should use the chi-square test to test any hypotheses that you propose, if a chi-square test is possible for your hypothesis. Don't forget to give phenotypic and genotypic diagrams of all relevant crosses, with results and your conclusions. You may work in pairs and just turn in one report per pair. There is a grading rubric for each of these problems showing the characteristics expected in good write-ups of the problems (it is different than the one for monohybrid crosses that we have been using, so be sure to check it out - see below). this first assignment is due by 11 AM, Monday, February 7th. Below I will quickly walk you through setting up a dihybrid cross and analyzing the results with a chi-square test, or you can just get started with the actual cross (as with purple eye, do not write up the shaven and brown experiment described below, it's just to help you understand the process).

Setting up dihybrid crosses and doing Chi-square tests:

Sample walk-through: For a dihybrid cross we need two different traits to follow. Let's try shaven bristles and brown eyes.

Step 1, designing the flies:

  1. Log in to the FlyLab site
  2. Click on the button that says "Start FlyLab" and wait for the program to download to your computer (this may take a couple of minutes). When finished downloading you should see a a gray drawing of two fruit flies.
  3. As in VF 1, design a female fly with shaven bristles and a male fly with brown eyes and then mate them.
  4. You should get an F1 generation that is all wild-type (wt), suggesting that both of these traits are recessive. Now cross the wt F1 to produce the F2 generation.
  5. When the results come back you will see two wt progeny and an arrow pointing down, below the statement that there are "six fly images". If you look at the other images you will see flies with shaven bristles, like the parental female, flies with brown eyes, like the parental male, and at the bottom, flies with both shaven bristles and brown eyes. This is different than the result s we've seen before because we have a new fly phenotype that doesn't look like either of the parents or a wt.
  6. Click on "Analyze Results" to see the numbers for these different types of progeny.
  7. There's lots of different numbers here but if you look close you'll see that there is little difference between the numbers for males and females so select the radio button beside "Ignore sex".
  8. Now there should be just four sets of numbers, for wild-type, shown as a +, shaven (SV), brown (BW) and shaven and brown together, (SV,BW). The numbers will seem a little strange, but there should be much more wt than anything else and fewer SV, BW than the others.

Step 2, determining the expected ratios:

  1. If the traits are assorting independently (as Mendel's pea traits did) than we would expect 3/4 of the F2 to have wt bristles and 3/4 to have wt eyes. If you add together the + flies and the BW flies (which have wt eyes) the number should be about 3/4 of the total (if you used the default this will be about 750/1000).
  2. Probability theory says that if 3/4 of the flies have wt bristles and 3/4 of the flies have wt eyes and these two traits are independent, then 3/4 x 3/4 = 9/16 of the flies should be wt for both bristles and eyes, or about 560 to 570 out of 1,000.
  3. As 1/4 of the flies should have shaven bristles, then we would expect 1/4 x 3/4 (wt eyes) = 3/16 SV, about 185 to 190 out of 1,000
  4. The same type of calculation gives us 3/16 BW and 1/4 x 1/4 = 1/16 SV,BW. It may be hard to look at your numbers and see if you really got those ratios, especially as there can be a lot of variation in the results.
  5. To see if your numbers really match what we would expect for independent recessive traits, we need to do a statistical test called a chi-square test.

Step 3, doing a Chi-square test:

  1. Click on the tab labeled "Chi-square Analysis" near the top right corner of the results page.
  2. In the new window that appears we have the phenotypes and numbers from before along with a column of empty fields.
  3. First click on "Ignore Sex".
  4. To test our results we need to put in the expected ratios in the empty fields. As we expected the numbers of different fly types, as calculated above, to be in a ratio of 9 + : 3 SV:3 BW: 1 SV, BW enter a 9 opposite the +, a 3 opposite the SV, a 3 opposite the BW and a 1 opposite the SV, BW (you could also put in 9/16, 3/16, 3/16, and 1/16, but this is easier).
  5. Now click on "Test Hypothesis".
  6. You should get back a table with the Chi-square Term for each row and a total "Chi-square Test Statistic" at the bottom along with the degrees of freedom, which should be 3, and the probability of getting a Chi-square Test Statistic as large as the one you got if your hypothesis was true, the "Level of Significance".
  7. For scientific purposes, a level of significance above .05 is acceptable and the program will give a recommendation of "Do not reject your hypothesis".
  8. Most likely you have a chi-square score below 11 and a recommendation to not reject your hypothesis.
  9. However, 1 time out of 20 the test will reject your hypothesis, even if it is true.
  10. If this happens to you need to repeat the cross and try the test again.
  11. If the traits are not independent or the traits are not simple recessives with 3:1 ratios, then it will fail this test again and you will need to come up with a new hypothesis. This will almost certainly happen some of the time, so beware, .

Step 4, doing a test cross

  1. After returning to the lab, a good follow up cross is the test cross. In a test cross you cross one of the dihybrid F1's with a homozygous recessive. This should produce a 1:1:1:1 ratio if the genes are assorting independently, and if your hybrid cross failed the 9:3:3:1 test is usually easier to interpret to figure out what is going wrong, or to test your new hypothesis.
  2. Select one of the F1 progeny (they will be at the top of the scolling list of flies) and design a new homozygous recessive, in this case a brown, shaven fly.
  3. Cross the two flies
  4. Test the reults for a 1:1:1:1 ratio if independently asorting, or for the appropriate ratio that fits your new hypothesis.

For each of the dihybrid problems you should determine the inheritance pattern of each of the two traits, make a prediction for what will happen in a dihybrid cross, and test your prediction with a chi-square test. If the test fails then you will need to come up with a new hypothesis to explain your results, and , if possible, test that hypothesis. You should do both an F2 cross (cross two F1 flies) and a test cross of a heterozygous F1. If you're getting confused, you can always cross just one trait at a time, as in the first assignments, and then, once you are sure you understand the traits individually, try to determine what is going in crosses involving both traits. You do not need to include these side experiments in your report, unless they include necessary data yo need to explain your results.

Grading rubric to be used to evaluate the report for each problem below.

Criteria
Value
Evidence
1. All crosses are diagramed both phenotypically and genotypically with clear symbols that reflect the hypothesized inheritance pattern.
2
 Symbols for alleles are used to describe the genotypes along with the phenotypic symbols, and the allele symbols are used correctly to show the type of inheritance and correct number of alleles.

2. After each cross the results are analyzed and there is a clear statement of the current hypothesis
2
 Report has a short paragraph after each cross that discusses whether the results of the cross support the current hypothesis, and, if not, proposes a new hypothesis.
3. Hypotheses are tested statistically using the chi-square test in an appropriate manner
0.5
 The current hypothesis is used to calculate expected ratios and numbers for a chi-saquare test, and the resulting p-value is interpreted with respect to the validity of the hypothesis.
4. Predictions based on the hypothesis are made for each cross (after the first cross) before doing the cross and the crosses chosen are appropriate for testing the current hypothesis.
1
 After analyzing each cross there is a sentence or two describing what the next cross will be, what progeny ratios are expected in the progeny, and why those ratios are expected.
5. Crosses involving both traits simultaneously are used and the student shows an understanding of independent assortment by correctly predicting the results if independent assortment is true
1
 There is data for each cross that uses both traits and the forked-line approach is used to calculate the expected ratios based on the current hypothesis about the inheritance of the traits.
6. Student perseveres and attempts to figure out what is going on even when there is no obvious answer.
0.5
 If the results do not support a hypothesis it is stated in the report that the hypothesis is false and at least one alternative hypotheses is then tested.
7. There is a proper conclusion to the report.
1
 There is a summary paragraph at the end of the report that states the hypothesis that the student feels is most likely and describes the results that support the chosen hypothesis. Hypothesis explains the inhertiance of both traits and the results from crosses with both traits at the same time.
8. Student shows an understanding of all of the genetics principles covered so far
2
 Appropriate hypotheses are tested and are rejected if not supported by the data, and correct allelic and genotypic descriptions are given for P, F1 and F2 flies for both traits and for the combination of the traits.

 

2/7 Assignment, Sepia Eyes and Curved Wings due Monday, 11 AM (5 pts.)

Bell CSU Chico Library
This document is copyright of Jeff Bell
Last Update: Monday, February 7, 2005 11