20 Investigating Monhybrid Crosses Using the Graphing Calculator This activity will use the graphing calculator s random number generator to simulate the production of gametes in a monohybrid cross. The height of peas is the trait that can vary in peas. Peas can be tall or peas can be short. There is a gene that is responsible for this trait, and it has two forms or alleles: T for tall and t for short. The graphing calculator will simulate a cross of two peas that are heterozygous for being tall, Tt. This is based on the ability of the graphing calculator to generate 1 s and 2 s randomly much like flipping a coin to obtain random heads and tails. A 1 represents the T gamete for tall peas and a 2 represents a t gamete for short pea. The genotype for particular individual is found by adding both integers together. Thus a tall pea that is homozygous dominant, TT, is represented by the number 2. T T = 2 1 + 1 = 2 Other possible genotypes may be: Tt = 3 tt = 4 PURPOSE This exercise uses the graphing calculator to demonstrate genotypic ratios of a classic Mendelian Monohybrid cross. MATERIALS TI-83 plus graphing calculator PROCEDURE 1. Write a hypothesis predicting the phenotypic ratio for the offspring of a cross involving two peas that are both heterozygous for tall, Tt x Tt. Be sure and state your hypothesis in the If then format. 2. Turn on your calculator and press to clear the screen. 3. Clear all list by pressing, [mem]. Move cursor to ClrAllLists (by pressing the key OR press ) and then press two times. Done should appear on the screen. Laying the Foundation in Biology 529
20 4. * Optional If your teacher decides that your calculator needs to be seeded, then do the following steps. a. Key in your birthday (i.e. 100385 for October 3rd 1985) b. Press, then press and move the cursor at the top of the screen to PRB (probability) by pressing key (Figure 1). c. Then press to store this number to the random number function. Press a second time to execute the function (Figure 2). Figure 1 Figure 2 5. Press (Figure 3) and then. The list screen should appear. Figure 3 Figure 4 6. Put the cursor at the top of L1 (by pressing ) and press. A blinking black square will appear at the bottom after L1 =. 7. List 1 represents a parental pea plant that is heterozygous or Tt. The pea plant will produce 100 gametes either T or t. The calculator will randomly produce the gametes. This is done by randomly choosing the integer 1 or 2 one hundred times. If the calculator chooses the number 1, the gamete will be a T and if the calculator chooses the number 2, the gamete will be t. 530 Laying the Foundation in Biology
20 8. With the cursor still blinking at the bottom, press and move the cursor at the top of the screen to PRB (probability) with the key. 9. You want the calculator to choose either a 1 or a 2 randomly and to make that random choice 100 times. Move the cursor down to randint (Figure 4) with the, then press, OR press. This should return you to the list screen and at the bottom a blinking black square should appear after L1 =randint(. 10. At this time you want to direct the calculator to randomly select 1 s and 2 s one hundred times. Do this by pressing,,,,,,,. The screen at the bottom should now look like this L1 =. randint(1,2,100). See Figure 5. Press and L1 should be filled with 100 entries of either a 1 or a 2. Figure 5 Figure 6 11. List 2 represents the parental pea plant # 2, and it is also heterozygous or Tt. The male is to make 100 gametes either T or t. The calculator will randomly produce the gametes. Put the cursor at the top of L2 and repeat steps 7-10 (Figure 6). 12. Now the gametes from the female (L1) need to be fertilized by the gametes from the male (L2). This is done by adding the two lists. Put the cursor on L3 and press. At the bottom of the list screen should appear L3=. Now press,, [L1],,,, [L2] (Figure 7). Press and L3 should fill in with the sums of L1 and L2 (Figure 8). List 3 represents the genotypes that result from the fertilization from the various gametes to produce 100 offspring. The following numbers represent the following genotypes: a. TT = 2. b. tt = 3. c. tt = 4. Laying the Foundation in Biology 531
20 Figure 7 Figure 8 13. To view this graphically, press,, (Figure 9). At this time, make sure to put your cursor on PLOT 1 and press and move the cursor down to ON and press. Both PLOT 1 and ON should be highlighted. All the other plots should be inactivated. Figure 9 Figure 10 14. Move the cursor down and activate the bar graph, by putting the cursor on the bar graph and pressing. 15. The list that you want to display is L3. Move the cursor down to the next line and press, (Figure 10). 16. To view the bar graph, now press,. 532 Laying the Foundation in Biology
20 17. The bar graph should appear displaying the number of TT, Tt, tt genotypes. To look at this, press. Using the or, place the blinking cursor on the left bar (Figure 11). This represents the T T genotypes and the bottom screen n= displays the number. Use the to place the blinking cursor on the middle bar. This represents the heterozytotes, Tt and the bottom screen n= displays the number. Use the to place the blinking cursor on the right bar. This represents the homozygotes, tt, and the bottom screen n= displays the number. 18. Record the ratios of TT, Tt, and tt generated in the data table provided on the student answer sheet. Figure 11 19. Survey three other groups and compare your data. Discuss with your partner possible explanations for the variation found among different groups. Laying the Foundation in Biology 533
20 Name Period HYPOTHESIS Investigating Monhybrid Crosses Using the Graphing Calculator DATA AND OBSERVATIONS Predicted Number of Offspring Calculator Number of Offspring Difference TT (4) Tt (3) tt (2) 534 Laying the Foundation in Biology
20 CONCLUSION QUESTIONS 1. How do the predicted ratios differ from the calculator ratios? 2. How does this demonstrate what can be expected in actual crosses such as fruit flies? 3. Survey some of your classmates and determine if their results are similar or different from yours. Explain your findings. 4. What is the predicted phenotypic ratio for tall versus short offspring? In a sample of 100 offspring how many of each phenotype are expected? How many offspring of each phenotype were predicted by your calculator? 5. Based on the data produced by the calculator, determine a Chi-square value for both the phenotypes and genotypes produced. Remember the equation for Chi-Square is 2 (expected - observed) χ = expected What is the probability that your deviation is due to random chance? 2 Laying the Foundation in Biology 535
20 6. Are the results acceptable and meet the predicted results? Most biologists agree that deviations that have a chance probability greater than or equal to.05 (5% or 1 in 20) are not statistically significant. 7. If a person wanted to demonstrate a cross of Tt x tt with the graphing calculator, what changes in the procedure would need to be made? Table of Critical Values of X 2 p is the probability that the results could be due to chance alone. The numbers in parentheses below each value of p restate p in terms of chance: 9 in 10 likelihood that the results could be due chance alone. Degrees of freedom p = 0.9 (9 in 10) p = 0.5 (1 in 2) p = 0.2 (1 in 5) p = 0.05 (1 in 20) p = 0.01 (1 in 100) p = 0.001 (1 in 1000) 1 0.158 0.455 1.642 3.841 6.635 10.827 2 0.214 1.386 3.219 5.991 9.210 13.815 3 0.584 2.366 4.642 7.815 11.345 16.268 4 1.064 3.367 5.989 9.488 13.277 18.465 5 1.610 4.351 7.289 11.070 15.086 20.517 6 2.204 5.348 8.558 12.592 16.812 22.457 7 2.333 6.346 9.903 14.067 18.475 24.322 8 3.490 7.344 11.303 15.507 20.090 26.125 9 4.168 8.343 12.242 16.919 21.660 27.877 10 4.865 9.342 13.442 18.307 23.209 29.588 536 Laying the Foundation in Biology