The Chi-square Test and Genetics

1. In fruit flies (Drosophila melanogaster), wild type flies are normal looking and have no obvious mutations. Wild type traits tend to be dominant to many of the mutations that affect fruit flies. One recessive mutation in particular causes a fly to be born with white eyes. In 1910, Thomas Hunt Morgan noticed a white-eyed male fly in his experimental fly population. He bred this fly to several wild type females and 1,237 flies were produced in the F1 generation. Male and female flies were roughly in equal proportions, and all flies had normal red eyes. Morgan then allowed the F1 to mate with each other to produce the F2 generation. The F2 generation had mostly red-eyed flies, and some white-eyed flies, but all the white-eyes flies were males. a. Use Punnett squares to show how the white eye mutation was being passed on in the flies.

b. A student performed these crosses and, in the F2 generation, counted 824 flies with the wild phenotype (red eyes) and 297 flies with the white eye phenotype. Perform a Chi- square test to test the null hypothesis (H0) that the observed result of the crosses is statistically indistinguishable from the expected result.

Category Observed Expected Expected (O-E)2/E proportion Red eyed 824 3/4 840.75 0.33 White eyed 297 1/4 280.25 1.01 Total 1121 2 = 1.34

The critical value for 2 categories at 0.05 is 3.84.

Because 1.34 is less than this, the student accepts the null hypothesis (H0) that there is no statistically significant difference between the observed and expected result.

2. In the late 1890s, Austrian agronomist Erich Tschermak, German botanist Carl Correns, and Dutch botanist Hugo de Vries independently rediscovered Gregor Mendel’s work on genetics. Both Correns and Tschermak replicated Mendel’s experiments to test his hypotheses of independent assortment and segregation. For example, each crossed yellow and green (for cotyledon color) varieties of peas (Lathyrus odoratus), and self-fertilized the subsequent F1 progeny to get F2 progeny arrays. The F1 offspring were all yellow. Correns observed 1,394 yellow and 453 green, while Tschermak observed 3,580 yellow and 1,190 green. Are these values consistent with Mendel’s results? Use a chi-square test to compare each scientist’s results to what Mendel would have expected.

Correns:

Category Observed Expected Expected (O-E)2/E proportion yellow 1394 3/4 1385.25 .055 green 453 1/4 461.75 .165 Total 1847 2 = .220

0.220 is smaller than the critical value of 3.84 at 0.05

Tschermak:

Category Observed Expected Expected (O-E)2/E proportion yellow 3580 3/4 3577.5 .002 green 1190 1/4 1192.5 .005 Total 4770 2 = .007

0.007 is smaller than the critical value of 3.84 at 0.05

Comparing Correns’s results to Tschermak’s results using the Chi square test: 2 In both experiments, the was less than the critical value at 0.05, so H0 was accepted. In Correns’s experiment, the 2 value was 0.220, which means that the probability of his distribution occurring by chance was between 0.45 and 0.15. In Tschermak’s experiment,the 2 value was 0.007, which means that the probability of his distribution occurring by chance was more than 0.90. These differences could be attributed to the difference in sample size between the two experiments (1847 for Correns and 4770 for Tschermak).

3. A group of fish biologists were studying the genetics of eye color and body patterning in largemouth bass (Micropterus salmoides). They crossed a largemouth bass with stripes and red eyes with another largemouth bass that had black eyes and no stripes (plain). An F1 generation (brood) of 134 fish was produced and all the offspring looked the same. From this F1 generation, 5 males and 5 females were randomly selected, paired, and mated. Each breeding pair produced one brood (ranging between 45 and 187 little fish), thus creating the F2 generation. The results of the F1 cross (the F2 generation) are summarized below in Table 1.

Table 1. Results of a dihybrid cross between five pairs of Largemouth Bass parents.

Breeding Phenotype Pair Total Stripes/Red Eyes Stripes/Black Eyes Plain/Red Eyes Plain/Black Eyes 1 80 50 15 12 3 2 101 64 21 12 4 3 45 24 10 9 2 4 187 106 31 36 14 5 67 39 15 9 4 Total 480 283 92 78 27

a. What are the dominant phenotypes and what are the recessive phenotypes? Dominant phenotypes: striped body patterning and red eye color Recessive phenotypes: plain body patterning and black eye color

b. What is the genotype for all 134 fish in the F1 Brood? Striped with red eyes

c. Construct a Punnett Square that shows the predicted outcome for the phenotypes of the F2 generation.

d. Can we accept these results as those from a true dihybrid cross? Provide statistical evidence and a statement that argues in favor of the evidence.

Category Observed Expected Expected (O-E)2/E proportion Stripes/Red 283 9/16 270 0.62 Strips/Black 92 3/16 90 0.04 Plain/Red 78 3/16 90 1.60 Plain/Black 27 1/16 30 0.30 Total 480 2 = 2.56

2.56 is smaller than the critical value of 7.81 at 0.05 (H0 is supported) and the probability of the distribution occurring by chance is 0.50. Therefore, we can accept the evidence that these data are reflective of a true dihybrid cross.

Chi-Square Table of Critical Values

Probability of Distribution Occurring by Chance 0.99 0.95 0.90 0.75 0.70 0.50 0.30 0.25 0.10 0.05 0.03 0.01 0.01 # of df Categ Critical Values 1 2 0.00 0.00 0.02 0.10 0.15 0.45 1.10 1.32 2.71 3.84 5.02 6.63 7.88 2 3 0.02 0.10 0.21 0.58 0.71 1.39 2.40 2.77 4.61 5.99 7.38 9.21 10.60 3 4 0.11 0.35 0.58 1.21 1.42 2.37 3.70 4.11 6.25 7.81 9.35 11.34 12.84 4 5 0.30 0.71 1.06 1.92 2.02 3.36 4.90 5.39 7.78 9.49 11.14 13.28 14.86 5 6 0.55 1.15 1.61 2.67 3.00 4.35 6.10 6.63 9.24 11.07 12.83 15.09 16.75 6 7 0.87 1.64 2.20 3.45 3.83 5.35 7.20 7.84 10.64 12.59 14.45 16.81 18.55 7 8 1.24 2.17 2.83 4.25 4.67 6.35 8.40 9.04 12.02 14.07 16.01 18.48 20.28 8 9 1.65 2.73 3.49 5.07 5.53 7.34 9.50 10.22 13.36 15.51 17.53 20.09 21.95 9 10 2.09 3.33 4.17 5.90 6.39 8.34 10.60 11.39 14.68 16.92 19.02 21.67 23.59