3. Extensions to Mendelian Inheritance

In analyzing genetic data, how do we know whether deviation from the expected ratio is due to chance rather than to another, independent factor?

If a chi-square test produces a chi-square value of 7.83 with 4 degrees of freedom,

Above what chi-square value would you reject the chance hypothesis for an experiment with 7 degrees of freedom?

If a chi-square test produces a chi-square value of 7.83 with 4 degrees of freedom,

Is the result sufficient to reject the chance hypothesis?

If a chi-square test produces a chi-square value of 7.83 with 4 degrees of freedom,

In what interval range does the P value fall?

Researchers cross a corn plant that is pure-breeding for the dominant traits colored aleurone (C1), full kernel (Sh), and waxy endosperm (Wx) to a pure-breeding plant with the recessive traits colorless aleurone (c1), shrunken kernel (sh), and starchy (wx). The resulting F₁ plants were crossed to pure-breeding colorless, shrunken, starchy plants. Counting the kernels from about 30 ears of corn yields the following data.

What is the order of these genes in corn?

Researchers cross a corn plant that is pure-breeding for the dominant traits colored aleurone (C1), full kernel (Sh), and waxy endosperm (Wx) to a pure-breeding plant with the recessive traits colorless aleurone (c1), shrunken kernel (sh), and starchy (wx). The resulting F₁ plants were crossed to pure-breeding colorless, shrunken, starchy plants. Counting the kernels from about 30 ears of corn yields the following data.

Perform a chi-square test to determine if these data show significant deviation from the expected phenotype distribution.

An experienced goldfish breeder receives two unusual male goldfish. One is black rather than gold, and the other has a single tail fin rather than a split tail fin. The breeder crosses the black male to a female that is gold. All the F₁ are gold. She also crosses the single-finned male to a female with a split tail fin. All the F₁ have a split tail fin. She then crosses the black male to F₁ gold females and, separately, crosses the single-finned male to F₁ split-finned females. The results of the crosses are shown below.

  Black male x F₁ gold female:

    Gold         32

    Black        34

  Single-finned male x F₁ split-finned female:

    Split fin        41

    Single fin     39

Use chi-square analysis to test your hereditary hypothesis for each trait.

Experimental Insight 2.1 describes data, collected by a genetics class like yours, on the numbers of kernels of different colors in bicolor corn. To test the hypothesis that the presence of kernels of different colors in each ear is the result of the segregation of two alleles of a single gene, the class counted 12,356 kernels and found that 9304 were yellow and 3052 were white. Use chi-square analysis to evaluate the fit between the segregation hypothesis and the class results.

The basis for rejecting any null hypothesis is arbitrary. The researcher can set more or less stringent standards by deciding to raise or lower the p value used to reject or not reject the hypothesis. In the case of the chi-square analysis of genetic crosses, would the use of a standard of p = 0.10 be more or less stringent about not rejecting the null hypothesis? Explain.

To assess Mendel's law of segregation using tomatoes, a true-breeding tall variety (SS) is crossed with a true-breeding short variety (ss). The heterozygous F₁ tall plants (Ss) were crossed to produce two sets of F₂ data, as follows.

From the above analysis, what can you conclude about the importance of generating large datasets in experimental conditions?

To assess Mendel's law of segregation using tomatoes, a true-breeding tall variety (SS) is crossed with a true-breeding short variety (ss). The heterozygous F₁ tall plants (Ss) were crossed to produce two sets of F₂ data, as follows.

Using the X² test, analyze the results for both datasets. Calculate X² values and estimate the p values in both cases.

During your work as a laboratory assistant in the research facilities of Dr. O. Sophila, a world-famous geneticist, you come across an unusual bottle of fruit flies. All the flies in the bottle appear normal when they are in an incubator set at 22°C. When they are moved to a 30°C incubator, however, a few of the flies slowly become paralyzed; and after about 20 to 30 minutes, they are unable to move. Returning the flies to 22°C restores their ability to move after about 30 to 45 minutes.

With Dr. Sophila's encouragement, you set up 10 individual crosses between single male and female flies that exhibit the unusual behavior. Among 812 progeny, 598 exhibit the unusual behavior and 214 do not. When you leave one of the test bottles in the 30°C incubator too long, you discover that more than 2 hours at high temperature kills the paralyzed flies. When you tell this to Dr. Sophila, he says, 'Aha! I know how to explain this condition.' What is his explanation?

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.

Using any of the 100 progeny plants, propose a cross that will verify the conclusion you proposed in part (c). Plants may be self-fertilized, or one plant can be crossed to another. What result will be consistent with the 1:2:1 hypothesis? What result will be consistent with the 9:3:4 hypothesis?

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?

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.