**Lab 3 --Mendelian Genetics**

In the following lab exercises, you'll apply Mendel’s principles of segregation and independent assortment to analyze the inheritance of discrete traits in a range of organisms. You'll also grapple with the complicating effects of dominance, epistasis, and linkage on patterns of inheritance. These are the kinds of analyses biologists use to determine the inheritance of a discrete traits in organisms (the field of genetics).

I. Mendelian ratios, inheritance models, and probabilities

Do problems 1, 3, 4, 6, 8, 9, 10, 13, and 16 from your text (pp. 259-261). We encourage you to do this *before* lab. (There's another set of textbook problems under III below.)

II. Statistical tests of genetic models in maize

When Mendel crossed peas, he found phenotypic ratios remarkably close to those predicted by his model of inheritance. However, remember that the laws of heredity (a genetic model) predict the *probabilities* of certain combinations of traits occurring in offspring. In real unions of egg and sperm, we don’t expect to see ratios that correspond *exactly* to the probabilities predicted by a model.

Intuitively, we know that sample size affects how closely actual numbers correspond to probabilities predicted by some model. For example, flipping a silver dollar 10 times and having ‘Heads’ comes up 7 times would not be surprising. On the other hand, flipping the coin 100 times with 70 instances of "Heads" might lead one to suspect that the coin is not "fair." What we need is a test to determine how much deviation to expect (and allow) from the predicted ratio of 1:1. Imagine flipping a fair coin 100 times and writing down the number of "Heads," and repeating the process over and over. This would make it possible to determine an expected range of variation in number of "Heads." If, say, in 95% of the tests the number of "Heads" falls between 40 and 60, then finding 70 "Heads" out of 100 flips would lead one to reject the "fair coin" hypothesis for the silver dollar.

This is the concept behind testing real examples of genetic crosses against the predicted Mendelian ratios. This is a critical aspect of the practice of genetics. Fortunately, we don’t have to drive ourselves crazy by flipping coins over and over to determine confidence limits. Mathematical models can predict the probabilities of achieving different outcomes based on chance alone.

The test most often used in biology when you have categorical data like this is called the c
** ^{2}** (pronounced "k-eye-square")

1. Calculate the expected number of offspring of each phenotype by multiplying the total number of offspring by the number expected. It’s okay if this number is not an integer.

2. Calculate the c
^{2} value for *n *phenotypes, where c
^{2}

a. For each phenotype, calculate the difference between observed and expected values.

b. For each phenotype, divide the square of the difference by the expected value.

c. Add all these values together.

3. Determine the degrees of freedom (d.f.), which here is the number of phenotypes minus 1.

4. Compare the c
^{2} value to the critical values from the table below:

d.f. critical c
^{2} (p <0.05)

--------------------------------

1 3.84

2 5.99

3 7.81

4 9.49

5 11.1

6 12.6

7 14.1

If c
^{2} is **greater than** the critical value, the distribution of phenotypes is different from that expected to occur by chance 95% of the time. You should therefore reject your genetic model. Inheritance works in a different way than your model predicted.

For exercises A-D below, choose an ear of corn and record the numbers of different phenotypes of at least four rows of kernals. For each example, propose a genetic model and do a c
^{2} test to determine whether your model is supported. If you are forced to reject your model, consider alternative hypotheses and perform additional tests.

For Exercises A-D -- Background on the inheritance of kernal color in maize

The color phenotype of maize (corn) kernals usually depends on the color of the aleurone (a layer of cells between the endosperm and the pericarp). If the aluerone is colorless, then the kernal appears to be the color of the underlying endosperm.

The genes

Aleurone color -- The R allele produces a purple aleurone, and the r allele a yellow aleurone.

Aleurone Color inhibitor -- The C^{I} allele inhibits production of any color in the aleurone and thus exposes the color of the endosperm (here, yellow). The C allele allows other aleurone color genes to be expressed.

Starchy/sweet -- The Su allele controls the conversion of sugar to starch in the maturing kernel. The su allele stops the conversion of excess sugar to starch, resulting in a wrinkled kernel when dry (see explanation for similar phenotype in peas on pg. 249).

A. Monohybrid cross

A monohybrid cross investigates the inheritance of a single genetic locus. Two "true-breeding" parents are crossed, producing an F1 generation whose phenotypes are noted. These F1 individuals are then crossed to produce an F2 generation. With your partner, choose an ear from one of the following crosses and determine the mechanism of inheritance for these alleles at these three loci.

F2 generation of a cross between parental types C^{I}/C^{I} and C/C.

F2 generation from a cross between parental types Su/Su and su/su.

F2 generation from a cross between parental types R/R and r/r.

B. Testcross

Imagine you come across a group of individuals that display the phenotype expected from a dominant allele. How can you tell if they are heterozygous or homozygous? The testcross is a means of "revealing" the unknown genotype of such individuals by crossing them with recessive homozygotes. (When doing testcrosses of F1 generation individuals, we are often crossing the F1 with a parental recessive homozygote, in which case it is called a **backcross**.) ** **Calculate the expected ratios when backcrossing a member of the F1 generation. Test this hypothesis with either the Su or C^{I} alleles.

__C. Dihybrid cross I__

A dihybrid cross is just like a monohybrid cross, except that each true-breeding parent is homozygous at 2 different loci. Obtain an F2 ear from the dihybrid cross of (C^{I}/C^{I} Su/Su) and (C/C su/su). Test the expected ratios based on your knowledge of the inheritance of each of these traits.

D. Dihybrid cross II

Test the expected ratios from an F2 ear of a dihybrid cross of parental genotypes (C^{I}/C^{I} R/R) and (C/C r/r). Revise your hypothesis and retest a new one, if necessary.

III. Linkage and sex-linkage

Do problems 1, 6, and 7 from your text (pp. 279-280). It may be worthwhile to begin *before *lab.

IV. Virtual Flylab

In the last part of the lab, you’ll practice the techniques used by geneticists to determine the nature of character inheritance using "virtual" *Drosophila melanogaster* flies (much larger and faster breeding than in real life).

Go to the YMCA and start Netscape. Reach Virtual Flylab through your instructor's homepage or by moving directly to http://vflylab.calstatela.edu/edesktop/VirtApps/VflyLab/IntroVflyLab.html.

On the first page read "What is Virtual FlyLab," then scroll down the page to "Where to Begin" and click on the field "Design a cross between two flies." Read the Instructions section carefully. Note two things. (1) When you choose a parental type to cross with a wild type, the parental type is homozygous for the characteristics, *unless the allele is lethal in homozygous form*, in which case it is heterozygous. Can you guess if it’s dominant or recessive? (2) When you pick offspring to cross, you are picking one individual of that *phenotype*. In some cases, individuals of a phenotype can have one or more genotypes. Be aware of this.

1. First try a simple monohybrid cross.

- Click the button for a black body female and a wild type male.
- Scroll down the page to find the ‘Mate Designed Flies’ button and click on it.
- Carefully read the results page when it arrives. Notice that both parents and offspring are shown and the offspring are divided into male and female.
- After noting the phenotypes of offspring, choose a male and female of the F1s to mate by clicking buttons and then click the "Mate Selected Flies" button. What is the phenotypic ratio of the offspring? What is the basis of inheritance of the black body allele (BL)?

- Perform a c
^{2}Goodness-of-Fit Test by clicking the "Propose and Test a Hypothesis" field. Scroll down to "Results Ignoring Sex," enter the expected phenotypic ratio in the boxes, and click "Compute Chi-squared Statistic." Read the results. - Press the ‘Back’ button (upper left corner) 3 times to return the F1 generation page. This time backcross an F1 to the recessive homozygous parent. Do you get the expected results?

- Press the "Back" button to return to the "Design and Mate Flies" page and reset all mutations to wild type by pressing the ‘Wild Type" button before going to the next step.

2. Use the strategy of monohybrid crosses and backcrosses to determine whether the following alleles are dominant or recessive, sex-linked, or lethal. Take notes on your crosses and their results in your lab notebook. *Don’t forget to reset to Wild-type before each new allele! *

Eyeless (EY)

Curly Wings (CY)

Miniature Wings (M)

3. Perform a dihybrid cross between a wild type female and a ebony body (E)/incomplete wing vein (RI) male fly. What is the result of your c
^{2} analysis? Would the result support a hypothesis that the traits are linked?

An easy way to determine recombination frequencies is to backcross an F1 from a dihybrid cross to the homozygous recessive parent. The percent of recombinants equals the rate of crossing over (diagram this to make sure you understand why). In* D. melanogaster* , crossing over only occurs in females, so you should cross a female F1 with a male homozygous recessive parent.

- Determine the recombination frequency between the ebony body (E) and incomplete wing vein (RI) loci.
- Determine the recombination frequency between the spineless bristles (SS) and incomplete wing vein loci.
- Determine the recombination frequency between the ebony body and spineless bristles loci.
- Determine the order of these three loci. Explain why the map units don’t add up exactly (refer to your book, pp. 287-8).

On to Lab 4 - Populus--Population Genetics Simulations Sample

Back to Lab 2 - Sources of Phenotypic Variation

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