LABORATORY SIX

GENETICS AND STATISTICAL INFERENCE

OVERVIEW:

In this lab and the next you will use your powers of observation (and problem solving) to deduce the genetic makeup of simple traits in plants and animals, based on their appearance. This sounds relatively easy, but requires that you first understand something about chance and probability.

In today’s lab you will perform simple exercises, such as counting coin tosses and corn kernels, to learn how different results, from events like tossing a coin or randomly mixing genes during reproduction, can be explained in terms of how often they occur (i.e. sample size) or of the roles of chance versus non-random, directed influences. You will formulate hypotheses to explain your data, then use a basic statistical test called the Chi Square to see how well your prediction fits the data. After learning how to perform the Chi Square test on paper, you will use a computer program to work faster and handle larger amounts of data.

Once you understand the basis of inheritance, you can use ratios of phenotypes to infer not only the genotype of individuals, but also of the parents and of successive generations, after crosses.

OBJECTIVES OF LABORATORY:

·    To understand the genetic basis underlying phenotypic variation.

·    To relate phenotypic ratios to probabilities of inheritance using a Punnett Square.

·    To make statistical inferences from data and use the Chi Square test to evaluate the “goodness of fit” between data and conclusions.

·    To learn the terms class, deviation, and degree of freedom as used in statistics.

·    To explore the effects of sample size, chance, and external influences on statistics.

·    To observe genetic variation and test a hypothesis concerning the observation.

·    To observe simple human genetics traits.

·    To determine possible genotypes from phenotypes.

INTRODUCTION:

1.        Genes and chromosomes

Genetics is the science of heredity. Geneticists work to establish that patterns of inheritance occur - then they seek to explain those patterns. Much of modern genetics results from the fusion of two lines of research: that started by Mendel in the 1860s on genes, the units of inheritance, and that of the cytologists, or cell biologists, who discovered and studied chromosomes. The important results of this synthesis are that we now realize that genes occur on chromosomes, and because chromosomes are found in pairs in nearly all cells of all organisms, that means that genes are also in pairs.

Genes occur in alternative forms called alleles. Alleles can be detected because they cause differences in appearance, or phenotype, of the individual. There may be one, two, or many alleles of a single gene. However, because genes are found at very specific places on chromosomes, called loci, no individual can have more than two alleles of each gene. If both alleles are alike, the individual is said to be homozy­gous. If they differ, we call that individual heterozygous.

A complication of this situation is that some alleles can completely mask the effects of others. The allele that does the masking is called dominant and the masked allele is called recessive. If this situation occurs, the heterozygote will have the same phenotype as one of the homozygotes. The phenotype that is due to the recessive allele can only occur if the individual is homozygous for that allele.

2.          Phenotypic ratios and predictions

Last week you saw how great care is taken during cell division to parcel out the chromosomes as accurately as possible. During mitosis the chromosomes are duplicated and sorted so that each new cell gets exactly the same complement of chromosomes as the parent cell. However, during meiosis the duplication is followed by two cell divisions, so that while each cell gets one of each of the pairs of chromo­somes, and has half the number of the parent cell, which one of the pair the new cells get is determined at random. The cells so produced are gametes, eggs and sperm.

When fertilization occurs, the pairs of chromosomes are reconstituted, but one of each pair has come from the mother and one from the father. The alleles on these chromosomes may be the same or they may be different. Since it all happens at random, we cannot predict specifically what the phenotype of any individual offspring may be.

However, there are ways of determining what proportion of individuals from any mating will be of one phenotype or another, even though we can’t predict the phenotype of a single individual.

YOUR INSTRUCTOR WILL DEMONSTRATE THE USE OF A DEVICE CALLED THE PUNNETT SQUARE TO MAKE SUCH PREDICTIONS.

As you have just learned, we can predict the ratios in which different phenotypes occur provided we know the genetic makeup, genotypes, of the parents and the way in which the alleles for that particular gene interact. However, each group of offspring from a cross represents only a sample of all the possible outcomes - we cannot expect the ratios to appear in an exact form.

The cobs of corn you have before you are such samples. In theory, if we count the numbers of individuals representing each of the phenotypes present, the result could be exactly one of the genetic ratios just described by your instructor. But this is quite unlikely. What do we do if the ratio is different - if the numbers of individuals of each phenotype is not exactly as predicted?

3.           Statistical inference from data

One response might be to “guess” that the numbers are close enough (or too far off). But we have no real basis for deciding where to draw the line. In order to deal with such situations, geneticists turn to statistical inference. Statistical methods allow us not only to make a guess about the ratio represented, but also to say how good our guess might be. In other words, any guess might be wrong, but what are the chances that our particular guess is wrong? If the chance is less than 5% that we are wrong, we have more confidence in our guess than if the chances are 50% that we are wrong.

One statistical test used to see if data fit a particular ratio is the Chi Square test.

The next section explains how it is done, and your instructor will go over it with you. Since this is tedious, we can also use computers to do the Chi-Square test, for example, for the data you will collect on corn genetics.

CHI-SQUARE (GOODNESS OF FIT) TEST:

The Chi-Square test is a statistical method for determining whether experimental data are the result of some causative factor or simply due to chance.

As an example, consider coin tossing. If we predict that the chances of a coin coming up either heads or tails when tossed are 50:50, and we toss a coin 100 times, getting 50 heads and 50 tails, we have no problem accepting our hypothesis. The results are exactly as we predicted. Put another way, our hypothesis is that the outcome of each toss is determined by chance alone. Since there are only two sides of the coin, each side has an equal chance of turning up, and that’s exactly what happened. But suppose that we tossed the coin 100 times and got 60 heads and 40 tails? This raises some suspicions. It looks like there might be something involved that causes tails to come up more often than heads; in other words, an outside cause, such as an imbalance in the coin, is affecting the result. On the other hand, it could be argued that we simply have not tossed the coin often enough. Perhaps if we do it 1000 times, the results will even out. After all, on our way to 50/50 in the first experiment, we went through some times when heads, for example, might have come up three times in a row. Some variation from the predicted results is to be expected. But how much is allowable?

We also need to ask ourselves how many tosses are enough to settle the question. Tossing a coin 1000 times is boring. This is where the Chi-Square test comes in. By performing this test we will not only be able to decide about supporting or rejecting our hypothesis, we will be able to do so with a certain confidence that we have made the right decision. The degree of confidence, and even the degree of support for our hypothesis, will depend on how much data we have. The following two examples will show this.

In order to perform the test we will have to make up a table of values. An example is given below for the 60/40 coin tossing experiment.

Total Chi Square Value, x²=∑ (O-E)²/E = 4

Sixty heads and 40 tails are the observed values (O). However, according to our hypothesis, we expected 50 of each, so these are our expected values (E). We next want to know what the differences are between expected and observed, so we subtract: (O-E). Notice that the differences values cancel each other out; we don’t want this to happen, so we get rid of the negative sign by squaring the differences (O - E)². In the next step, we compare the differences to the expected values by dividing squared differences by the expected values: (O - E)²/ E. The sum total of these comparisons is the Chi-Square statistic, X². In the case of the 60/40 coin toss, it is 4.

In order to evaluate what the statistic is telling us, we have to go to a table which gives the correspondence of X² values to the percentages of the time chance would produce the observed deviation. The table is given next.

At the far left of the table is a column giving “degrees of freedom,” defined as one less than the number of different outcomes possible in each trial - in this case since each coin has only two sides, 2 - 1 = 1.

 Find out where our X² value of 4 fits in along the row across from 1 on the far left. It is between 3.841 and 6.635. Reading down to the bottom row, we see that this corresponds to a percent value between 5% and 1%. In other words, the test is telling us that less than 5% of the time, this kind of deviation would be produced by chance alone. There may be other variables involving the coin itself.  Is it weighted on one side giving us skewed results? We would be amply justified, in this case, in rejecting the hypothesis. There is definitely something going on!  One may need to repeat the experiment many times.

Try going through this same procedure having tossed a coin only 10 times with the result of 4 heads and 6 tails. Are the results the same as when we used 100 tosses and got the same proportion of heads and tails? Does this result tell you anything about sample size?

A final note: Usually scientists hypothesize that there is a cause for a pattern in nature. In your work today, your hypothesis will be that the corn kernels you count fit a Mendelian ratio, and that any deviations you observe from these ratios are due only to chance. If the probability of the observed deviation occurring is less than 5%, that means your hypothesis should be rejected. Something you don’t know about is working to mess up your data!

CORN GENETICS:

Now that you have had practice with data taking and statistical treatment of that data relative to simple genetics ratios, we will continue studying genetics by observing variation in plants as well as variation in some of our own traits (simple human genetics).

The first activity requires that you and your partner make some observations about seedlings that were planted approximately two weeks ago. After you determine the variation in the seedlings and count the number of individuals in the classes, calculate the Chi Square value.

Make careful observations concerning the seedlings that you are given. What are the variations that you observe in the individual seedlings? How many classes can you observe? Some of the classes may involve combinations of characteristics. Make a hypothesis concerning the data that you have taken from your observations. In addition to corn seedlings, we will use dried corn seeds (i.e., kernels on cobs) to investigate different genetic ratios. You will count different seeds and apply these data to phenotype and genotype, and hypothesize, and test, using Chi Square, a pattern of inheritance.

HUMAN GENETICS:

In these exercises you will determine your own phenotype, and possible genotype, for some fairly easily observable traits. This should prove interesting to you. When you are at home again, notice these characteristics of your parents and siblings. Making observations about these human traits should help your understanding of genetics, and family trees of traits, or pedigrees, can be very interesting in themselves. Also, observing this variation in our class reminds us how unique each of us is.

The phenotypes of some human traits are easy to describe. These traits are determined by single gene pairs with only two alleles possible for each trait.

Determine your phenotype and possible genotype for the following characteristics. Record the information in your notebook. Notice the determinations made by your neighbors of their characteristics. Be prepared to discuss how the distribution of these characteristics makes each of us unique.  Notice that most of these traits are carried on the non-sex chromosomes called autosomes. Traits carried on the autosomes are referred to as autosomal.

Darwin tubercle - Examine the rim of your ear (and your neighbor’s or have him examine yours!). A thickening of the cartilage of the upper rim is called a Darwin tubercle and is controlled by a dominant allele, N. No tubercle would be homozygous recessive or nn.

Attached ear lobes - Examine your ear lobes and compare them to the drawing that is available at your desk. If your ear lobes are detached from the side of your face even slightly, you carry the dominant allele E for “detached ear lobes.” If you have attached ear lobes, you are ee, or homozygous recessive for attached ears.

PTC taster - Place a piece of control PTC (phenylthiocarbamide) paper on your tongue. Then place a piece of PTC paper on your tongue. If you detect a bitter taste with a PTC paper that you did not detect with the control paper, you are a taster and carry a dominant allele Tp’ If the PTC paper tastes like the control paper, you are homozygous recessive (t_pt_p).

Sodium Benzoate taster - Follow the instructions above with sodium benzoate paper. The ability to taste this compound is due to a recessive allele (t_bt_b), while non-tasters carry the dominant allele T_b. Exactly how the paper tastes to you can vary. People report salty, sweet, bitter, or sour tastes, but it is not known how this is controlled. However researchers have found that people who find the taste of sodium benzoate salty, and that of PTC bitter, are more likely to enjoy sauerkraut and buttermilk!

Thiourea taster - -Follow the instructions above with thiourea paper. Thiourea is closely related chemically to PTC, but the inheritance of the ability to taste it is controlled by yet another gene. The dominant allele (T_t) produces tasters, nontasters are homozygous recessive (t_tt_t).

Tongue rolling - If you can roll your tongue into a tube (as pictured in the drawing available at your desk), you carry the dominant allele R. If you are unable to roll your tongue, your genotype is rr.

Widow’s peak - Notice if your hairline forms a V in the front. (See the drawing at your desk.) Having a widow’s peak is determined by a dominant allele, W. Straight hairlines are homozygous recessive, ww.

Bent little finger - Place your hands lightly on the desk top. Notice your little fingers. If the end joint bends inward towards your ring finger, you carry a dominant allele (F) for this trait of bent little finger. The homozygous recessive (ff) has straight little fingers in this position.

Hitchhiker’s thumb - Hold your hand in the hitchhiker’s pose. Examine your thumb. If the end segment of your thumb is at an angle to the rest of your thumb (see drawing), you have the dominant allele for the trait hitchhiker’s thumb (H). The straighter thumb in this position is the homozygous recessive (hh).

Mid-digital hair - Your fingers have three segments. Look at the middle segment, and determine if hair grows there. If you have hair, even “peach fuzz,” you have the dominant allele D for mid-digital hair. If you don’t have hair on the middle segments of any of your fingers, you are homozygous recessive for this trait (dd).

Thumb crossing - Clasp your hands together. Notice which thumb is on top. If your left thumb is on top, you carry the dominant allele for thumb crossing (C). What is the genotype for the right thumb on top?

Iris pigment - If you have blue eyes, you are homozygous recessive for eye pigment, or ii. If you have any non-blue color eyes, you carry a dominant allele for pigment (I).

Dimpled chin -If you have a dimple in your chin, you carry a dominant allele for this trait (D). If you do not have a dimpled chin, what is your genotype?

Hapsburg lip - If you have a narrow, undershot lower jaw and a protruding lower lip, you carry a dominant allele for the Hapsburg lip (P). Notice the pictures available at your desk. If you do not have this trait, you are homozygous recessive (pp).

Red-Green colorblindness - Red-green colorblindness is an X-linked trait (carried on the sex chromosome called the X). Use the materials available on the front bench to check your color vision. The allele for red-green colorblindness is recessive (b) but is properly displayed on the X as X_b..A male with normal vision is written as X_BY. How would a female carrier for red-green colorblindness be shown? What would be the proper representation for a female who is red-green colorblind? How could that happen?

Assignment:

Study for next week’s practical that will include labs 1 through 6.

Name ______________________________

EXERCISES:

Corn Genetics Monohybrid cross (Class tall/dwarf or green/albino), 3:1 ratio,

 CHOOSE ONE CORN SEEDLING TRAY:

                        Observed        Expected                                                                     (O-E)²

Classes                (O)                    (E)                         (O-E)               (O-E)²                  E     

____________________________________________________________________

____________________________________________________________________

Total ________________________                     Chi-square total=__________

Using the chart on page 6-4, determine the probability that the deviation from the

expected that you observed would be due to chance. Probability = _________________  

Explain what this means.

Dihybrid cross (Corn Cob with: Purple/Smooth, Purple/Wrinkled Yellow/Smooth, Yellow/wrinkled OR  Corn Seedlings with: Tall/Green, Tall/Albino, Dwarf Green, Dwarf Albino), 9:3:3:1 ratio. CHOOSE EITHER SEEDLING TRAY OR CORN COB.

                        Observed        Expected                                                                     (O-E)²

Classes                (O)                    (E)            (O-E)               (O-E)²                  E     

____________________________________________________________________

____________________________________________________________________

____________________________________________________________________

____________________________________________________________________

Total _____________________                       Chi-square total_____________

Using the chart on page 6-4, determine the probability that the deviation from the

expected that you observed would be due to chance. Probability = _________________  

Explain what this means.

Name ___________________________

Data Sheet for Human Genetics