MendelWeb Homework Sets
For now, sets of questions are provided for each section of Mendel's
paper. In the second 1997 edition of MendelWeb, I will replace these
with a new set, and post a key for the current set,
consisting of my solutions and comments, and including particularly
good answers submitted by MendelWeb users. Answers should be submitted
to mwscribe@netspace.org, along with an acknowledgement that
they may be used in future editions of MendelWeb; I will let you know
if/when your solutions will appear.
1. The technique of artificial fertilization is crucial to Mendel's studies of hybrids. Name four species of flowers on which artificial fertlization can be performed, and explain whether they are equally suitable for an experiment that tries to discover whether the characters of the hybrids can be predicted given the characters of the parents.
2. Give an example of a "law" from either physics or chemistry, and explain the difference between scientific law and the definition of a scientific term.
3. Briefly describe how botanists in the late 20th century decide whether two plants, that seem similar but are not identical in appearance, are members of the same species. Make sure to note the sources for your information.
4. Calculate the mean of the following sequence of numbers, which represent the results from a test given to a high school algebra class (the range of the test was 0-100):
5. Explain the different meanings "average" could have in each of the following, and how readings such statistics could be misleading if the method of calculation (i.e. mean, median or mode) was not known to the reader.
1.In plants grown from garden peas, the keel of the flower appears sealed while fertilization takes place, so that in order to perform an artificial fertilization, Mendel had to cut open the keel. Which of the three requirements for experimental plants, listed by Mendel, is satisfied by the closed keel of the pea plant?
2. Mendel describes subjecting each of the 34 varieties of peas he obtained to a two-year trial. During this time he let the plants self-fertilize and observed their offspring. What was he looking for, and what was the purpose of doing this two-year trial?
3. Give an example of a biological phenomenon for which no scientific law has been discovered. Do you think a law for this phenomenon could be discovered? (this will probably require a lengthy explanation).
4. Give an example of a question in biology, chemistry or physics that cannot be answered by observations alone, but requires that experiments be performed. Give an example of a question in chemistry that can be answered by observation alone.
1. Name at least three difficulties Mendel would have encountered in the design of his experiments had he chosen to study animal rather than plant hybrids. Would there have been any advantages to studying animals?
2. Give an example of a species of plant or animal, other than the pea species mentioned by Mendel, that exhibits several sharply defined characters that appear in only two forms.
3. Mendel mentions a species of beetle (Bruchus pisi) that can interfere with the normal development of Pisum; indeed, a large beetle infestation can wipe out pea crops altogether. Give an example of an animal actually helps in the normal development and survival of a species of plant.
4. Suppose someone gives you a bag of yellow garden peas and a bag of green garden peas in the early Spring of 1996. You plant them immediately and find that in the Fall, the pods on the plants grown from the green peas contain all green peas, but the pods on the plants grown from the yellow peas contain both yellow and green peas. What, if anything, can you conclude about the difference between yellow and green coloring in peas? How would you test your conclusions, and how long would your experiments take?
1. Suppose you transfer pollen from a true-breeding tall pea plant to eggs on a true-breeding short pea plant. What do you have to do (and how long will it take) to observe the hybrid offspring from this cross? Will there be one or many offspring? What, according to Mendel's results, will the offspring look like?
2. In humans, apparently, the presence of dimples is a dominant characteristic. If the inheritance pattern of dimples is like that of pea color (i.e. two forms, dimples and no-dimples, one dominant and one recessive), described by Mendel, could non-dimpled parents give birth to a dimpled child? If non-dimpled parents do give birth to dimpled children, what if anything does that tell you about how dimples are transmitted in reproduction?
3. Give two examples of vegetable characteristics that exhibit dominant and recessive forms as defined by Mendel. For example, in summer squash, white "meat" or "fruit" is dominant and yellow is recessive.
4. Give two examples of plant or animal characteristics that seems to exhibit "blending" inheritance (i.e. hybrids look like a blend of parental forms), and two that do not seem to exhibit blending.
1. Humans have been performing artificial crosses on fruits and vegetables for thousands of years, producing hybrid forms for their own consumption. Find an example of two fruits or vegetables that can be crossed to produce fertile offspring. Design an experiment to investigate what sorts of offspring the hybrids will produce. Describe your experiment(s) in enough detail so that others could perform them.
2. Someone gives you a bag of yellow peas and you plant them in the Spring. Can you predict the color of the peas that will appear in the pods on the plants grown from these peas? Would your answer be different if you had received a bag of green peas?
3. Calculate the ratio of yellow to green pea color for the first ten plants shown in the table for Experiment 2.
4. Suppose Mendel had reported the median ratio rather than the mean. Do you think it would have been closer to 3:1 than the mean?
5. When doing experiments it is usually necessary to have some sort of rule to decide whether an outcome confirms the predicted result, or whether it doesn't confirm the prediction. For Mendel's experiments, suppose we adopt a "square-root of n" (sqrt[n]) rule, which says that, if the predicted ratio of dominants to recessives is 3:1, we expect to find a ratio of 3:1 +/- sqrt[n].
For example, in the first plant reported in Experiment 1, we expect a ratio of round:angular of 3:1 +/- sqrt[57]. With 57 peas, a perfect 3:1 ratio would be about 43:14; and since the square-root of 57 is about 7, we would consider 43+/-7 to be a good result. The result Mendel reports is 45:12, which is well within the sqrt[n].
Apply the "sqrt[n]" rule to each of the 10 plants in Experiment 1, and see whether each of the results fits the ratio 3:1 +/- sqrt[n].
1. Explain what Mendel means when he writes that the 3:1 ratio observed in the first generation from the hybrids "resolves itself" into a ratio of 2:1:1.
2. Someone hands you a round and green pea in the Spring and you plant it. Can you predict what sorts of peas will be produced in the next generation? If you let the next generation's peas grow and fertilize themselves, can you predict the form of the peas produced in the following generation?
3. Someone hands you a round and green pea. Describe how, through artificial fertilization, you could exactly predict the forms of peas in the second generation grown from that round and green pea.
4. You have a plant with only green (unripe) pods that eventually contain yellow peas, and another plant with yellow unripe pods that eventually contain only green peas. You plant the peas from these plants the following Spring. In the summer you take pollen from one of the flowers on the plant grown from a green pea, and dust it on the stigma of a single flower on a plant grown from the yellow pea. You the let the fertilized plant grow into pods, which contain peas.
1. Suppose you start a growing experiment by planting twice as many green peas as true-breeding parental yellow peas. Since there are many more stamens than stigmas, you take pollen from the flowers on the plants from the yellow peas and dust the stigmas on the plants grown from the green peas. You let the fertilized flowers grown into pods which contain peas.
2. Show how Mendel derives the numbers in the third row (generation) of his table (i.e. 28:6:28) from those in the second row.
3. Suppose you learn that the average height of the students (grades 9-12) at Muscamole High School, in Muscamole, Minnesota, is 5'10" (about 178 cm). Describe how the information conveyed by this statistic could be very different depending on whether this number is the mean, the median or the mode.
4. Mendel uses the series A + 2Aa + a to model the first generation from the hybrids. He then uses this model to generate predictions for the forms of future generations grown from the hybrids. Give an example of another model, from biology, physics or chemistry, that can be used to make predictions.
5. You begin with a single true-breeding yellow pea, and a single green pea, and plant them. Describe in detail a series of crosses in the next generations, such that you will end up with a ratio of yellow: green peas of 7:1 (you will need to be clear about your assumptions concerning the number of peas on each plant). What will be the ratio of parental dominant: hybrid: recessive in your 7:1 ratio?
1. Suppose you have a yellow and round pea that comes from a pod that is yellow when unripe. You plant it in the Spring, let it fertilize itself, and wait for the pods to appear. Can you predict the color of the unripe pods? Can you predict the color and shape of the peas in those pods when they ripen?
2. Suppose instead that you planted the pea from #1, and when the flower appeared, you transferred some of its pollen to the stigma of a flower on a plant that was grown from a green and wrinkled pea, that came from a pod that was green when unripe. You let that fertlized flower produce pods, which contain peas. What color will the pods be? What shape and color will the peas be?
3. You plant the peas we left off with in #2, and let the flowers on the plants fertilize themselves, and produce pods.
4. Let unripe pod color be represented by G and g, and pea color be represented by Y and y and pea shape be represented by R and r. Write the representations for the cross you carried out in #2, and the combination series for the results you predicted in #2 and #3.
1. The experiments reported in this section, and designed to reveal the kinds and proportions of reproductive cells made by the hybrids, are sometimes called "back-crosses to the recessives" or simply "back-crosses." Why is a back-cross better than a self-cross, for the purposes of learning the sorts of reproductive cells produced by the hybrids?
2. What does Mendel mean by the phrase "repeated hybridization"?
3. Consider a plant that is tall with axial flowers and inflated pods. Using letters to represent characters, as Mendel does, how would you represent this plant if it is hybrid for all three characters (for the purposes of this example, ignore the other characters)? At least how many different kinds of pollen and eggs are produced by such a plant, according to Mendel's theory of reproductive cells? How does this relate to the number of "constant" forms that this plant will produce when it allowed to self-fertilize and produce offspring? How does it relate to the number of terms in the combination series which can be used to express the proportions of parental dominant, hybrid and recessive forms in the offspring?
4. Consider a plant with pods that are inflated and green when unripe. How will an artificial cross with a plant with pods that are pinched and yellow when unripe reveal what sorts of pollen and eggs are made by that plant? How will the kinds of pollen and egg made by that plant tell you whether the plant is hybrid or parental for either or both pod shape and color?
5. Suppose you allow a large number of tall plants, all known to be hybrids, to self-cross. If 2000 plants are thus produced, what is the probability of getting exactly 1500 tall and 500 short offspring? of getting exactly 1400 tall and 600 short offspring? (you will need to know something about calculating combinations to answer these questions).
1. Suppose the appearance of a particular trait in a bean plant is produced by the combination of two "Mendelian" characters (i.e. characters that behave like those Mendel observed in Pisum). How many different visible forms of that trait could there be? How many different "internal" forms of that trait could there be (i.e. constant and hybrid)?
2. Mendel gives an example of a two-character model that could produce a range of forms, so that the ratio of the recessive to the others was 1:15. If he had assumed three characters were responsible for flower color, could the ratio have been as small as 1:31?
3. What is the point of Mendel's claim that "our cultivated plants, with few exceptions, are members of various hybrid series."?
4. In his 1967 essay, "Mendel and the Gene Theory", the geneticist A. H. Sturtevant wrote:
5. Mendel mentions experiments designed to "transform" one species into another. Although we think today that what these experiments did was transform one variety into another, has there ever been a verified report of the transformation of one species of any animal or plant into another through hybridization? (this question may require some research)
1. The table presented by Mendel in the eighth section of his paper gives the results of his second experiment involving a multiple-character cross. How did he know there were 14 AaBC and 48 AaBbc? That is, when he wrote "further investigation showed," what exactly did he mean (i.e. what specifically did he do)?
2. Explain how Mendel relates both Gärtner's claim about the "constant hybrids" (i.e. the hybrid forms that breed true), and the discussion of species transformation, to the explanations of hybrid form and development in Pisum.
3. In a species of mouse, it is accepted that all the mice exhibit the same form of a particular character. Suppose you think that the character is actually "Mendelian", with two forms, one dominant and the other recessive. You hypothesize that the reason the mice all exhibit the same form of the character is because the recessive is lethal. Design and describe an experiment, or series of experiments meant to test this hypothesis.
4. Mendel mentions experiments designed to "transform" one species into another. Although we think today that what these experiments did was transform one variety into another, has there ever been a verified report of the transformation of one species of any animal or plant into another through hybridization? (this question may require some research)
5. In 1900, the geneticist William Bateson, perhaps the greatest promoter of Mendel's work at the turn of the century, wrote: