Mendel's Plant Experiments - Case Notes

SCI Home | SCI Faculty Page | Cover Sheet | Reference List | Users Notes

Author - Tom Huber - Spring 1997

Background

The following summarizes what can be learned from a careful reading and discussion of Mendel’s Experiments on Plant Hybrids:

• Importance and usefulness of reductionism: Mendel, unlike previous experimenters, only looked at one or two or three traits at a time, rather than at all possible traits. He did, however, eventually combine his separate empirical laws into one grand empirical law that predicted hybrid "behavior" when looking at many traits.
• Distinction between empirical laws and theoretical laws: This can be developed by bringing out the distinction between his various (empirical) laws describing (or governing) the formation and development of hybrids over several generations and his (theoretical) law that sought to explain how germ cells might be constituted in order to give rise to the observed empirical laws. The empirical laws are stated by Corcos and Monaghan, or by Mendel, as follows (p. 97; p. 113):
  • Law 1. The hybrid offspring of parents, each true-breeding for one of the contrasting characters of a trait, are all alike and like one of the parents. No intermediate types are formed.
  • Law 2. Reciprocal fertilizations yield the same hybrid forms. That is, the hybrid trait will be that of the dominating parent regardless of whether that is the seed parent or the pollen parent.
  • Law 3. When the hybrids are allowed to self-fertilize, the offspring always appear in two classes: one class like the hybrids and like one of the original true-breeding parents (the dominating); and one class like the parental character not visible in the hybrid generation (the recessive). No intermediate forms are produced. The two classes occur in approximate ratio of 3 dominating to 1 recessive.
  • Law 4. (a) When the recessive offspring of the hybrids are allowed to self-fertilize, they always breed true. (b) When the dominating offspring of the hybrids are allowed to self-fertilize, approximately one-third of them breed true while two-thirds of them behave exactly like the hybrid generation.
  • Law 5. The combination series law: The complex series of traits (the breeding structure or the characters) from a poly(n)hybrid cross is really a combination of the n simple series and, in fact, can be produced mathematically by means of a term-by-term combination of the simple developmental series for the individual traits. Or as Mendel stated it: The progeny of hybrids in which several essentially different traits are united represent the terms of a combination series in which the series for each pair of differing traits are combined. This also shows at the same time that the behavior of each pair of differing traits in a hybrid association is independent of all other differences in the two parental plants.

The assumptions leading up to his theoretical law are also stated by Corcos and Monaghan (p. 128):

• Assumption 1. In the ovaries of hybrids as many kinds of germinal cells are produced as there are possibilities for constant combinations of traits in their progeny.
• Assumption 2. In the anthers of hybrids as many kinds of pollen cells are produced as there are possibilities for constant combinations of traits in their progeny.
• Assumption 3. The combinations of traits present in the germinal and pollen cells correspond to the combinations of traits present in the constant forms in the progeny.
• Assumption 4. In a hybrid, the different kinds of germinal and pollen cells are produced, on the average, in equal numbers.
• Assumption 5. Fertilization occurs equally often in each possible combination.

The theoretical law describes a mechanism by which "hybrids produce germinal and pollen cells that correspond in equal numbers to all the constant forms resulting from the combination of traits united through fertilization." (p.141)

Also, the predominant pattern of thinking differed in deriving the differing types of laws. Inductive reasoning was emphasized with the empirical laws and deductive reasoning was emphasized with the theoretical laws.

• Importance of appropriate experimental organism for question being asked: Mendel himself recognized that the "experimental plants must necessarily Possess constant differing traits. Their hybrids must be protected from the influence of all foreign pollen during the flower period or easily lend themselves to such protection. There should be no marked disturbances in the fertility of the hybrids and their offspring in successive generations." (p. 63) In addition, the plants must be grown easily and with a minimum of space, reproduce rapidly, and reproduce in large numbers.
• How science is "rewritten" by subsequent writers and, especially, textbook writers: Mendel does not talk about "inheritance" or "laws of inheritance." He talks about hybrids and the laws governing the formation and development of hybrids. One looks in vain for "Mendel’s law of segregation" and "Mendel’s law of independent assortment," if one is thinking of genes or chromosomes. However, the seed of these ideas is clearly in the paper.
• The importance of technical terms, abstract symbolic notation, and descriptive statistics: Phrases like dominating character, recessive character, parental character, and hybrid character take on new, and important, specific meanings. Mendel’s method of symbolically representing crosses simplified the information and made it easier to think about it. Finally, Mendel’s knowledge of the importance of the mean (average) as the best representative value of a large number of observations, and the relationship between sample size and accuracy (and precision) make it clear that he attempts to apply statistical methodology to his experimentation.
• The unexpected ability of a theory to explain other, seemingly unrelated observations, thus increasing the "power," validity, and believability of the theory: Mendel was able to explain the tendency of hybrids to revert to their parental types when reproduced by self-fertilization for several generations by using his developmental series law over several generations.
• The ability of the results of one study to direct research to new studies: In his conclusion, Mendel talks about the "elements" that are combined during fertilization from each of the gametes; however, he was not able to describe the nature of these elements. It is apparent that he believed them to be material and constant. Only later would chromosomes, and then genes, be determined as the carriers of the information.
• The usefulness of tests of significance when deciding whether or not to accept a null hypothesis: Although Mendel did not submit his results to a test of significance like Chi-Square, his results (or ones gathered in the class) can be used to test his various hypotheses. This could be done in class or as a homework problem.

Teaching Suggestions Useful approaches to the unit:

• Great Books approach: This paper is particularly suited for a Great Books, or large group, discussion approach to the text. Fewer than twenty pages, the text could be divided into three sections for a week-long unit. The first day would include the following sections: Introductory remarks, Selection of experimental plants, Arrangement and sequence of experiments, and The form of the hybrids. The second day would include: The first generation from hybrids, The second generation from hybrids, The subsequent generations from hybrids, and The offspring of hybrids in which several differing traits are associated. The third day would include: The reproductive cells of hybrids, Experiments of hybrids of other plant species, and Concluding remarks.
• Investigative approach: The biology department has ears of corn representing the various generations of mono- and dihybrid crosses for the parental, the F₁ and the F₂ generations. We also have a photographic slide set that displays enough about corn reproduction to explain that each kernel of corn on an ear results from an independent fertilization event between a pollen grain produced by the tassel and an egg cell at the base of a single silk. Students could discuss ways to effect the needed crosses given an understanding of corn reproduction. Also, working in groups of four, students could be given, sequentially, the ears resulting from various crosses and asked "what to do with them" in order to record important observations. An explanation as to what "true-breeding" means should result from consideration of the parental generation, if it is provided that self-crossing produces constant characters for the given traits. The traits of the F₁ generation "look like" one of the parental characters, but not the other. Language can be developed to distinguish the two characters. The result of self-crossing the F₁ generation to produce the F₂ generation should reveal that the "hybrid character" is not identical to the one "parental character," i.e., that is it is not true-breeding. New language may have to be introduced at this point and students asked to articulate what it may mean. Eventually, ratios should be considered and, perhaps, some of Mendel’s "laws" outlined. Unfortunately, this approach suffers from students who have "studied" Mendel’s laws in high school, which, of course, are only ascribed to him for his seminal role in this branch of research and not found in his paper. We (unfortunately) do not have F₃ generation ears, which would demonstrate the very important distinction between the 3:1 phenotypic ratio (modern language) in the F₂ generation of a monohybrid cross, and the 1:2:1 genotypic ratio (modern language) in the F₂ generation of a monohybrid cross.
• Small group discussion approach: A modification to the Great Books approach is possible in order to include as many students as possible in the discussion. Students, who have already read the entire text once, are asked to nominate issues that might be of concern or importance to the way science is done. The resulting list (hopefully similar to section II above) is reduced to six by the class (with faculty guidance) and students are assigned to groups of four, in order to investigate how these issues are raised and dealt with by the text. Some time at this first meeting might be taken explaining basic reproduction in peas. Each group is then assigned one of the issues to investigate, using only the text and their collective thinking. Students are told to reread the text with their group’s specific issue in mind before the next class meeting. They should be warned not to trust what they may have learned in high school about "Mendel’s" laws and not to trust what any current college text book says about Mendel’s laws. (In fact, perhaps one should get this on the table first, and even assign a group that compares what a text book says about "Mendel’s" laws and what Mendel actually wrote. The focus here might be on inheritance and the laws of segregation and independent assortment. A focused reading by this group for generative phrases for these ideas may prove very useful.) On the second class day, each group should designate a scribe who keeps a written record of topics the group considered and what their tentative thinking on each topic was. It should be clear to the group that, eventually, they will report to the class a summary of their deliberations, which can be questioned by anyone in the class (including the professor!). During this second day, the faculty member can walk around and help groups during their deliberations. At the third meeting (and perhaps a fourth) the groups should present to the class the results of their deliberations, and the faculty member can help to lead a discussion along the paths of a Great Books discussion.