A Problem-Solving Simulation for Classical Genetics

I 4.

Problem-SolvingSimulation for Classical Genetics

Jim Stewart

For several years I have used Bio- 1. How many traits exist in the population? QUEST's Genetics Construction Kit or Downloaded from http://online.ucpress.edu/abt/article-pdf/58/8/478/47735/4450215.pdf by guest on 27 September 2021 GCK (1994) with high school and uni- 2. What are the trait names? versity students as well as their in- 3. How many genes code for each trait? structors. Instructors like GCK as it 4. How many variations exist for each trait? allows students to solve problems that 5. What are the names of the variations? require them to generate and analyze 6. How many alleles exist in the population for each gene? data as they reason from effects (given 7. How many alleles exist in an individual for each gene? phenotypes) to causes (underlying ge- 8. What combinations of alleles can exist in individuals within the population? netic mechanisms) that are, in part, 9. Will the genes that code for a trait assort independently of those for other responsible for the effects. Yet, there traits? (It is possible to have students develop models for meiosis with are always instructors who do not have linkage in which they have to consider the effects of different map enough computers to allow their stu- distances). dents to have the best experience with 10. If there is linkage, are the genes linked on autosomes or on the X GCK. So, for the last two years I have chromosome? been developing and using a non-com- 11. What are the "relationships" between the alleles? (Does one get expressed in puter version of GCK. the presence of the other-a relationship of dominance; or are they both expressed-a codominance relationship?). 12. How do the allele combinations identified in #8 map to the variations The Simulation identified in #5. (This forces students to think about heterozygosity and homozygosity). The simulation was designed to be 13. What are all of the cross possibilities, given the various allele combinations, used by groups of three or four stu- that can occur? dents each. Two groups are necessary 14. What are the phenotype outcomes of all of the crosses identified in #13? to conduct the simulation. During the simulation each group will assume two Figure 1. Questions used to design a problem structure. different roles. One is to generate problems and the second is to be a research group, probing the problem created by for generating data for the research research group. To do this they need to the other group. The problem genera- group. consider the number of organisms to tor group produces a field collection of A good way for students to begin to be in it, how to make it look like a organisms and offspring for the crosses develop a problem structure is to an- random collection in terms of pheno- performed by the research group. The swer questions like those in Figure 1. type, sex, and in terms of its genotype research group performs crosses and Example answers to the questions for a distribution. They also need to decide interprets data in order to understand codominance problem are shown in if all possible phenotypes and geno- the genetics of the population they are Figure 2.1 While students need a basic types will be represented in the field investigating. The responsibilities of understanding of genetics in order to collection. The field collection is given the groups are as follows. develop a problem structure, their un- to the research group as a Field-Collec- The Problem Generator Group has derstanding of genetics will improve as tion Card (see Figure 3). two responsibilities. The first is to de- they develop the structures. The generator group also creates velop a structure for the genetics of the Once a group has developed a prob- Offspring Cards to provide to the re- problem (e.g. simple dominance, lem structure they use it to produce a search group in response to crosses codominance, multiple alleles, autoso- field collection of organisms for the that they perform. The number of cross mal linkage, etc.). Their second respon- possibilities will depend on the genetic the The students sibility is to use the structure as a basis I structure of problem. Note that genotypes (alleles) are repre- have to consider all possible genotype sented by numbers, rather than letters. I have done this because numbersare a more combinations that can be crossed and Jim Stewart is a Professor at the Uni- generic representationthan letters, particu- all of the possible offspring phenotypes versity of Wisconsin-Madison, 225 N. larly in solving problemswhere it is impos- that can be produced from those Mills St., Madison, WI 53705. sible to assign letter symbols prior to know- crosses. They then create Offspring ing how genes are expressed as variations. Cards to give to the research groups as

478 THEAMERICAN BIOLOGY TEACHER, VOLUME 58, NO. 8, NOVEMBER/DECEMBER1996 cross results to be given to the research 1. Number of traits? 1 group with little delay. 2. Name of trait? Antennae Shape Preparingthe structurefor the prob- 3. Number of genes (loci)? 1 lem, along with the Field Collection 4. Number of variations? 3 and OffspringCards, takes time. How- 5. Names of variations? Hooked; Knobby;Split ever, the knowledge of genetics gained 6. Number of alleles in the population? 2 is worth the effort.The structuresand 7. Number of alleles in an individual? 2 cards, once produced, can be used 8. Possible allele combinations? 1,1; 1,2; 2,2 again. 9. Independent assortment? Yes The Research Group has the respon- 10. X-linkage? No sibilities of using the field collection 11. Allele relationship? Codominant and the results from crosses to develop 12. Alleles to variation mapping? 1,1 Hooked; 1,2 Knobby;2,2 Split an explanation of the genetics operating in the population. To produce off- 13/14. Cross possibilities? spring data they need to identify, for Male x Female Offspring3 the GeneratorGroup, organisms that 1. 1,1 x 1,1 All Hooked will be the parents of the next genera- 2. 1,1 x 1,2 1/2 Hooked; 1/2 Knobby tion. For the first cross they are limited 3. 1,1 x 2,2 All Knobby to selecting a male and a female from

4. 2,2 x 2,2 All Split the field population. Subsequent Downloaded from http://online.ucpress.edu/abt/article-pdf/58/8/478/47735/4450215.pdf by guest on 27 September 2021 5. 1,2 x 1,2 1/4 Hooked; 1/2 Knobby;1/4 Split crosses can be made with parentsfrom 6. 1,2 x 1,1 1/2 Hooked; 1/2 Knobby the field collection or from the various 7. 2,2 x 1,1 All Knobby offspring generations. Students can 8. 1,2 x 2,2 1/2 Split; 1/2 Knobby performas many crosses as they want 9. 2,2 x 1,2 1/2 Split; 1/2 Knobby and do statisticaltests as they generate 3These ratios are those that could be expected with large numbers of offspring. data and hypotheses about their popu- Students should be made aware that the outcome for any single cross may vary lation of organisms. from this ratio.

Figure 2. A structurefor a codominanceproblem. Some Background Related to the Simulation From eight years of work with stu- Trait (Nose Shape) Male x Female Offspring dents solving GCK problems (Stewart Variations Females Males & Van Kirk 1991; Stewart, Hafner, 1. 1,1 x 1,1 Blue Johnson & Finkel 1992) I now realize Straight 10 6 2. 1,1 x 1,2 Blue how different solving effect-to-cause Curly 7 8 3. 1,1 X 2,2 Blue problems is for them. During this time Hooked 12 7 4. 2,2 x 2,2 Black many students have helped my col- 5. 1,2 x 1,2 3/4 Blue; 1/4 Black leagues and me develop ideas that help Figure 3. A Field Population Card for a 6. 1,2 x 1,1 Blue codominance problem. in the solving of genetics problems. 7. 2,2 x 1,1 Blue These ideas are listed below and then 8. 1,2 X 2,2 1/2 Blue; 1/2 Black described in more detail. 9. 2,2 x 1,2 1/2 Blue; 1/2 Black they perform crosses. The types of 1. Use a general genetics problem- cards necessary for a simple domi- Figure4. Types of OffspringCards for solving agenda. nance problem are shown in Figure 4 simple dominance. 2. Systematicallyexplore the search and examples of the cards are shown in space of the problem. Figure 5. Enough Offspring Cards will be needed so that a range of offspring Trait: Eye Color ratios could result from any particular Parents: Male: Blue Eyes cross of the same genotypes. By mak- Female: Black Eyes ing multiple cards for the same cross, Offspring: Male: 13 Blue Eyes students come to realize that offspring Female: 17 Blue Eyes ratios are probabalistic rather than de- terministic. It works well if the major- Trait: Eye Color ity of cards have offspring with pheno- Parents: Male: Blue Eyes Black Eyes type numbers that are within one or Female: 11 Black Eyes two of the expected numbers and a few Offspring: Male: 13 Blue Eyes; 17 Blue 14 Black Eyes in which the numbers are more ex- Female: Eyes; treme. When Offspring Cards have Color been produced it is useful if students Trait: Eye Male: Blue Eyes organize them similar to what is shown Parents: Female: Blue Eyes in Figure 6. The organization is based Male: 12 Blue Eyes on phenotypes as that is how the re- Offspring: Female: 17 Blue Eyes search group will be making crosses. This organization facilitates the gener- Figure 5. Sample Offspring Cards for simple dominance. ator group's record keeping and allows

CLASSICALGENETICS 479 trait is greater than two). To become Male x Female Offspring more systemic and complete in search- Category 1: ing the space of possible crosses it (Blue x Blue) helps to use a Cross Matrix. Students 1. Blue (1,1) x Blue (1,1) Blue can be encouraged to check the crosses 2. Blue (1,1) X Blue (1,2) Blue that they have completed in the appro- 3. Blue (1,2) x Blue (1,2) 3/4 Blue; 1/4 Black priate box in the matrix. By doing so 4. Blue (1,2) x Blue (1,1) Blue they have a record of the crosses that Category 2: they have performed compared to all (Blue x Black) that could be performed. An example 1. Blue (1,2) x Black (2,2) 1/2 Blue; 1/2 Black of a Cross Matrix is shown in Figure 7. 2. Black (2,2) x Blue (1,2) 1/2 Blue; 1/2 Black 3. Blue (1,1) x Black (2,2) Blue Thinking Qualitatively 4. Black (2,2) x Blue (1,1) Blue Category 3: It is not necessary, particularly early (Black X Black) in a solution, to be overly concerned 1. Black (2,2) x Black (2,2) Black with numbers and ratios. Generating initial hypotheses is important and can Figure 6. An organization for Cross Possibility Cards for: simple dominance be done with more qualitative data. For problems. example, if there are two variations for any trait in the field population, then it Downloaded from http://online.ucpress.edu/abt/article-pdf/58/8/478/47735/4450215.pdf by guest on 27 September 2021 3. Think qualitatively throughout 7. Considering modifiers of basic in- is reasonable to hypothesize that sim- the solution process. heritance patterns (i.e. sex link- ple dominance is operating (the hy- 4. Treat the solution as a case of age, penetrance). pothesis may need to be changed if hypothesis generation and test- 8. Checking solutions by performing additional variations appear as more ing. additional crosses or by doing sta- crosses are performed). If the field col- 5. Consider multiple explanations tistical analyses. lection includes traits with four var- or hypotheses for cross results iations then hypotheses of simple and for the entire solution. Systematic Explorationof dominance and codominance are inap- 6. Think genotypically. propriate while ones of multiple alleles 7. Think generationally. a Problem'sSearch Space and gene interaction are appropriate. 8. Make predictions about cross re- When solving problems it helps if sults rather than only explaining students keep track of the phenotypes Hypothesis Generation & them. they have crossed out of all possible Testing 9. Check the final solution. phenotypes that could be crossed. This 10. Use general problem-solving is especially important in problems Geneticists view a problem as a sit- heuristics. with large search spaces (i.e. trihybrids uation that requires hypothesis gener- or when the number of variations for a ation and testing. Students need to be Use a Problem-Solving Agenda Trait: Eye Color Student problem solving improves when they use a general agenda for solving problems. I don't teach the agenda to students before they have solved problems, nor do I teach it as an Male algorithm to be followed mechanically. Rather, I introduce it as students solve Female Black Blue problems over a period of several days. A helpful problem-solving agenda includes: 1. Redescribing data-describing the initial field collection in terms Black of the number of traits and variations of those traits. 2. Using the data redescription to generate initial hypotheses about inheritance patterns (i.e. if there are two variations for a trait, consider simple dominance). Blue 3. Using hypotheses to decide what crosses to perform. 4. Redescribing cross data. 5. Interpreting cross data in the light of hypotheses. 6. Considering alternate hypotheses Figure 7. Exampleof Cross Matrix. that would fit the data.

480 THEAMERICAN BIOLOGY TEACHER, VOLUME 58, NO. 8, NOVEMBER/DECEMBER1996 encouraged to do the same. One way to think genotypically. However, for ge- 2. So that the variation is unlike that promote this is to ask a group of stu- notypic thinking to occur students ben- associated with either of the like dents what explanatory hypotheses efit if they have a "big picture" of pairs (the 'co-ops' relationship of they are entertaining and what empir- genetics, including how genes map to codominance). would ical evidence they have (or traits. For example, one locus/gene Thinking this way makes it easier to value of having need) to support it. The may map to a single trait (as in simple understand multiple alleles, which in- a hypothesis is that it is a structure for dominance, codominance, and multi- volves various combinations of 'masks' the problem solution. By hypothesiz- ple alleles), or one locus/gene may and/or 'co-ops' relationships. ing simple dominance the implication map to more than a single trait (as in Along with establishing the big pic- there are two alleles in the is that pleiotropy) or more than one locus ture there are two representations that population and in any individual; that may map to a single trait (as in gene help students to think genotypically. the alleles interact in particular ways; interaction, epistasis, and polygenic in- One is the phenotype-to-genotype ex- that combinations of two alleles map to heritance). pression chart. An example of a phe- phenotypes in particular ways; and notype-to-genotype expression chart that there is a set of cross combinations Another aspect of the "big picture" is how gene, allele, trait and variation are occurs in 13/14 of Figure 2. The value operating. Something like the structure of the expression charts is that they that the generator group used to pro- related to one another. Students can be encouraged to think of trait as a vari- represent a general pattern for all sim- duce the problem is a useful tool for a ple dominance or codominance situa- able concept and of variation as a value research group to develop and use. If tions. Thus, they focus students' think- concept for the variable concept trait. Downloaded from http://online.ucpress.edu/abt/article-pdf/58/8/478/47735/4450215.pdf by guest on 27 September 2021 asked about the implications of their ing on a search for those mappings can think of as a hypotheses, students are encouraged Similarly, they gene specific to the problem being solved. to generate hypotheses that guide their variable concept, and allele as a value While the expression charts are help- data generation and interpretation. concept for the variable concept gene. ful for problems involving simple By thinking of the relationships at the dominance or codominance, they are Considering Multiple phenotype and genotype levels as be- less useful for those that involve mul- ing instances of variable-value relation- tiple alleles. For multiple alleles, a Hypotheses or ships, the two levels become linked: more general representation, pheno- Explanations Alleles relate to genes as variations type-to-genotype graphs, is appropri- relate to traits, and genes relate to traits ate. A phenotype-to-genotype graph are influ- Students, like most of us, as alleles relate to variations. consists of nodes (representing homozy- enced by their initial hypothesis or Another feature of the "big picture" gotes) and lines (representing heterozy- explanation for a problem and typi- concerns generalizations about allele gotes) that connect the nodes. Since the cally seek confirming, rather than dis- interactions. These include that, while number of homozygotes determines confirming, evidence. Confirming a hy- the number of nodes, the shape of a pothesis is important. Yet, many many alleles may exist at a locus in a population, no more than two of them graph is a function of the number of important contributions to science homozygotes possible for an inheri- have been made by attempts to discon- will normally occur in an individual. Given this, there are three ways of tance pattern. For simple dominance firm the most cherished hypotheses of and are two combining two alleles, two at a time: codominance there nodes; a research community. for multiple alleles, the number of 1,1; 1,2; and 2,2. More important is the Students can be encouraged to con- nodes is a function of the number of recognition that there are two ways sider alternate explanations for their alleles that are possible at a locus. Fig- to data (at two different levels). The first is that an unlike allele pair may map ure 8 depicts generic phenotype-to-ge- a within hypothesis level. For example, variations: notype graphs for simple dominance, if a research group has crossed two codominance, and multiple alleles. individuals with the same phenotype 1. So that the variation is the same as In addition to encouraging students and the offspring all have the parental the variation associated with one to use these two representations it is phenotype, students typically interpret of the like pairs (the standard also important to encourage them to this as evidence that the parents were 'masks' relationship of simple talk with members of their research homozygous recessive. At this point dominance). groups, other students, and yourself they could be asked to imagine other genotype combinations that might have produced their data. The second level at which it is important for stu- Galapagos * Amazon * Inca Ruins dents to consider alternate explanations is that of the overall solution. For *EconomicGalapagos tours since January 1979. example, upon seeing a trait with three variations it is reasonable to consider a *Weeklydepartures/in conjunction with SAETAAirline. hypothesis of codominance. However, *MainlandEcuador tours/Galapagos group scuba dives. it is important to have students con- *Peru(Machu Picchu)Bolivia, other SA and C4 countries. sider what other mechanism might produce the same number of variations (e.g. a three allele system, gene interac- LATINAMERICAN SPECIALIZED TOURS tion, or epistasis). 43 MillstoneRoad 440 EastBroadway Randalistown,MD 21133 Louisville,KY 40202 ThinkGenotypically (410) 922-3116 Hablamos (502) 583-8634 To solve problems that require ef- Fax:(410) 922-5538 Espaflol Fax:(502) 899-5452 fect-to-cause thinking it is important to

CLASSICALGENETICS 481 quately searched the problem's 1, 2 cross space. 1,1 2,2 4. Predict the results of crosses (either crosses between phenotypes Simple Dominance or Codominance not yet crossed, or repeating a cross that they have already done). 5. Make a case that the results of these crosses are consistent (both qualitatively and quantitatively) with their predictions. 1,1 6. Make a case that their solution is consistent with meiosis. Initially a solution justification is prompted in response to the instruc- tor's questions. However as time goes on, the justifications should become 1,3 1,2 part of a research group's normal be- havior. Downloaded from http://online.ucpress.edu/abt/article-pdf/58/8/478/47735/4450215.pdf by guest on 27 September 2021 Using General Problem- Solving Heuristics Students can also be encouraged to use general problem-solving heuristics. 3,3 2,2 By teaching these general heuristics in 2,3 specific disciplines, it is possible that students may use them in other sub- jects. The following list includes some Multiple Alleles with Three Alleles useful general heuristics and a genetics-specific example for each.

Figure 8. Phenotype-to-genotypeexpression graphs. 1. Setting subgoals-Working with one trait at a time in a dihybrid problem, or establishing the in- about genotype possibilities of the in- for explaining cross results and pre- heritance pattern first, then check- dividuals (or classes of individuals) in dicting cross outcomes. Students, un- ing for a modifier such as sex- their problem. It also helps to request like geneticists, rarely make predic- linkage. that students illustrate their problem tions prior to performing a cross. They 2. Working backwards-Explaining solution in terms of meiosis. This re- consistently perform a cross and then the results of a cross in terms of a quires them to show chromosomes la- attempt to explain the results. While stated hypothesis. beled with the alleles and to take those explanation is important, students who 3. Working forwards-Predicting chromosomes through a meiotic divi- rely on it, at the expense of prediction, the results of a cross based on a sion. do not develop an understanding of hypothesis or specific genotype to the genetics associated with their hy- phenotype mapping. potheses nor do they develop a critical 4. Redescribing data-Identifying a ThinkingGenerationally attitude about the relationship of hy- number of variations and traits as pothesis to data. The amount of pre- associated with a possible inheri- Students haven't done classical ge- dicting can be increased dramatically if netics until they have at least three tance pattern. teachers encourage research groups to 5. Generating hypotheses from re- generations of data. In order to pro- talk about their explanations, and to mote generational thinking, students descriptions-Assuming simple use them to predict the results of dominance if there are two varia- can be encouraged to produce lineages crosses suggested by the teacher. of at least three generations and to tions per trait. depict those lineages as pedigrees with 6. Considering alternate hypothe- the genotypes of individuals, or groups ses-Recognizing that the pheno- typic data of two variations of individuals, labeled. Generational Checking the Solution per thinking can also be promoted by hav- trait could indicate a modifier ing students make predictions about When checking a solution for consis- such as lethalityin a codominance expected cross results, rather than al- tency it is important for students to: pattern as well as the more obvi- ways explaining the results after a ous simple dominance. cross has been performed. 1. Consider other mechanisms that 7. Checking results-Explaining could have produced similar data. cross data in terms of assumed 2. Make a case, at a qualitative level, solutions. Prediction& Explanation that their solution is consistent 8. Learning from problem solv- with their data. ing-This point is especially im- A hypothesis and the causal expla- 3. Construct a cross matrix to dem- portant as students need to be nation that underlie it provide the basis onstrate that they have ade- encouraged to think beyond just

482 THEAMERICAN BIOLOGY TEACHER, VOLUME 58, NO. 8, NOVEMBER/DECEMBER1996 getting answers to problems to 2. The number of variations per trait is a necessary basis for under- how getting that answer has led is used as a clue to possible inher- standing inheritancepatterns. to some new insights about prob- itance patterns. 7. Expressinga solution in terms of lem solving or about the concep- 3. Qualitative redescription is taught an inheritance pattern, and of tual aspects of genetics. in terms of clues or patterns that checking or verifying the solution lead directly to a tentative hy- for accuracyand completeness, is Summary pothesis about an inheritance pat- essential. Providing students with opportuni- tern and solution to a problem. ties to solve realisticgenetics problems 4. Hypothesis generating and test- Acknowledgments ing is taught as the strategy used allows them to experience how classi- For the past several years, numerous cal geneticists think as to solve problems. This is because they attempt to people have contributedto my under- explain data in hypotheses provide direction as phenotype terms of standing of how students and geneti- mechanisms. to genetic However, this ex- what crosses to do and how to cists solve problems. The results of needs to be perience guided by teach- interpret the results of crosses. their efforts have had a positive influ- ers who are alert to insure that their 5. Selection of parents from previous ence on how I think about teaching students experience instruction in generations, in order to create fa- genetics. They include: Bill Albright, which: milial lines, is important in estab- Angelo Collins, Michael Dale, Liza 1. The relationships between con- lishing the genotypes of individu- Finkel, Bob Hafner, Sue Johnson,John cepts (i.e. chromosomes,genes, al- als. Jungck,Craig Rusbult, Mary Sue Slack, Downloaded from http://online.ucpress.edu/abt/article-pdf/58/8/478/47735/4450215.pdf by guest on 27 September 2021 leles, traits and variations)are ex- 6. Understanding the relationships Patti Soderberg, Norm Thomson and plicit. between genotype and phenotype Cindy Wynne.

nnovation in Science Education Announcing the 1997-1998 H. Dudley Wright Fellowships for Science Teachers

Withfunding from the H. DudleyWright Foundation, Tufts University has established the Wright Center for InnovativeScience Education. Each year the Center awards full academicyear WrightFellowships which providesupport for the studyand professional advancement of scienceteachers of grades6-12.

Fellowshipsare awarded to teacherswhose significant educational work on the local,state or nationallevels has improvedstudents' understanding of science.

Fellowsreceive a stipendof $35,000plus an equipmentand tiavel/relocation budget. Faculty benefits, as well as healthinsurance, are included. Fellows will be in residencefrom September through June at Tufts Universityin Medford,Massachusetts. The major activity of theFellows will be to furtherdevelop their innovativeapproach to scienceteaching and to disseminatetheir expertise to otherteachers.

......

Forfurther information,including an applicationform, write:

Fellowships WrightCenter for ScienceEducation lufts University 4 ColbySt. Medford MA 02155 (617) 628-5000 x5394 FONDATIONHi.DUDLEY WRIGHT

Applicationsmust be postmarked no laterthan February 1, 1997.Fellows will be notifiedby March1, 1997.

CLASSICALGENETICS 483