Charlotte K. Omoto
Department of Genetics and Cell Biology
Washington State University
P. O. Box 644234
Pullman, WA 99164-4234
Voice: (509) 335-5591
Fax: (509) 335-1907
Most students, whether non-science majors or life-sciences majors,
have difficulty in using what they learn of basic Mendelian genetics
to deduce the underlying genetic rules from the results of crosses.
This is especially true for organisms that have relatively few
offspring and thus the result of any one cross does not often
result in the predicted ratios of phenotypes. Being able to predict
ratios of genotypes and phenotypes of a cross from known parental
genotypes is but a first step in understanding Mendelian genetics.
The true utility of Mendelian genetics is to be able to deduce
the underlying genetics from a pedigree. I have devised a simple
coin toss game that allows students to get a grasp on how Mendelian
genetics works. This hands-on activity requires very little preparation
or materials but provides a clear and meaningful way to demonstrate
the fundamentals of Mendelian genetics. This exercise is only
appropriate for simple Mendelian traits, that is, those traits
determined by a single nuclear gene in a simple dominance or recessive
relationship. It is not suitable for cytoplasmic/mitochondrial
inheritance, nor for the complexity of varying penetrance. This
exercise is most useful after the students have been introduced
to Mendelian genetics and Punnett square. This simple exercise
can be fun and challenging not only for non-science majors but
for biology majors as well.
A Macintosh computer program written in Director 5.0 which uses the genetics of parakeet is available for downloading.
The main materials for this exercise are sets of pedigree charts.
We also use a coin and a marker pen which students can provide. The pedigree charts already have the circles and squares connected by lines. Each group of 3-5 students is provided with pedigree charts; one "genotype" chart and several blank "phenotype" charts. The genotype chart has the genotype of select individuals noted (Fig. 1a and Fig. 3) and whether the trait to be simulated is dominant, recessive, or sex-linked recessive. The phenotype charts have the same number and orientation of squares and circles connected by lines but are otherwise blank. The exercise involves filling in the genotype chart by tossing a coin to determine which of the two alleles is inherited by an offspring. Thus the exercise simulates nature; each offspring is a result of random choice of one of the two copies of the gene in each parent.
Instructors can make their own pedigree charts. One can make
a blank pedigree chart using as a guide the pedigree charts on
Figure 3 and adding and/or deleting individuals or generations.
Alternatively one can use one's own or other families' pedigrees.
Then decide upon the type of trait, dominant, recessive, or sex-linked
recessive. Then keeping in mind the type of trait, pick the genotype
for select individuals. It is easiest to indicate the genotype
of the oldest (top) part of the pedigree and new individuals that
marry into the pedigree.
1) First note the genotype for select individuals on the genotype chart. In the example given in Figure 1a, the father is heterozygous and mother is homozygous recessive.
2) Next decide which copy of the gene corresponds to heads and tails, for example, heads = A and tails = a. Once decided, keep it the same throughout.
3) Now determine the genotype of an offspring by tossing a coin. Toss the coin for the father. This determines which copy of the gene the father contributes to his offspring. By tossing a coin, we have 50:50 chance of getting heads, that is A or getting tails, that is a. In the example on Figure 1, the chance of getting a from the mother is 100%, or 1.0, and chance of getting A or a from the father is 50% or 0.5. Thus there is 1.0 times 0.5 equals 0.5, that is 50% chance of offspring with genotype Aa and 50% chance of offspring with genotype aa. However, with the small number of offspring, the coin toss may result in all Aa or all aa offspring or any combination in-between.
Similarly, the sex is determined by the sex chromosomes. In mammals,
females have two X chromosomes and males have an X and a Y. The
probability of the father contributing an X is 50% and Y is 50%,
so on average, the offspring should be roughly 50% female and
50% male. In Figure 2, I have indicated vertical lines to indicate
offspring but there are no squares or circles below the lines
to indicate their gender.
Try tossing the coin, with X as heads and Y as tails to determine the sex ratio of the ten offspring. If everyone in the class did it, the overall ratio of male to female offspring will be close to 50% but many individual pedigree charts will have ratios different from 50:50.
In Figure 1, if the mother was also heterozygous, Aa, then the probability of an offspring with genotype aa is the probability of father contributing an a, 50%, and the mother contributing an a, 50%, that is 0.5 times 0.5 which is 0.25 or 25%. The same calculation will apply for an offspring of genotype AA. In calculating the probability for an offspring with genotype Aa, since either the mother or the father can contribute A and then the mother or the father can contribute a, the probability of genotype Aa is 2 times 0.5 times 0.5 which is 0.5 or 50%. This is the probability that one derives from using the Punnett square. However, the results from coin toss for the small number of offspring in any of the pedigrees may not match these expectations. This is what makes this exercise a challenge.
Note: You need not toss a coin for any homozygous parent. For example, in the example given here, you need not toss the coin for the mother since she can only contribute a. You also need not toss the coin for a father in the case of a sex-linked trait since the sex of the offspring requires that either the X or the Y chromosome is contributed by the father.
4) Continue for each individual that does not have the genotype written. Faithfully note the result of each coin toss. Even if the expected ratio of offspring genotypes is 1Aa: 1aa like in this example, if each time you tossed the coin for the father you came up with heads, that is A, write Aa for each offspring.
5) As you determine the genotype or after completing the genotype pedigree chart, fill in the phenotype pedigree chart appropriate for the trait noted on your genotype chart. For example, if your genotype chart looked like Figure 1b, and the trait was dominant, the phenotype charts would look like Figure 1c. On the other hand, if the trait was recessive, the phenotype chart would look like Figure 1d. 6) Produce a phenotype chart for your group, one for the instructor, and for each of the other groups in the class. Of course, all the phenotype charts from one group should be identical.
7) Keep the genotype chart and a copy of the phenotype chart
for your group and distribute phenotype chart to each of the other
I instruct each group to look at their own phenotype chart and
discuss within their group whether one can unambiguously decide
whether the trait was a dominant, recessive, or sex-linked recessive.
The challenge for the instructor is to provide genotype charts
that result in unambiguous phenotype charts most of the time.
One way to ensure that particular genotypes arise is to indicate
the genotype for key individuals or have a cross to an individual
with a particular genotype. Some examples of genotype charts I
have used in class are given in Figure 3.
It is useful to have a variety of genotype charts, some with many offspring, others with more generations, and others with combinations of these. One may choose to have a genotype chart that often results in ambiguous phenotype chart, since it is important that students recognize that pedigrees can be ambiguous. In those cases in which the resulting pedigree is ambiguous, I instruct the students to write the genotypes consistent with the alternative.
Once the group has finished analyzing their own phenotype chart, they can then discuss the phenotype charts of other groups. The challenge here is to determine the genetic rules by which such a phenotype chart can result. Depending on the number of groups, I allow greater time for group discussion. This group discussion time among students is valuable for learning and should not be hastened.
While students are doing this, I reproduce each of the phenotype charts on an overhead transparency that I have prepared before class of each blank phenotype chart. This is also the time for the instructor to check on the phenotype chart, first to ensure that it can result from the assigned genotype, and second to determine whether the phenotype chart unambiguously indicates one type of trait.
After students have had adequate time to analyze the phenotype
charts, I lead a class discussion of each phenotype chart. A good
starting point is to ask the group producing the phenotype chart
whether they feel that the rules of inheritance for the trait
can be decided unambiguously. If the group decided that the chart
is ambiguous, the rest of the class can go through the exercise
of what the genotypes of individuals must be if it is recessive,
dominant, or sex-linked. In this process, sometimes it may be
determined that the group was wrong and that the trait can only
be due to one or another type of inheritance. In any case, it
is valuable for the instructor to lead the discussion assuming
that the group producing the phenotype chart has reached the correct
conclusion. Inevitably, the group discussion will reveal the error
and why it is erroneous. If the group producing the phenotype
chart decided that the chart is unambiguous, it is the job of
the rest of the class to decide which type of trait it is. This
can be quite lively with students providing the reason for suggesting
one or another type of trait and another student saying "well
but what about that individual." By this process, students
truly grasp the meaning of dominant, recessive and sex-linked
inheritance. Also in this process, students learn the importance
of having multiple generations and more offspring in determining
the rules of inheritance for a particular trait.
After this exercise, students are better able to appreciate pedigrees in textbooks and historical pedigrees such as that of hemophilia in Queen Victoria's large family found in variety of human genetics textbooks reprinted from McKusick (1969).
A good follow-up homework assignment is to have students research their own family pedigree. It may be helpful to provide a list of Mendelian human traits, those traits determined by single nuclear genes found in many genetic texts, though many emphasize disease traits. A handy list of non-disease physical traits can be found in Winchester & Wejksnora (1996). A good resource for human genetic disease is the Online Mendelian Inheritance in Man, OMIM (TM).which lists over 5,000 human genetics diseases.
One pedigree that most students can construct uses the ABO blood type which is actually a co-dominant trait. An example of a genotype and phenotype chart for blood type is given in Figure 4. In this case of codominance, O is recessive to A and B, but A and B are codominant, that is, both forms are expressed. So if an individual has A blood type, their genotype can be either AA or AO. Similarly, B blood type can be due to either BB or BO. The genotype of AB, however, can only be AB.
Understanding the fundamentals of Mendelian genetics is important
for biological sciences majors as well as the general public.
This coin toss game graphically illustrates simple Mendelian inheritance
and the difficulty in determining the genetics of traits by just
looking at the pedigree. The exercise is useful for a wide range
of student backgrounds. By having students actually "do"
crosses, key features of basic Mendelian inheritance is vividly
grasped by the students.
McKusick, V.A. (1969) Human genetics, 2nds edition. Prentice-Hall, Inc. Englewood N.J.
Online Mendelian Inheritance in Man, OMIM (TM). Center for Medical Genetics, Johns Hopkins University (Baltimore, MD) and National Center for Biotechnology Information, National Library of Medicine (Bethesda, MD), 1996.
Winchester, A.M. and Wejksnora, P.J. (1996). Laboratory manual
of genetics. 4th ed. pp 117-119. Wm.C. Brown Publ. Dubuque, IA.