In an earlier paper (Smith & Baldwin, 2015), we explained the basic concepts of the Hardy-Weinberg equilibrium (HWeq) principle needed for meaningful understanding and for good teaching, emphasizing distinctions that are sometimes ignored at the cost of coherent understanding, and identifying nine shortcomings of most available Hardy-Weinberg activities and problem sets. In the present paper, we provide a 5E lesson plan based on that analysis and designed to avoid the shortcomings identified, including providing original data and focusing on understanding and topics that are interesting and meaningful to young people.

Introduction

In an earlier paper (Smith & Baldwin, 2015), we identified nine shortcomings common to available Hardy-Weinberg exercises. These exercises often: (1) fail to focus on understanding; (2) are unclear about which specific gene is involved in the problem (e.g., “tasters”); (3) are unclear about the characteristics of the population being studied (especially size); (4) assume that the HWeq exists in the population but do not say so explicitly; (5) assume students have certain biological knowledge about the gene involved in the problem; (6) make assumptions that are contradicted in fact or are likely impossible; (7) ask for judgments about populations that are constituted by members of multiple generations; (8) ask for calculations that are meaningless in the given context; and/or (9) ask for solutions that have no apparent value/are not related to genuine research questions (i.e., fail the “So what?” test).

A particularly prevalent shortcoming is the presentation of an activity with colored buttons or other manipulatives that fails to focus on transferring the activity into biological meaning and thus into understanding of basic HWeq concepts and of population genetics and evolution. Also frequently missing is a focus on the conditions required for HWeq and, more often, on understanding why these conditions are required. Most importantly, students all too often are “doing a thing with buttons” instead of learning about HWeq. This is a transfer issue, but it is also a failure to communicate to students why the HWeq was and is of such importance, that is, how it relates to the rest of biology, how it can be relevant to their personal lives, and even more important, how it can be interesting!

We describe here a proposed lesson plan that aims to avoid these shortcomings. It is based on a three-stage learning cycle model designed by Atkin and Karplus (1962) in the Science Curriculum Improvement Study (SCIS) program and expanded to the current five-stage model in 1978 by the Biological Sciences Curriculum Study (Bybee et al., 2006). The model is strongly supported by a body of literature documenting its effectiveness (BSCS, 2006, and citations therein) and is widely employed in science education, including in this journal (e.g., Chudyk et al., 2014). 5E instruction is an inquiry learning approach that “exposes students to problem situations (i.e., engages their thinking) and then provides opportunities to explore, explain, extend, and evaluate their learning,” in contrast to simply giving students information, such as answers to questions they do not have (Bybee et al., 2006, p. 4).

The goal of the activity below is therefore to understand the “big ideas” about the HWeq that are involved in evolution (Table 1), which we derived from the previous analysis (Smith & Baldwin, 2015).

Table 1.
Big Ideas about Evolution and the Hardy-Weinberg Equilibrium (in simple digenic—2 allele—traits; adapted from Smith & Baldwin, 2015).
1. The HW equilibrium principle is a central part of population genetics. Population genetics is a central part of understanding how evolution occurs. 
2. Variation in a population is required for evolution to occur by natural selection. 
3. Allele and genotype frequencies in populations change over time when some members of a population have increased reproductive success due to an inherited trait. 
4. Allele and genotype frequencies in infinite populations do not change over time if certain things do not occur (mutation, random mating, etc.). 
5. If a population is in H-W equilibrium with respect to a gene/locus of interest: 
 
  • After one generation of fully random mating, BOTH the genotype and allele frequencies are fixed until one of the Conditions 1–6 (Table 2) is violated.

  • The frequencies of each genotype in a population can be predicted from the allele frequencies in that generation. (Allele frequencies can always be calculated from the frequency of the homozygous recessive individuals.) Being able to compute the likelihood that a given individual is heterozygous (a “carrier” of the trait) can be very useful information, e.g., in genetic counseling.

  • Genotype frequencies in the next generation can be computed from the allele frequencies in the current generation.

 
6. If the observed frequencies of genotypes in a population do not match the predicted frequencies, then the population cannot be in H-W equilibrium. 
7. The value of knowing that a population is not in H-W equilibrium is that researchers then know to look for what is throwing the population “out of balance”, which sometimes helps us understand the trait better. 
1. The HW equilibrium principle is a central part of population genetics. Population genetics is a central part of understanding how evolution occurs. 
2. Variation in a population is required for evolution to occur by natural selection. 
3. Allele and genotype frequencies in populations change over time when some members of a population have increased reproductive success due to an inherited trait. 
4. Allele and genotype frequencies in infinite populations do not change over time if certain things do not occur (mutation, random mating, etc.). 
5. If a population is in H-W equilibrium with respect to a gene/locus of interest: 
 
  • After one generation of fully random mating, BOTH the genotype and allele frequencies are fixed until one of the Conditions 1–6 (Table 2) is violated.

  • The frequencies of each genotype in a population can be predicted from the allele frequencies in that generation. (Allele frequencies can always be calculated from the frequency of the homozygous recessive individuals.) Being able to compute the likelihood that a given individual is heterozygous (a “carrier” of the trait) can be very useful information, e.g., in genetic counseling.

  • Genotype frequencies in the next generation can be computed from the allele frequencies in the current generation.

 
6. If the observed frequencies of genotypes in a population do not match the predicted frequencies, then the population cannot be in H-W equilibrium. 
7. The value of knowing that a population is not in H-W equilibrium is that researchers then know to look for what is throwing the population “out of balance”, which sometimes helps us understand the trait better. 

Observation 1. As long as a population satisfies biological Conditions 1–5 (see Table 2), the allele frequencies (p and q) remain the same in each generation.

It is also crucial to know the conditions that are required in order for HWeq to exist (Table 2).

Table 2.
Conditions required for Hardy-Weinberg Equilibrium to exist (from Smith & Baldwin, 2015).
1. There is no migration (gene flow) in or out of the population. 
2. Natural selection is not occurring. 
3. Mutation is not occurring. 
4. Each member of the population is equally likely to breed.* 
5. The population is infinitely large. 
6. (Full random mating) Each pair from the population is equally likely to breed. 
1. There is no migration (gene flow) in or out of the population. 
2. Natural selection is not occurring. 
3. Mutation is not occurring. 
4. Each member of the population is equally likely to breed.* 
5. The population is infinitely large. 
6. (Full random mating) Each pair from the population is equally likely to breed. 
*

Often “random mating” is used to refer to both conditions 4 and 6. Random mating means that the frequency of mating of an individual or of any pair of individuals does not depend on the genotype.

Teachers who are not familiar with this instructional design may find this lesson difficult to implement until you have had practice using the technique with less complicated content. Teacher questioning that focuses on helping biology students build their understanding step by step instead of lecturing can be challenging until you have mastered it, especially with activities in which biology students are building mathematical models. Like most inquiry-based instruction, the role of the teacher here is as a facilitator—the guide on the side, not the sage on the stage.

Species evolve as the frequencies of various alleles change over generations. Change in allele frequency is caused by natural selection and genetic drift, among other reasons. Population genetics is the study of these changes. New species arise when these changes accumulate to the extent that breeding with earlier forms is no longer possible (Big Idea 1). Alleles are different forms of a gene; some alleles confer increased reproductive success on the individual and will increase in frequency in response to natural selection (Big Ideas 2 and 3). Constancy of allele frequency requires that no factors such as mutation, natural selection, or migration are adding or deleting alleles (Big Idea 4). The Hardy-Weinberg equilibrium principle explains how genotype and allele frequencies are maintained (Big Idea 5) and can be used to identify populations in which equilibrium does not exist (Big Idea 6), which can signal to researchers that they should seek the causes of this state (Big Idea 7).

The proposed lesson focuses on understanding these Big Ideas first by introducing students to Huntington's Disease (HD) (Engagement). Next, a set of manipulatives is introduced by which students can model the frequencies of HD alleles; then students generate models to predict HD allele frequency change from one generation to the next in the absence of natural selection (Exploration). Students compare and improve their models, and compare these against the current scientifically accepted model (the HWeq) (Explanation). Finally, students apply their new understanding to a new case—the CCR5 deletion that reduces HIV binding to T-cells (Elaboration).

The target audience is high school biology or AP biology and introductory college biology students with some experience with modeling (especially mathematical modeling) and with the 5E instructional approach. Minimal understanding of DNA structure, Mendelian genetics, and basic evolution and natural selection is assumed. For high school classes, the activity should take three to five 45-minute periods. Detailed solutions, explanations, and other teacher guide information are provided in Supplement 1: Teachers Guide, along with a copy master for the Student Worksheet. The activity targets the Next Generation of Science Standards (http://www.nextgenscience.org/next-generation-science-standards), including the disciplinary core ideas of natural selection (LS4.B) and adaptation (LS4.C) as well as the practice of “using mathematics and computational thinking.” This activity also targets AP Biology science practices 2 and 6, essential knowledge 1.A.1g–h, 4.C.3c, and learning objectives LO 1.6, 1.7, and 4.26:

LO 4.26 The student is able to use theories and models to make scientific claims and/or predictions about the effects of variation within populations on survival and fitness. (College Board, 2015)

Activity Objectives

At the end of the activity, students should be able to:

(For a simple Mendelian, digenic [2-allele] trait)

  1. Explain why variation is important for evolution to proceed.

  2. Explain why dominant traits do not eliminate recessive traits in a population, even if the recessives are very damaging.

  3. Define evolution in terms of changing allele frequencies in a population.

  4. Explain what the Hardy-Weinberg equilibrium principle is, and apply it to individual populations.

  5. Identify the six conditions required for HWeq to exist, and explain why each is required.

  6. Compute allele frequencies from the frequency of the individuals of various genotypes.

  7. Explain why traits that are expressed only after reproductive age of the individual do not affect allele frequency.

  8. At HWeq: Given the allele frequencies in the current generation of a population, compute genotype frequencies in that or the subsequent generation.

  9. Given the distribution of the three genotypes in a population and data from which to determine the allele frequencies, determine whether or not the population approximates HWeq.

  10. Describe the value of knowing that a population is not at HWeq.

Time required: Two to three 45-minute periods, depending on student expertise and familiarity with 5E instruction.

Materials

Engagement Phase

Large Group

Students typically find fascinating the story of Nancy Wexler, her mother who died early of Huntington's Disease, and the work to identify the determinants of the disease among the inhabitants of the village of Barranquitas on the shores of Lake Marakibo in Venezuela (Figure 1). Begin this activity by asking: What human genetic diseases do you know much about? Have you ever met someone with a genetic disease? Then show “Nancy Wexler in Venezuela” (BBC) 0–3:30 (https://www.youtube.com/watch?v=D6LbkTW8fDU).

Figure 1.

Nancy Wexler with HD patients in Barranquitas. Used with permission from Nancy Wexler: La cazadora del gen (The Gene Hunter) [El Blog]. Retrieved from http://loquierogritar.blogspot.com/2011/08/nancy-wexler-la-cazadora-del-gen.html

Figure 1.

Nancy Wexler with HD patients in Barranquitas. Used with permission from Nancy Wexler: La cazadora del gen (The Gene Hunter) [El Blog]. Retrieved from http://loquierogritar.blogspot.com/2011/08/nancy-wexler-la-cazadora-del-gen.html

Ask and allow students to discuss (do not give answers yet):

  • Have you ever heard of Huntington's Disease? If it is so bad, why doesn't it disappear? (Objective 2)

  • Do you think the frequency of people with HD in Barranquitas will change over time (increase or decrease)? How could we predict?

Exploration Phase

Pairs or Small Groups

In the Exploration Phase, students seek to find answers to their own questions and those you pose. Ask the following questions:

  • What else would you like to know about Huntington's Disease? (Use the Internet.)

  • What does “inherited” mean? How is HD inherited?

  • So why doesn't the HD mutant allele disappear in the Barranquitas population? How could we predict how the number of people with HD might change over time—from one generation to the next? (Objectives 2, 3)

  • What is a population?

Activity: Ask students to use the paper clips provided to represent a random sample of 100 people of Barranquitas in the generation aged 40 to 59 and their Huntington alleles (homozygotes of each type and heterozygotes), using the data from Wexler's research in Table 3. Make sure that each of the students' “individuals” consists of two “alleles” (2 paper clips), representing all three possible genotypes (see Figure 2).

Figure 2.

Paper clip models of the two possible homozygotes and the heterozygote. (HH = 2 of one color; Hh = 1 of each color; hh = 2 of other color).

Figure 2.

Paper clip models of the two possible homozygotes and the heterozygote. (HH = 2 of one color; Hh = 1 of each color; hh = 2 of other color).

Table 3.
Prevalence of individuals* diagnosed with Huntington's disease in the village of Barranquitas (Venezuela), 2002, in deciles (from Julie Porter for Nancy Wexler, Hereditary Disease Foundation, Columbia University; personal communication, January 8, 2015).
Age (in deciles)Number with HD diagnosisTotal population
0–9  0  867 
10–19  5 1995 
20–29  23 2102 
30–39  77 1904 
40–49 150 1475 
50–59  96  905 
60–69  30  500 
70–79  7  297 
80–89  2  116 
90–99  0   54 
100–109  0   12 
Age (in deciles)Number with HD diagnosisTotal population
0–9  0  867 
10–19  5 1995 
20–29  23 2102 
30–39  77 1904 
40–49 150 1475 
50–59  96  905 
60–69  30  500 
70–79  7  297 
80–89  2  116 
90–99  0   54 
100–109  0   12 
*

Individuals for whom all data (including diagnosis and age) were available.

  • Ask: So how many of the people with HD are heterozygous? Homozygous?

  • Answer: Unknown (unless population is at HWeq).

  • Ask: What is the frequency of each allele in the generation aged 40- to 59-year-old population? (Objective 6)

  • Ask the students to model the offspring from any pair of individuals (HH X HH; HH X Hh; HH X hh; Hh X hh; hh X hh). (Remember from the Wexler video that HD is caused by a dominant autosomal mutation.) Then ask students to come up with a way to model all possible matings in the population, in their proper relative frequencies (by drawing random pairs of alleles from the entire population of alleles, with allele pairs separated), modeling the change in allele frequency from one generation to the next.

  • Ask: So, how did the allele frequencies in the current generation compare to that of the next generation? The number of H alleles doesn't decrease. Does this surprise you? It surprised some scientists in the early 1900s when this question first came up! And did everyone get the same thing, even though you started with different proportions of HH and Hh individuals? What do you predict will happen to the allele frequencies in the next generation?

  • Ask: Do you think the frequencies of HD alleles stay the same from generation to generation in nature? What kinds of things could change allele frequencies over time? (Objective 4, 5).

  • Ask: How could you predict what the genotype proportions should be if there are no external forces acting on the population and mating is completely at random? What mathematical model could you come up with to predict these proportions?

Guide Model Generation and Testing by Student Groups

When HD genotype testing was developed, it appears that 2 of the 246 HD individuals of the 40–59-year-old generation in Barranquitas were likely homozygous for the mutant allele (HH) (Table 4). How do these observed genotype frequencies compare to your predicted frequencies? Does this generation appear to be in HWeq? (Objectives 4, 9) Hint: Remember: At HWeq, the frequencies at the present and at the subsequent generations should be the same.

Table 4.
Frequencies of individuals with each documented HD genotype in Barranquitas, aged 40–59, 2002: Observed vs. expected (based on Wexler et al., 2004).
GenotypePredictedObserved
HH   7   2 
Hh  238  244 
hh 2135 2134 
Totals 2380 2380 
GenotypePredictedObserved
HH   7   2 
Hh  238  244 
hh 2135 2134 
Totals 2380 2380 

Reconvene the large group. Allow groups to present their models for questioning and critique by peers.

Explanation Phase

Large Group

During the Explanation phase, the accepted scientific answers and explanations are explained and discussed, and related to those generated by the students.

  • Ask: Do you think we could ever predict the proportion of this population that would be heterozygotes? Why or why not? What conditions would have to be true for our predictions to be accurate? (Objective 5; Table 2)

  • Ask: Which conditions are likely to be violated in this case?

Here the teacher discusses the work of Hardy and Weinberg (see Smith & Baldwin, 2015) and explains the HWeq principle and the conditions required. Relate this model to student (successful) models and critique.

  • Ask: Suppose we find out that a particular population is not in HWeq. What does this tell scientists? (One or more of the HWeq conditions is violated.) (Objective 10)

In the current sample, 90 percent of those who show symptoms of HD showed those symptoms by age 60 (see Table 3). Many biology texts simplify the discussion of HD by incorrectly assuming that the symptoms do not appear at all until after reproductive age. In contrast, individuals with a certain inherited eye disease (age-related macular degeneration, AMD, the leading cause of blindness in the elderly) do not have any symptoms until well past typical reproductive age.

  • Ask: Would the effects of natural selection be different for AMD than for HD? How? Why? (Objective 7)

Elaboration Phase

HIV Deletion in CCR5 (Large group, then alone or in small groups)

Now, to see how well the students have understood so far, present a new situation.

Ask what the students know about HIV. Then ask if they know that a few very rare people seem to be immune to HIV—they don't get infected even though they are exposed to it many times! How could that be? Show CCR5 video (0–1:12). Give students copies of the ideogram (Figure 3) of human Chromosome 3 and ask them to find and mark the CCR5 locus. Briefly explain how to read the map. (The HD locus is found on the short arm of Chromosome 3.)

Figure 3.

Ideogram of human Chromosome 3. Arrow indicates CCR5 locus (3p21.31). Used with permission from Genetics Home Reference, CCR5 gene (n.d.). Retrieved from http://ghr.nlm.nih.gov/gene/CCR5

Figure 3.

Ideogram of human Chromosome 3. Arrow indicates CCR5 locus (3p21.31). Used with permission from Genetics Home Reference, CCR5 gene (n.d.). Retrieved from http://ghr.nlm.nih.gov/gene/CCR5

Explain that people who are homozygous for (have two copies of) a certain 32-bp (base-pair) deletion mutation of the CCR5 gene found on human Chromosome 3 make a defective protein that will not bind to HIV very well. These homozygotes are largely resistant to HIV infection. (HIV resistance is therefore a recessive trait.)

Students now work alone or in small groups. Hand out the following problem for students to solve:

Susan is a 17-year old Caucasian American woman who is at increased risk of HIV infection because she has multiple sex partners. She heard about CCR5 and that it is most common among Caucasians. On the Internet she found out about a study of 1318 random Caucasians of child-bearing age in the United States, of which 1102 were found to be homozygotes in which neither allele had this deletion (Glass et al., 2006). Assume that the U.S. Caucasian population is at HWeq at this locus.

    • What is the probability that Susan has little reason to worry about HIV infection (i.e., that she is homozygous for the deletion)? (Objectives 5, 7)

    • How do you figure out the frequency of each allele? Of each genotype? Can you know the frequency of the heterozygotes without knowing the allele frequencies? (Objective 4) Without knowing that the population is in HWeq? Does the allele frequency of each allele change from one generation to another if the population is in HWeq? lf the population is NOT in HWeq? How do you figure out the genotype frequencies in the current population? (Objective 8) What are you assuming?

    • How would you predict the genotype frequencies in the next generation? (Objective 8) What are you assuming?

  1. Why is variation in the frequency of alleles in a population so important? (Objective 1)

  2. What is the predicted proportion of U.S. Caucasians who are carriers of the protective deletion? (Objective 8)

  3. How many heterozygotes would be expected in this sample?

  4. Why is it useful to know the frequency of heterozygotes in a population? (Objective 10) To know if the population is in HWeq or not? (Objective 10)

    • Before HIV appeared, would you have expected the population to have been at HWeq at this locus? (Objective 5)

    • Why or why not? State your assumptions. (Objective 4)

    • What kinds of things could put the population out of HWeq balance? (Objective 5)

    • In the absence of effective HIV treatments, what would you expect to happen to the allele frequencies over time? (Objective 4)

    • How would you expect the allele frequencies to change over time once effective HIV treatment was in use? Why? (Objective 4)

  5. Assume a population is not at HWeq, but suddenly all the Hardy-Weinberg conditions are met. How many generations would it take for the population to get to HWeq? (Objective 4)

  6. What is your conclusion?

Evaluation

Formative Assessment: The teacher gives frequent feedback to individuals in groups as they participate in the Explanation and Elaboration phases of the lesson. Focus on the Big Ideas!

For suggested evaluation items, see Supplement 2: Summative Assessment Options.

Summary

The 5E lesson plan proposed here differs substantially from many available HWeq instructional designs in which the nine shortcomings identified in our earlier article may be found. Most importantly, the central focus throughout is on understanding the “big ideas” of HWeq (Table 1) and on making this learning interesting and relevant to the world outside the classroom and less focused on calculation. We encourage teachers to test this lesson plan in their classrooms. Feedback to the author is welcome.

References

References
Atkin, J. M., & Karplus, R. (
1962
).
Discovery of invention?
Science Teacher
,
29
,
45
.
Bybee, R. W., Taylor, J. A., Gardner, A., Van Scotter P., Powell J. C., Westbrook, A., & Landes, N. (
2006
).
The BSCS 5E instructional model: Origins, effectiveness, and applications.
Available at http://bscs.org/sites/default/files/_legacy/BSCS_5E_Instructional_Model-Executive_Summary_0.pdf.
Chudyk, S., McMillan, A., & Lange, C. (
2014
).
Using the Eastern Hellbender salamander in a high school genetics & ecological conservation activity
.
American Biology Teacher
,
76
,
338
344
.
College Board
. (
2015
).
AP Biology: Course and exam description (rev.).
New York
:
Author
. Available at https://secure-media.collegeboard.org/digitalServices/pdf/ap/ap-biology-course-and-exam-description.pdf.
Glass, W. G., McDermott, D. H., Lim, J. K., Lekhong, S., Frank, W. A., Pape, J., Cheshier, R. C. and Murphy, P. M. (
2006
).
CCR5 deficiency increases risk of symptomatic West Nile virus infection
.
Journal of Experimental Medicine
,
203
(
1
):
35
40
.
NGSS Lead States
. (
2013
).
Next Generation Science Standards: For states, by states
.
Washington, DC
:
National Academies Press
. Available at http://www.nap.edu/catalog/18290/next-generation-science-standards-for-states-by-states.
Smith, M. U., & Baldwin, J. T. (
2015
).
Making sense of Hardy-Weinberg equilibrium
.
American Biology Teacher
,
77
,,
577
582
.
U.S.–Venezuela Collaborative Research Project
& Wexler, N. S. (
2004
).
Venezuelan kindreds reveal that genetic and environmental factors modulate Huntington's disease age of onset
.
Proceedings of the National Academy of Science
,
101
(
10
):
3498
3503
.