The Hardy-Weinberg principle and associated calculations are often challenging for students to learn for three reasons. First, several assumptions need to be understood to correctly apply the principle. Second, a series of calculations are required for proper application. Third, the principle, assumptions, and calculations are often taught separately from students observing population changes over time. We describe a classroom activity in which students investigate how the allele frequencies of soft-shell clam (Mya arenaria) populations change over time as a result of environmental disturbances by simulating the effects on population data. These classroom population changes are then compared to authentic research data collected on populations of M. arenaria. This activity was implemented at three institutions in introductory- and senior-level biology courses. Students reported that the activity helped them better understand and apply both the principle and its calculations.

## Introduction

The Hardy-Weinberg (HW) principle is a fundamental topic that students are expected to learn in many college-level introductory and advanced biology courses. The principle describes the expectations for a population to change over time under certain conditions. Two scientists in the early 20th century, G. H. Hardy and Wilhelm Weinberg, first independently described this principle (Stern, 1943). Since its first articulation, the utility of the HW principle ushered in the burgeoning field of population genetics, which is now its own rich and thriving biological subdiscipline (Crow & Dove, 1988). The principle has two components. The *concept* of the principle is relatively simple: if a very large population (with no genetic drift) has random mating, no migration, no mutation, and no selection, then the allele frequencies will remain constant from one generation to the next. The *equation* of the principle is p^{2} + 2pq + q^{2} = 1, where p and q are the frequencies of two alleles of a gene. Additionally, it can be easily extended to loci with more than two alleles. This equation allows biologists to calculate allele frequencies and determine whether a population is in Hardy-Weinberg equilibrium (HWE) between generations. When a population is out of HWE, a biologist can then examine the five assumptions of the HW principle (large population, random mating, no migration, no mutation, no selection) to see which evolutionary forces might be driving changes in allele frequency.

The HW principle is a useful construct for detecting microevolution, but students can find it challenging to effectively understand and apply it (Mertens, 1992; Masel, 2012). Difficulties arise for various reasons. Some students struggle to see the practical implications of the HW principle, given that its five assumptions are rarely true in actual biological populations (Mertens, 1992). Other students lack the mathematical proficiency to compute allele frequencies and use the equation to quantify how populations change over time (Ortiz et al., 2000). Inspired by these challenges, biology educators continue to design and implement a variety of classroom and lab activities to help students achieve a deeper conceptual understanding of the principle, and the tools needed to make the necessary computations (e.g., Christensen, 2000; Winterer, 2001; Pongsophon et al., 2007). Such tools are useful and represent significant and positive steps forward in the teaching and learning of the HW principle. Here, we describe a new classroom activity that (1) explicitly connects the HW principle to actual biological populations; (2) provides an opportunity to observe and track populations over time; and (3) describes a complete example of trait evolution from nucleotides to cell function to local-scale biogeographical patterns.

## Learning Outcomes

Students should be able to

use HWE terms in their proper context (i.e.,

*genes, alleles, genotype and allele frequencies, genetic drift, natural selection, evolution*);predict and calculate the allele and genotype frequencies of a population;

describe hypothesis testing and why HWE is a null hypothesis; and

construct graphs and tables to understand the effects of natural selection and/or genetic drift on allele and genotype frequencies in a population over time.

## Description of Activity

Our two-part activity makes use of “just-in-time” teaching (Novak, 2011), hands-on learning, and connections to authentic research data. The activity contextualizes HWE through the evolution of toxin-resistance in the soft-shell clam, *Mya arenaria*, an Evo-Ed Case (http://www.evo-ed.org; White et al., 2015). Students are not expected to have prior knowledge about this case, thus enabling them to “discover” differences in their populations and the driving evolutionary forces in real time. The Evo-Ed website provides curricular materials to support teaching evolution as an integrated process, connecting events across biological scales, from nucleotides to populations. We used this framework to develop and test our activity addressing HWE in actual populations, with a trait where the complete pathway (*genes*→ *proteins*→ *phenotype*→ *fitness*→ *selection*) is known. Part 1 of the activity introduces HWE in the context of clams spawning in the ocean; part 2 illustrates the effects that selection and drift can have on allele frequencies within clam populations across generations.

## Course Details

We implemented the clam activity in one upper-level evolution course (14 junior/senior biology majors) and two introductory-level survey courses (71 first-year biology majors; 28 sophomore biology majors) across three diverse institutions in the northeastern and southeastern United States. In the evolution course, the two parts of the activity were implemented over two consecutive 55-minute class periods. In both introductory-level courses, students completed the entire activity in one 3-hour lab session.

## Activity Part 1: Clam Spawning

The following materials are required (Figure 1):

Bag of 100 red marbles/beads

Bag of 100 yellow marbles/beads

Bag of 100 mixed marbles/beads, 50% red and 50% yellow

Shared spreadsheet to record student spawning data (http://evo-ed.org/pages/resources.html#abt_resources)

Worksheet that students complete during the activity and discussion (Figure 2; http://evo-ed.org/pages/resources.html#abt_resources)

Students act as individual soft-shell clams in a classroom population that represents an idealized population that experiences no selection, migration, mutation, drift, or nonrandom mating (i.e., it fulfills the requirements of HWE). The activity proceeds as follows:

Each student entering the classroom chooses a handful of beads from one of three bags: red, yellow, or mixed. These beads represent the clam gametes that each student will subsequently broadcast out into the spawning environment.

Students record their spawning gametes (i.e., numbers of red and yellow) and place them in a community bucket.

The instructor records the total number and color of student gametes in the bucket on a class spreadsheet.

Here, the instructor may choose to spend a few minutes describing how clams reproduce by releasing gametes into the water column (broadcast spawning). This teaching and learning can be augmented with textbook materials or an online video on broadcast spawning. Although the primary goal is to introduce HWE, this activity introduces it through basic probabilities, a concept that should already be familiar to students. The instructor can then relate probabilities to HWE.

The instructor displays the classroom population data and asks students what the probability is of pulling a red bead out of the community gamete bucket. The instructor can demonstrate probability by having multiple students randomly select 10 beads and count the number of each color.

With only two bead colors, students should be able to determine the yellow bead frequency given the red bead frequency.

Once students understand the relationship between color frequencies in the gamete pool and probability, the instructor then demonstrates probability rules by pulling various bead combinations (i.e., two reds, two yellows, and a red and yellow in any order). This last part of the activity provides the framework for HWE.

Building upon student knowledge of probability, HWE can then be introduced simply as the probability of each possible gamete combination (i.e., Red-Red, Yellow-Yellow, Red-Yellow).

The expected genotype and allele frequencies within a population are now generated from the class gamete pool using the HW equation.

The calculated values are then compared to “actual” values, determined by each student randomly pulling two new gametes (beads) from the gamete bucket to make a developing zygote.

The genotypes of these developing zygotes are recorded, then the class calculates the genotype and allele frequencies from this new “population.”

These frequencies, generated from the “actual” population, are then compared to the counts calculated for the “expected” population (completed earlier) using a chi-square test.

Random gamete selection, counting genotypes, and calculating allele frequencies are core tasks of part 2. Thus, the end of part 1 is an opportune time to clarify any conceptual or mathematical challenges associated with these tasks.

## Activity Part 2: Comparing Actual Populations

The following materials are required (Figure 1):

Bag of red and yellow marbles (100 of each color)

Organizing tray (a 24-well ice-cube tray works well; wells labeled 1–24)

Sets of “event cards” (or a die), corresponding to the populations being used (http://evo-ed.org/pages/resources.html#abt_resources); each set of event cards is randomly shuffled

A data sheet and student worksheet to record genotype and allele count and frequency data and student worksheet (http://evo-ed.org/pages/resources.html#abt_resources)

In part 2, students work in groups of two to four to simulate changes to the allele frequencies in different populations of *M. arenaria*. Students track two alleles (resistant and sensitive) of the gene responsible for producing the voltage-gated sodium channel in its neuron cell membranes (Bricelj et al., 2005). The resistant (R) allele is the result of a mutation from adenine (A) to cytosine (C), causing a change in amino acid from glutamic acid (E) to aspartic acid (D). The change in amino acid causes the voltage-gated sodium channels in resistant clams to have a lower binding affinity and, as a result, less sensitivity to saxitoxin (Connell et al., 2007). Saxitoxin, a potent neurotoxin, is produced by dinoflagellates during red-tide algal blooms. Clams with a sensitive (S) allele have voltage-gated sodium channels that readily bind saxitoxin, causing pathology and death. Saxitoxin binds to the extracellular gate of the voltage-gated sodium, causing dysfunction and channel blockage. Clams with the R allele accumulate the neurotoxin but are largely unaffected by its paralytic properties (for a more complete description, see http://www.evo-ed.org).

We framed part 2 using data from Connell et al. (2007) that characterized five populations on the eastern seaboard of North America (Figure 3). Each population has its own set of event cards. These cards describe events that may disrupt or change a population, leading to drift and natural selection. Event cards vary by population, as different clam populations are subjected to different environmental stressors. For example, Havre-Aubert and Lawrencetown have no history of dinoflagellate blooms (Figure 3); therefore, the event cards associated with those populations contain only drift events, whereas Lepreau Basin, Essex, and Orleans have a documented history of dinoflagellate blooms and therefore contain drift and selection events.

The instructor can start the activity with some background on the different populations of clams and a review of the learning outcomes from part 1 (see resources at http://evo-ed.org/pages/resources.html#abt_resources). The activity then proceeds as follows:

Each student group is assigned one of the five populations and its associated event cards. Their task is to manage their population by following the instructions given by the event cards and modifying their population, as needed.

All populations begin with the same allele frequency (p = 0.5, q = 0.5); each group should have one bag of alleles with 100 marbles of each color to represent the gamete pool of their population.

The organizing tray (Figure 1) is used to count out 24 individuals randomly created from the gamete pool (two marbles per well).

Students work in groups, following the instructions on the worksheet (http://evo-ed.org/pages/resources.html#abt_resources) and drawing event cards, which can result in allele changes in their population.

After each event card, students calculate and record their new allele frequencies from the standing population because these individuals are going to contribute gametes to the next generation.

The students then reset their gamete-pool bag to reflect the new allele frequencies.

They should continue to draw a card and record the new allele frequencies for at least four to six generations.

Students then graph changes in allele frequencies across generations and describe these changes in relation to the events their population experienced (for examples of student results, see Figure 3).

In addition to generating a summative figure, groups might also test for a statistical measurement of evolution in their population using a chi-square test to compare the allele frequencies of their initial and final populations.

Finally, the instructor recaps the activity by having groups share out their results and discussing the suite of outcomes.

## Analysis of Activity

To measure student perception of the activity, we administered a seven-item attitude survey one week after the activity with five Likert-scale and two open-ended questions (Box 1; St. John Fisher College IRB no. 3859-031518-08, University of Pittsburgh at Bradford IRB no. PRO17110037, and Spelman College IRB no. 67F2E5). Students across all three courses largely agreed that the activity helped their understanding of HWE, though students in the upper-level evolution course were split on the utility of the exercise (questions 1 and 2; Figure 4). It is possible that some students had been exposed to HWE in prior biology courses and, thus, the activity served more as a refresher. Despite this exception, students in all three courses felt that the activity was useful for learning HW calculations and was engaging (questions 2 and 3; Figure 4). We also found a diversity of opinions on whether the activity was challenging, which may have been influenced by the level of the course and the amount of scaffolding provided (question 4; Figure 4).

Indicate how much you agree or disagree with the following questions:

The

*Clam Activity*helped me better understand the Hardy-Weinberg principle.[Strongly Agree] [Agree] [Neutral] [Disagree] [Strongly Disagree]

The

*Clam Activity*helped me better understand how to do Hardy-Weinberg calculations.[Strongly Agree] [Agree] [Neutral] [Disagree] [Strongly Disagree]

The

*Clam Activity*was engaging.[Strongly Agree] [Agree] [Neutral] [Disagree] [Strongly Disagree]

The

*Clam Activity*was challenging.[Strongly Agree] [Agree] [Neutral] [Disagree] [Strongly Disagree]

The

*Clam Activity*should be used in future iterations of this course.[Strongly Agree] [Agree] [Neutral] [Disagree] [Strongly Disagree]

What was one positive aspect of the

*Clam Activity*?What was one negative aspect of the

*Clam Activity*?

Furthermore, students in the upper-level evolution course clearly conveyed that this activity should be used in future iterations of the course, whereas students in the introductory courses were more neutral in their recommendation (question 5; Figure 4). The upper-level students consistently rated their experiences with the clam activity higher on the positive aspects and rated difficulty as comparatively low (Figure 4). Again, one explanation is that these students had previous exposure to concepts of genetics, evolution, and the HW principle. For example, many commented that they appreciated the activities much more because they recalled initially learning the material in a more traditional manner. They already knew how to calculate allele frequencies with the HW principle, but they did not feel that they had a strong understanding of the concept or its utility until after our activity.

In response to the first open-ended question, students brought up five positive aspects of the activity (Table 1A). About a third of the students mentioned the two most common aspects: (1) the activity helped them understand/learn the HW principle and (2) it was hands-on/engaging. When students were asked about the negative aspects of the activity, six themes emerged (Table 1B); the most common response (25%) was that the instructions were confusing, and about 18% said there were no negative aspects.

Theme of Comment . | Number of Students Mentioning This Aspect . |
---|---|

(A) Positive Aspects | |

The activity helped in the learning or understanding of the HW principle. | 36 |

The activity was hands-on or engaging. | 33 |

The activity helped me understand or gave practice with HW calculations. | 17 |

The activity involved a real-life scenario. | 12 |

The activity was fun or interesting. | 12 |

(B) Negative Aspects | |

The instructions were confusing. | 29 |

There are no negative aspects of this activity. | 21 |

The activity was difficulty/tedious/challenging. | 19 |

The activity was time consuming. | 17 |

The spreadsheet interface/component was confusing. | 9 |

Not enough background information was provided. | 5 |

Theme of Comment . | Number of Students Mentioning This Aspect . |
---|---|

(A) Positive Aspects | |

The activity helped in the learning or understanding of the HW principle. | 36 |

The activity was hands-on or engaging. | 33 |

The activity helped me understand or gave practice with HW calculations. | 17 |

The activity involved a real-life scenario. | 12 |

The activity was fun or interesting. | 12 |

(B) Negative Aspects | |

The instructions were confusing. | 29 |

There are no negative aspects of this activity. | 21 |

The activity was difficulty/tedious/challenging. | 19 |

The activity was time consuming. | 17 |

The spreadsheet interface/component was confusing. | 9 |

Not enough background information was provided. | 5 |

Overall, students seemed to appreciate the activity. Much of the frustration occurred during part 2 because students were working alone in their groups doing calculations and using Microsoft Excel to track their populations. There was a learning curve to working through the simulations and “events.” As a result, we recommend completing the first generation as a class even though most groups will likely have different events. The most time-consuming aspects of part 2 were the allele frequency calculations and setting up the gamete pool in between generations. One way to save time after students have demonstrated that they can do the calculations on their own is to use formulas in the spreadsheet to calculate the allele frequency and gamete pool repopulation.

## Discussion

Our two-part lesson is an engaging alternative to static, equation-based discussions that have students “plug-and-chug” their way through HWE. Students actively participated throughout both parts 1 and 2 across all classes. Although the instructions for part 2 can be complicated because each group is carrying out their own simulation with their own event cards, in the end students observed that each group changes in different ways because of different events (drift, natural selection, or both). Using authentic research data to validate simulation results provided a meaningful and impactful experience through real-world application of a biological mathematical model carried out through simulations.

Some existing HW activities and problem sets emphasize “working the math weakness” out of students by presenting allele and genotype frequency calculations lacking biological context, but that approach leaves students with the perception that the goal is to plug numbers into an equation rather than applying a model to a biological phenomenon. Smith and Baldwin (2015) evaluated several HW problems, and although some were problem sets with actual allele frequencies, many activities fell short of providing context or linking microevolution to existing problems that are broadly accessible to students. In contrast, our clam activity gives students simulated populations and natural-selection-type and drift-type events whereby students can experience the resulting changes to allele frequency in the context of actual biological examples. Broadcast spawners like clams facilitate understanding of a gamete pool more readily than organisms with internal reproduction, such as humans. Here students have the opportunity to see fusing gametes (using a video) and then apply the principles of HWE. The context of resistant and sensitive alleles in the clam populations provides real-world examples to observe and manipulate, combined with the ability to relate simulated results to authentic research data.

## Acknowledgments

This collaboration began as a working group at the 2017 BioQUEST Curriculum Consortium meeting at Michigan State University. We are grateful to Kristin Jenkins and the BioQUEST/QUBES staff for their role in facilitating this project. We also thank Merle Heidemann, who played a key role, both in the development of the original Evo-Ed Clam Case and in the clam activity working group. Partial support for this work was provided by the National Science Foundation's DRK12 program (award no. DRL-1620746). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.