Appendix A: Modeling Biology Instruction with Excel Modeling Tools

Appendix A: Modeling Biology Instruction with Excel Modeling Tools

The engineering design challenge. The unit introduces the concepts of population ecology and natural selection in terms of an invasive species bioengineering design challenge. This challenge focuses the learning of the students for the entire four-week unit. To introduce the design challenge, the introductory task familiarizes the students with the wide scale damage produced by one specific highly invasive species familiar to many students in the United States: the Brown Marmorated Stink Bug (BMSB). This is contrasted against the native Southern Green Stink Bug (SGSB), which does not produce severe economic damage to agricultural products. The design challenge of controlling the BMSB using eco-friendly methods is introduced and becomes a theme throughout the entire unit. It is during this initial activity that NGSS Engineering practices, such as identifying the problems and defining success criteria, are introduced. These practices are woven throughout the unit. Since the design challenge initially requires students to develop an environmentally safe plan for controlling BMSB on apple farms in Virginia, and then later applying solutions to other targeted areas involving food production and heavily populated areas across the United States, the materials move student thoughts away from harsh insecticides. Student groups develop a problem statement for the design challenge that incorporates “who” needs “what” and “why”.

Development of the population growth model. In the introduction, it was mentioned that one fundamental concept of population ecology that is essential to student understanding of evolution is population growth. Therefore, the population ecology section begins by asking students to evaluate growth of different types of stinkbugs in different environmental contexts. The population ecology section (shown on the right half of the figure 1) initially asks students to analyze and graph provided population data by hand for both BMSB and SGSB on three separate farms in order to introduce them to different growth curves. This introduction leads the students to hypothesis possible causes for the population changes observed on each farm. On one specific farm, they observe a decline in BMSB population over time. This leads the students to identify questions that need to be answered, constraints on the project, resources needed, and criteria for success. During pilot testing of the curriculum, the questions that the students asked led to the development of an additional data analysis task that restricts the possible causes for the differences in populations growth between the farms to one: a parasitoid wasp that preys on stink bug eggs. Using a simulation, students perform a count of samples of the wasp population on the farms to determine what the wasps are doing at each farm (i.e., on which type of stink bug eggs are they preying). It is through this series of tasks that the NGSS science practices of analyzing and interpreting data are introduced as well as using mathematical and computational thinking.

The unit then builds on the understanding of the phenomenon of population growth achieved through the analysis and interpretation of data by turning to the development and refinement of a model grounded in systems thinking about populations by having the students postulate what they would need to do to “grow” enough wasps to answer the design challenge. Throughout the unit, students are encouraged to represent the models being developed with numerous coherent hand-drawn representations, such as storyboards of stages of change, tables of growth data, and hand-drawn line graphs of growth data. Examples of students’ initial models of population growth can be seen in Figure 2.

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Because doing everything by hand becomes tedious and error-prone, students are encouraged to recognize the need for computer simulations in order to investigate the growth of the wasps over multiple generations as well as for long periods of time. The early hand-drawn representations provide the biological foundation as well as the rationale for a sequence of increasingly sophisticated computer simulations they will work with throughout the rest of the unit that will help to generate numerous representations of the emerging model. The intent of the first Excel modeling simulation task is to help students determine how specific parameters affect population growth, using as a specific example the wasps that inhabit the various farms, see Figure 1. Therefore, the unit has students “purchasing” wasp samples from various farms with specific traits and testing out their ideas of what parameters might affect population growth over 30 generations. The parameters that students usually investigate include sample size, male/female ratio, birth rate, death rate, and limited versus unlimited resources. See Figure 3a for the initial input page of the simulation.

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Students have access to multiple output sheets in an Excel workbook. On the first output sheet, students focus on the predicted versus observed growth curves. The students are tasked with adjusting the input variables until the observed and predicted curves match as shown in Figure 4a (i.e., matching hypothesized and actual graphical representations based on previously developed mathematical or verbal representations). This task has students developing an understanding of what the growth curve looks like when there are limited and unlimited resources. This introduces them to computational thinking about analyzing models in terms of how the curve of the line (a model output) is affected by specific inputs. Secondly, the students then focus on the output sheets for the specific wasp traits and determine that trait proportions within the population remain relatively stable over time as long as the trait is not an environmentally acquired trait. If it is environmentally acquired trait, such as shredded wings, then within one generation in the lab the trait disappears from the population. Thus, the simulation also allows students to grapple with two common alternative conceptions: that trait proportions will change over time to the phenotypically dominant trait; and 2) that acquired traits will be inherited and are a driver behind evolutionary change. This new understanding of traits helps students recognize the need for selective pressure if they are to shift the traits in a population over multiple generations.

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Development of the model of natural selection. After the students develop a strong grasp of population growth, the curriculum focuses them on developing the model of natural selection; one of the most often studied and misunderstood mechanisms of evolution. This section of the curriculum guides the students in developing the model of natural selection by allowing them to explore what changes in the population are induced by selective pressure. The flow of this section of the unit can be seen on the left side of Figure 1. In the initial task used to develop a model of natural selection, the students use a second Excel workbook simulation to investigate the effects of two selective mechanisms (i.e., killing and resources) on the wasp traits. This simulation differs from the one used to develop the population growth model as it removes acquired wasp traits (since they are now understood to be irrelevant) and adds type and amount of selective pressure as well as allowing for multiple trials, see Figure 3b. If students choose to test the selective pressure of “killing,” then they can select the percent of native egg-preferring wasps to remove from the population. If they choose the resource selective pressure, they can test the effect of the amount of BMSB eggs to provide to the wasps as they grow. The students can observe what happens to the percent of wasps demonstrating the desired phenotype of invasive egg preference over the course of 800 days very quickly for different types and strengths of selective pressure. This output graph will also graph the number of trails selected as well as the overall average (see Figure 4b). However, when they observe the percentage of wasps preferring invasive eggs output graph, they will find that they can never obtain 100% no matter how strong the selective pressure chosen. In addition, when observing graphs of other wasp traits that are not linked to the selective pressure such as eye color, they will find that there is no change in the percentage of traits over generations, further developing their conceptual understanding of the model of natural selection.

To connect an understanding of allelic frequency and natural selection, the next task requires the students to use their prior understanding of meiosis and alleles to develop and test models using hands-on manipulatives. This allows students to physically determine why is it highly unlikely that they would ever be able to remove the trait preference for native stinkbug eggs from the population. The hands-on modeling also reinforces why computer simulations are used in science to model multiple generations since it is quite time consuming and impractical for large populations over multiple generations. The unit then guides students to further develop their natural selection model by determining how allelic frequency is affected by selective pressure over 30 generations using an additional Excel workbook simulation, which now shows allelic frequencies.

At this point the students can round out their representations by adding a mathematical representation of not only population growth but also of natural selection. The set of representations developed for both models become very robust as the students are challenged during rigorous problem solving that is grounded in real situations.

Development of engineering design challenge solutions. Once the students develop a robust model of natural selection, they can then grow a population of wasps that they believe can be used to control the BMSB population on one of the farms in Virginia. The Excel computer simulation models what happens to not only the BMSB but also the SGSB over time as well as what happens to the traits in the population of wasps when they comingle with the populations of wasps that already exist on the farm. This Excel test plot simulation allows the students to test their lab grown wasps in a variety of conditions to further their understanding of the complexity of nature as well as the continue to increase their computational thinking skills. The students learn that, by controlling one population, the other populations in the ecosystem can be drastically affected. For example, the introduction of BMSB egg preferring wasps can produce large increases in the SGSB population. The final graphs allow them to determine what will happen over time to the wasp, BMSB and SGSB populations.

The last task of the unit brings home the design challenge to produce a method to control the BMSB population in multiple environments. Each student group’s final project is to develop a specific method to control the BMSB on at an assigned location in the country, taken from a pool of rural, urban, and suburban locations. The complexity of the issue (e.g., the dependence of solution details on situation details) rapidly becomes evident to the student groups.

In conclusion, Figure 1 summarizes the cycle of modeling and engineering design events encountered during the unit. The students initially observe population growth patterns and predator-prey relationships leading to the development of a robust model of population growth. Using their new understanding of population thinking, students observe the effects of selective pressure on their population of wasps in order to develop their model of natural selection. Finally, their natural selection model is deployed in a new context, refined and then used to develop a final solution to their engineering challenge. During the engineering challenge the students are given time to explore improvements to their final solution. The intent of the unit is to conclude with a peer to peer presentations of the multiple engineering solutions.

Supplemental FIGURES:

Figure 1 Flow of Curriculum Unit

3a: Population Growth

3b: Natural Selection

Figure 3: Excel Modeling Simulation Input Pages

4a: Population Growth Curves

4b: Natual Selection Curves

Figure 4: Excel Modeling Simulation Output Pages