Unit 2: Modeling Population
These materials have been reviewed for their alignment with the Next Generation Science Standards as detailed below. Visit InTeGrate and the NGSS to learn more.
OverviewIn this unit, students develop a computational model to simulate population dynamics. They use their models to perform a series of experiments to test relationships between variables and develop explanations for change over time, using the foundational concept of carrying capacity.
Science and Engineering Practices
Developing and Using Models: Develop, revise, and/or use a model based on evidence to illustrate and/or predict the relationships between systems or between components of a system HS-P2.3:
Developing and Using Models: Develop and/or use a model (including mathematical and computational) to generate data to support explanations, predict phenomena, analyze systems, and/or solve problems. HS-P2.6:
Constructing Explanations and Designing Solutions: Make a quantitative and/or qualitative claim regarding the relationship between dependent and independent variables. HS-P6.1:
Constructing Explanations and Designing Solutions: Construct and revise an explanation based on valid and reliable evidence obtained from a variety of sources (including students’ own investigations, models, theories, simulations, peer review) and the assumption that theories and laws that describe the natural world operate today as they did in the past and will continue to do so in the future. HS-P6.2:
Cross Cutting Concepts
Stability and Change: Stability might be disturbed either by sudden events or gradual changes that accumulate over time. MS-C7.3:
Stability and Change: Feedback (negative or positive) can stabilize or destabilize a system. HS-C7.3:
Disciplinary Core Ideas
Interdependent Relationships in Ecosystems: Ecosystems have carrying capacities, which are limits to the numbers of organisms and populations they can support. These limits result from such factors as the availability of living and nonliving resources and from such challenges such as predation, competition, and disease. Organisms would have the capacity to produce populations of great size were it not for the fact that environments and resources are finite. This fundamental tension affects the abundance (number of individuals) of species in any given ecosystem. HS-LS2.A1:
Ecosystems: Interactions, Energy, and Dynamics: Use mathematical and/or computational representations to support explanations of factors that affect carrying capacity of ecosystems at different scales. HS-LS2-1:
This material was developed and reviewed through the InTeGrate curricular materials development process. This rigorous, structured process includes:
- team-based development to ensure materials are appropriate across multiple educational settings.
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- real in-class testing of materials in at least 3 institutions with external review of student assessment data.
- multiple reviews to ensure the materials meet the InTeGrate materials rubric which codifies best practices in curricular development, student assessment and pedagogic techniques.
- review by external experts for accuracy of the science content.
This page first made public: Sep 15, 2017
In developing their models, students learn about basic concepts in population ecology, including trophic levels and food chains, exponential and logistic growth, environmental limits that lead to fixed or variable carrying capacities, and the tendency for populations to catastrophically overshoot their carrying capacities. At the end of the exercise they are asked to synthesize what they have learned in order to advise a member of Congress who is considering whether to vote in favor of providing federal funding for family planning services.
Upon completing this module, students are expected to be able to:
- Create models of population growth using STELLA.
- Differentiate between balancing (negative) and reinforcing (positive) feedbacks on population growth.
- Use a predator-prey model to explore trophic relationships and population dynamics.
- Explain how carrying capacity leads to a stabilization of population.
- Experiment with an Easter Island population and resources model to explore the conditions that allow sustainable use of resources versus collapse of civilization.
Context for Use
This unit is intended to be used in a three- to four-hour class period that meets once a week. It can be used as part of this modeling course or it can be adapted as a lab exercise for courses in environmental science. For this module, students should come to class prepared to take a short quiz on the assigned reading. Thereafter they will be led through a series of prompts designed to help them create and experiment with a number of simple models using the iconographic box modeling software STELLA (see https://www.iseesystems.com/store/products/ for different options for purchasing student or computer lab licenses of STELLA or for downloading a trial version).
For those learning to use STELLA, we suggest the online "play-along" tutorials from isee systems. You can find them here: isee Systems Tutorials.
Description and Teaching Materials
In preparation for the exercise, students should read the following: Unit 2 Student Reading.
Students should take the following quiz prior to coming to class to ensure they have done the assigned reading: Population modeling reading quiz (Microsoft Word 2007 (.docx) 47kB Aug11 16). An answer key for the reading quiz can be found here:
In class, students should be provided with the exercise found here: Population modeling student exercise (Microsoft Word 2007 (.docx) 2.2MB Nov15 16)
An answer key for the exercise can be found here:
Instructors can download a version of the lynx and hares predator-prey model by clicking here: Lynx & hare predator-prey model (Stella Model (v10 .stmx) 15kB Aug11 16), the logistic growth model by clicking here: Logistic growth STELLA model (Stella Model (v10 .stmx) 7kB Aug11 16), and the Easter Island model by clicking here: Easter Island collapse model (Stella Model (v10 .stmx) 13kB Aug11 16). All models were created using STELLA Professional and should open on any subsequent version of STELLA. If you are using an earlier version of STELLA, the complete model graphics and equations can be found in the answer key so that you can reconstruct the models yourself.
Teaching Notes and Tips
We generally post the readings and assignments for students to an LMS site (e.g. Moodle, Blackboard, Canvas). Students can open the assignment in Microsoft Word on the same computer they are using to construct each STELLA model and then answer the questions by typing directly into the document. Students can then either print a paper copy to hand in to the instructor or email their modified file to the instructor. It is straightforward to copy graphs and model graphics from STELLA and to paste them into Word. Simply select the items to be copied, hit copy in STELLA, and then paste into Word. There is no need to export graphics to jpg.
We teach the course in a three- to four-hour block once a week because we have found that models require a lot of uninterrupted time to construct. If students have a 50- or 75-minute class period several times a week, they spend at least 20 minutes of subsequent class periods trying to figure out where they were in the exercise at the beginning of the week. This is not a good use of time, hence the recommended three- to four-hour class session once per week. However, we also know that sustaining attention for this length of time can be difficult. We therefore recommend allowing students the freedom to take breaks throughout the modeling session to get snacks or coffee.
A typical four-hour class session might be broken up into the following sections:
- 20-minute discussion of the reading to ensure all the students are familiar with the mathematics behind the model
- 1.5 to 2 hours to build the model
- 1.5 hours to conduct experiments
For instructors who have more limited contact hours with their students, we suggest that the model construction parts of this exercise be assigned as a pre-lab to be handed in a day or two before class along with the completed STELLA model itself. This would allow the instructor to determine whether students' models are working correctly and to provide feedback to address errors in construction, omissions in documentation, problems with unit conversions, and inappropriately sized time steps that might lead to spurious model behavior. Class time could then be devoted to running experiments and analyzing the results. If access to STELLA outside of class time is impossible due to computer lab scheduling or to financial constraints that prevent students from purchasing their own STELLA licenses, students could be asked to create a pencil and paper sketch of what their model should look like, annotated with equations and then sent to the instructor in advance of class for feedback. This should facilitate a faster model construction time during the limited class hours.
References and Resources
Barnosky, A.D., Matzke, N., Tomiya, S., Wogan, G.O.U., Swartz, B., Quental, T.B., Marshall, C., et al., 2011, "Has the Earth's Sixth Mass Extinction Already Arrived?" Nature, v. 471, p. 51–57.
Bologna, M. and Flores, J.C., 2008, "A simple mathematical model of society collapse applied to Easter Island," EPL, v. 81, doi: 10.1209/0295-5075/81/48006.
Cohen, J.E., 1995, How Many People Can the Earth Support? New York: W.W. Norton & Company, 532 p.
Cook, B.I., Anchukaitis, K.J., Kaplan, J.O., Puma, M.J.,, Kelley, M., and Gueyffier, D., 2012, "Pre-Columbian deforestation as an amplifier of drought in Mesoamerica," Geophysical Research Letters, v. 39, n. 16, article n. L16706.
Diamond, J., 2005, Collapse: How Societies Choose to Fail or Succeed, New York: Viking Press, 575 p.
Hunt, T., "Rethinking the fall of Easter Island," American Scientist, September-October 2006.
Kaufmann, R.K., and Cleveland, C.J., 2008, Environmental Science. Boston: McGraw Hill Higher Education, Chp. 5.
Kolbert, E., 2014, The Sixth Extinction: An Unnatural History, New York: Henry Holt & Company publishers.
Merritts, D.J., Menking, K.M., and DeWet, A.P., 2014, Environmental Geology: An Earth System Science Approach, 2nd Edition. New York: W.H. Freeman, Chp. 7.
Mieth, A., and Bork, H.-R., 2005, "History, origin and extent of soil erosion on Easter Island (Rapa Nui)," Catena, v. 63, p. 244-260.
Ricklefs, R.E., 2008, The Economy of Nature, 6th Edition. New York: W.H. Freeman, Chp. 15, 18.
Turner, B.L., II, and Sabloff, J.A., 2012, "Classic Period collapse of the Central Maya Lowlands: Insights about human–environment relationships for sustainability," Proceedings of the National Academy of Sciences, v. 109, p. 13908-13914.
Additional web resources include:
World Population Clock, from Worldometers
What Happened On Easter Island — A New (Even Scarier) Scenario, an NPR blog entry by Robert Krulwich.
Researchers challenge old theory of Easter Island population collapse, a Washington Post article by Justin Wm. Moyer.
Rethinking the Fall of Easter Island New evidence points to an alternative explanation for a civilization's collapse, an American Scientist Online article by Terry Hunt.