Christopher X J. Jensen
Associate Professor, Pratt Institute

Online tools for teaching the basics of population growth

Posted 08 Sep 2011 / 5

WARNING: Unfortunately, the applets that I discuss below (“Otherwise”) no longer meet Java security specifications. As a result, they won’t work on computers with the most updated version of Java. Please see the other tools listed in the Comments section below as alternatives. I am still searching for the perfect user-friendly package to teach about exponential growth and carrying capacity.

The Otherwise population growth simulator

In what now seems like an infamous episode in my early career, I once tried to deliver a sample lesson on population growth during an all-day interview for a full-time teaching position at a fairly prestigious liberal arts college.  What made this interview and sample lesson a bit more challenging was that my audience of sitting faculty was not composed solely of biologists: because the position I was being interviewed for was in a Master of Arts in Teaching program, the faculty were composed of folks from all disciplines. Although the actual students I would be teaching had I gotten the job would have been science majors, the test audience for my sample lesson was basically a group of non-majors.

Let me explain to you how best to destroy your chances of getting a job through a sample lesson dedicated to population growth: let the faculty who are pretending to be your students do all the math on their own, or better yet try to teach them on-the-fly how to use a spreadsheet to do the calculations. That was my lesson, a great dry mathematical train wreck. It was not simply that many of my pretend students were somewhat befuddled by the mathematics they were asked to do; even those who easily gravitated to the math involved were so utterly bogged down in calculations that they were unable to appreciate any of the important facets of population growth that I was trying to convey. Since this disaster, I have realized that the topic of population growth can only be taught in a compelling manner if there is some sort of simulator which can quickly produce population growth trends for particular conditions. Students do not need to practice the basic mathematics that underlie population growth (either they have those mathematical skills, or they do not), they need to be able to play around with different growth parameters so that they can understand the effects these parameters have on population growth.

The kind of ideal tool that students need to understand the basics of population growth would be pretty basic itself. First of all, students should be able to see the results of their simulations quickly translated into easy-to-read graphs. For most people, seeing population growth numbers represented as either counts in a table or cartoon versions of organisms does not really capture the essence of how populations grow: graphs capture this essence. In addition, students should be able to play around with key parameters to understand how changes in these parameters affect the pattern of population growth. Really only three parameters are critical for understanding the basics of population growth: initial population size, growth rate, and carrying capacity (if any is imposed). Given that students will want to play around with different values of these three parameters so that they can understand their effects, it would also be nice for students to be able to simultaneously plot growth trends based on different parameter values.

The requirements that I lay out above for a basic population growth stimulator seem pretty bare-bones, but sadly I have not been able to find an available free online tool that meets even these simple requirements. In my ecology class I have been using a pair of online tools produced by a somewhat mysterious entity called Otherwise. These tools allow students to explore exponential growth and logistic growth using Java applets. In some ways this set of tools is pretty nice: there is the possibility of changing the growth rate and the carrying capacity, and students can retain graphs of previous simulation runs, which allows for easy comparison of different parameter values. The growth rate can be changed on the fly, which allows students to think about the effect of sudden changes in the environment.

But there are some serious shortcomings associated with this tool as well. First off is the fact that the “growth rate” is called the “birth rate”, a conceptual error in the way the program is labeled that leads to all sorts of conceptual errors in my students: right after I teach them that survival and fecundity are the components of the growth rate, the program goes and labels this rate as strictly related to fecundity (i.e. birth rate). The starting population cannot be altered from the default value of two, so the only way to compare the effect of larger starting populations is to let the simulation run up to your target population size, pause, and then run from that population as if you are starting anew. The program also is incapable of handling numbers much larger than 100,000, which limits the ability to compare faster growth rates over a longer time period. The simulator has an annoying “view habitat” option that basically just fills the screen with fish: not all that instructive! And although all platforms are vulnerable to compatibility and obsolescence problems, I find Java to be particularly troublesome and finicky, which is a minor additional downside to these Otherwise simulation tools.

In previous years I have gone searching rather half-heartedly for alternatives. Whenever I go looking, I always feel there must be something better out there. Invariably, I do not find anything. So this year I decided that I would do a very thorough web search looking for the perfect population growth simulation tool. After the search, I can say that it does not exist for free.

There are  a few candidates, but all of them come with large drawbacks. The Population Growth Simulation page by Jeff Knisley does allow for control of both initial population size and growth rate, but the plotting function does not work in real time and the carrying capacity is hardwired into the simulation. This is also not the most user-friendly interface, which might cause problems for non-major ecology students. Another fairly random simulator called Simulation of the effects of natural enemies on an insect population  involves complex details such as specific types of mortality, stage structured growth, and  stochasticity. Stripped of some of the details, the simulator also produces basic population growth patterns, but also does not feature a real-time graph of simulation results.  For some reason, the site is also littered with Google ads. And finally in the “inexplicably weird” category is McGraw-Hill’s Virtual Lab on Population Growth, which allows you to play with virtual eyedroppers but not actually see any valuable population growth patterns.

In this day and age of on-demand apps and plug-ins, it is kind of surprising that no one has bothered to make a simple teaching tool that helps users to understand the basic dynamics of population growth. But perhaps the demand or expectation of free quality software in this area is too much: if you want to pay for classroom simulation software, SimBio’s EcoBeaker Isle Royale module seems as though it contains all the features I outlined above, all at $3 a student. Am I being cheap by looking for free software? Maybe, but I also cannot imagine going through all the hassles involved in ordering this software and guiding my students through the purchasing process just for one little lab exercise.

The opportunity it ripe for someone to make a better freely-available population growth simulator!

Carrying Capacity, Ecological Modeling, Educational Software and Apps, Lesson Ideas, MSCI-270, Ecology, Population Growth, Teaching Tools

5 Comments to "Online tools for teaching the basics of population growth"

John R. Jungck 19th February 2012 at 10:13 am

Dear Dr. Jensen:

I stumbled on your blog while I was looking up evolutionary game theory.

To answer your question, we have distributed software for modeling numerous biological phenomena for 26 years. Please look at our Microbes Count, ESTEEM, NUMB3R5 COUNT, BEDROCK, and BioQUEST Library sites.

I look forward to hearing from you. Jeff Kniseley who you mention is a friend who has used much or our stuff and who I hope will become a contributing author in the feature.



Chris Jensen 25th January 2013 at 8:54 am

Ben Ford of Sonoma State University has created a pair of cool population growth applets using the free Geogebra mathematics software:

A great feature of these little applets is that they allow users to simultaneously plot different growth equations and then use “sliders” to change parameters and instantly see the resulting change in growth patterns. The only downside I see in this feature as compared to the Otherwise software discussed above is that it does not model for students the actual time-progression of growth. While those who understand that algebraic equations ‘predict’ behavior over time won’t stumble on this characteristic of the applet, some students may be confused about what they are looking at as they shift parameters and the the entire time series shifts (because this applet ‘plots instantly’ rather than ‘plots incrementally’). While those who already understand the concept of a time series will prefer the ‘instant’ output, students may understand the concept of growth better if the actual time steps are incrementally plotted, allowing students to ‘watch the growth happen’.
This applet should be used with students who understand the abstractions of algebra.

Ben Ford 20th November 2013 at 5:07 pm

I just made a few changes to the applets mentioned by Chris, in response to some of his suggestions. The second one is animated over time and so does show the time-progression of growth (and in fact you can hide the algebraic pane completely if you wish). Geogebra now creates both html5 and java versions, so they are now hosted on geogebratube rather than my own website:
Static graphs of several models, with slider-adjustable parameters:
Animated graphs of several models, with slider-adjustable parameters:

Chris Jensen 11th February 2014 at 6:34 am

This simulator is free and web-available:

The worksheets for this activity are here:

There are a few limits that I see with this simulator:

  1. It is not quantitative. There’s no way for students to really appreciate any numerical differences in parameter settings.
  2. While you can lower equilibrium density through the predation intensity, there’s no way to change the carrying capacity via available resources, which might give students the mistaken idea that equilibrium densities can only be affected by predation.
  3. In general there are a lot of factors thrown at students at once in these simulations, so one would have to work hard to get students to really isolate the influence of different factors on the resulting growth patterns. There might be a lot of opportunities to “poke it and see what happens” in this simulation, but I worry that the “poking” will end up be somewhat random and uncontrolled, leading students not to know why they got the results they see on the screen.
Dustin Haines 11th April 2014 at 3:24 pm

Don Alstad, an ecologist at the University of Minnesota, developed a very nice free program for exploring all kinds of population growth models, including some natural selection and genetics simulations. It’s called “Populus”, and it runs via Java. Here’s the link:

It also has pretty thorough documentation, and it can very easily be implemented as a teaching tool in a lab/classroom setting with computers (I taught population growth using it multiple times, and the students always seemed to get a lot out of it).

I highly recommend checking it out!

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