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WHAT IS IT?
The Worm simulation is a model of a population of virtual "worms". The model explores the relationship between individual behavior and population dynamics. It can easily stand alone, but it was developed as an enrichment activity following several weeks of a standard mealworm biology lab. It is suitable both for an introduction to population dynamics, and as an introduction to agentbased modeling in biology. Although quite simple, the simulation can produce complex dynamics that could be suitable for discussion up through a high school level.
HOW IT WORKS
The simulation consists of essentially just two elements, a field of "grass" which is the food source of the worms, and the worms themselves. We measure the grass in terms of its "length", which is recorded in the _grass_ variable owned by patches. The grass also grows at a rate defined by the Growth_Rate slider, with length going from zero (black patch color) up to a maximum defined by the MAX_GRASS_HEIGHT constant (bright green patch color). The worms own _life_ and _energy_ attributes. Energy derives from food consumed, while life (lifespan) acts as a counter limiting the amount of time the worm has left to live. In each tick, worms 1. crawl, 2. eat, 3. metabolize and 4. reproduce.
1. crawl  this is essentially random motion forward and within 20 degrees to the left or right
The interaction of resourcedependent population growth with resource limitations gives rise to surprisingly complex population dynamics. At the beginning, unbounded exponential growth is observed. As the worm population approaches the environment's carrying capacity, growth saturates and, depending on the rate of grass regrowth and the maximum energy reserve per worm, the population may experience a mass dieoff due to starvation. In this case, eventually the population rebounds and after several oscillations will stabilize at some intermediate value. Otherwise, the population simply levels off.
HOW TO USE IT
As mentioned above, this simulation was originally developed as a followon to a mealworm biology lab, but can easily stand alone. The virtual "worms" in this simulation are far simpler than real mealworms (which are actually beetle larvae, not real worms). It is helpful to introduce the simulation starting with just a single worm and introducing the four behaviors one by one. The simulation can be run with each of the four behaviors (described above) commented out and then incrementally uncommented. In particular, commenting out the "metabolize" function in the "to live" procedure essentially turns off the worms' life counter, meaning that no worms die. This is a good way to show the consequences of unbounded population growth, given the (unrealistic) assumption that there are no limitations on resources.
As usual, "setup" should be executed before "go".
The various sliders, some of which discussed are above, control the following variables:
THINGS TO NOTICE
The Food_Conversion slider has a direct impact on the steadystate carrying capacity of the environment. It also has indirect effects on the dynamics of the population. For instance, a very large value of Food_Conversion has the effect of reducing the reproduction rate, since it is relatively more difficult for a worm to obtain enough food to eat. Coupling large Food_Conversion with small Life_Span values may easily make the worms go extinct.
The combination of a large reproductive rate with a high Energy_Reserve value might seem to be quite advantagous to a worm population. However, this combination tends to have the unexpected effect of sustaining a population boom that exhausts the carrying capacity of the environment (particularly when grass regrowth is slow), resulting in mass dieoffs and cycles of population boom and bust that may or may not stabilize. When the Energy_Reserve value is low, and lifespan short, the population of worms tends to respond directly to the amount of food available, rather than with a time lag, and hence rather than oscillating the population merely plateaus at the carrying capacity.
THINGS TO TRY
A number of basic questions can be answered with this model. What is the effect of initial population on final population? (It effectively jumps the clock forward, but otherwise has no effect). What is the effect of reproductive rate and life span on final population size? And so on.
For more advanced classes, it is interesting  and challenging  to characterize what combinations of parameters produce:
It is also interesting and challenging to describe the population dynamics analytically. This is discussed more below.
EXTENDING THE MODEL
This model can be extended in a number of ways. A trivial extension that would be appropriate to relate the model to some other reallife lab (such as bacterial growth) would be to change the turtle appearance from a worm to some other creature (especially for students who may feel squeamish about worms!) Similarly, characteristics of grass growth, worm metabolism, etc. may all be tailored.
One basic extension that was used with an earlier version of this model was to add a population of birds that preyed on the worms. This gives rise to familar predatorprey dynamics. It is also straightforward to add some characteristic (such as length) to worms which affects their food gain, to see how random variations in that characteristic may over time lead to natural selection for longer or shorter worms. A characteristic such as length may also, when predators are present, be used to illustrate competing influences on survival. For instance, large worms may live longer (and hence produce more offspring), but may be easier prey for birds.
It would also not be difficult to add state variables that could be used to plot ideal population dynamics according to standard exponential growth and decay models, so that comparative analysis could be accomplished.
RELATED MODELS
The Wolves and Sheep model is similar in some respects. There is also a more mathematically oriented population dynamics model in the library which can be related to this one.
CREDITS AND REFERENCES
This model was written by Mathew Davies through the NSFsponsored GK12 program at the School of Engineering and Applied Sciences at Columbia University, for use in 8thgrade science classrooms at I.S. 143 (Eleanor Roosevelt intermediate school, Washington Heights) in Manhattan, New York in the fall of 2004. The author may be contacted at the email address:
This simulation, along with other technologybased classroom resources, may be found at the website 
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