1. 1.0 Introduction
1.1 Simulation Theory
Model is a representation of an object, a system or an idea in some form other than that of the
entity itself (Shannon). Types of model are divided into two, which are physical and
mathematical. Physical model is like scale models and prototype plants while mathematical
model is like analytical queuing models, linear programs and simulation.
A mathematical model is an abstract model that uses mathematical language to
describe the behaviour of a system. Mathematical models are widely used in the natural
sciences and engineering such as biology, physics and electrical engineering. These models
are also used in the social sciences such as sociology, political sciences and economy. The
frequent users of these models are physicist, engineers, computer scientists and economists.
A simulation of a system is the operation of a model, which is a representation of that
system. The model is amenable to manipulate which would be impossible, too expensive, or
too impractical to perform on the system and attempts to simulate an abstract model of a
particular system. The operation of the model can be studied by the user. From this, the
properties related to the behaviour of the actual system can be concluded.
One of the main advantages of using simulation in teaching and learning is the
process of teaching and learning becomes more interesting and exciting as the learners can
explore everything in various types of experiments. If they have the software of simulation,
they can explore it early when they are not in the class. These can make them more inspiring
to study and discover a new thing. Besides, simulation also can help the teachers to teach the
abstract content to the students. It is meant that, the simulation can make the student easy to
understand as they can use the simulation and not just imagine on what have been taught by
the teacher. Other advantages of using simulation are very quick development of complex
models, short learning cycles and no programming is needed. So, only minimal errors will
occur.
However, this simulation also can give disadvantages to the students that do not have
computer or limited availability of computers. They will not have the opportunity to explore
after they have learnt in the class. Their learning process will happen only in the class. In
addition, this simulation also can give a big problem to the users that do not know how to use
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2. computer. The users need to do two things in one time, which are learning about the
computer and also learning about the simulation. So, may be the user will be lag behind the
others. Besides, many simulations require intensive pre simulation lesson preparation. So, it
takes time if we want to use the simulation in a short period. High cost of software also
include as the disadvantage of the simulation. Only the trial one can be used by the users.
But, after 30 days, it cannot be use anymore. In addition, limited scope of applicability and
also limited flexibility. This is because the variation of the topics is not too many. Some of
them may not fix with the users specific.
1.2 STELLA Software
STELLA is a new software program that has been developed to enable very broad,
non technical audiences to conceptualize, construct and analyze system dynamic models. One
of the goals of the development of STELLA is to enhance the learning process. This software
offers a practical way to visualize and communicate how complex and ideas really work. It
consists of endless questions, which make the users more attracted to use it. As this software
is easy to use, it has been used widely in education from economics to physics, chemistry to
public policy and literature to calculus. This model allows the user to communicate how a
system works. Generally, STELLA software is really useful for the visual learners because
the animation, diagram and charts in that software can help them discover the relationship
between variables in an equation. While for verbal learners, visual models with words are
more suitable for them.
STELLA is being used to stimulate a system over time, jump the gap between the
theory and the real world as the simulation is closely like the real one, enable students to
creatively change the systems by changing the value or variables, teach the students to look
for the relationships by seeing a big picture and clearly communicate system inputs and
outputs and demonstrate outcomes.
1.3 Experiment Theory
STELLA has been used in the experiment of Predator-Prey Dynamics. Predator-prey
theory is traced from its origin in the Malthus-Verhulst logistic equation, through the Lotka-
Volterra equations, logistic modification to prey and predator equations, incorporation of the
Michaelis-Menten-Holling functional response into the predator and prey equations and the
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3. recent development of ratio-dependent functional responses and per capita rate of change
functions.
In the study of the dynamics of a single population, we always take into consideration
such as factors of natural growth rate and the carrying capacity of the environment. In this
experiment, we study an interaction between two species, which are prey and predators. Prey
is the species that has been eaten while predator is the species that eats the others.
Predation is only one of several agents that cause population cycles. Other factors that
contributed in the population cycles are mass emigration, genetic changes in the population
and physiological stress due to overcrowding. Population cycles are difficult to achieve in the
laboratory. Usually, the predators search out every one of the prey and then they go to
extinction due to lack of food.
The predator-prey model may be stabilized by making two assumptions about the
growth rates of the prey and also about the growth rates of the predator. If the preys or
predators are destroyed at the same rate by some outside agent, the prey will proportionally
increase and the predators will proportionally decrease. This is because the birth rate of the
prey is not affected, the death rate of the prey is reduced and the birth rate of the predator is
reduced.
2.0 Content
This STELLA software provides three parts for the users, which are background and
content of the experiment in details, explore the model and experiment. So, as we want to
conduct an experiment about predator and prey, we can choose the last part, which is
experiment. Before we choose that part, we can read the background first in order to know
what is the experiment tells about.
Background of this experiment tells that predator-prey oscillations are common in
many simple ecosystems. According to Odum’s classic ecology textbook, interesting and
only partly understood density variations are those which are not related to seasonal or
obvious annual changes, but which involve regular oscillations or cycles of abundance with
peaks and depressions every few years, often occurring with such regularity that the
population size may be predicted in advance. The best known cases concern mammals, birds,
insects, fish, and seed production in plants in northern environments. Among the mammals,
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4. the best-studied examples exhibit either a 9- to 10- year or 2- to 4- year periodicity. A classic
example of a 9- to 10- year oscillation is that of the snowshoe hare and the lynx.
The background also tells us about the purpose of this experiment despite of the
predator and prey. After we have read the background, we can conduct the experiment. The
interface of this simulation will show all of the variables involved. For this experiment, the
size of one time lynx harvest is the manipulated variable while, years is the responding
variable.
There are few buttons that we can click in order to see how the simulation is
functioning. The buttons are ‘run’, ‘pause’, ‘stop’ and ‘reset’. All of the button can be click to
see what will happen to the simulation software. Exploring is important before we start to
conduct the experiment. In order to start the experiment, ‘run’ button should be click. But, if
we want to cancel it, we can click the ‘reset’ button.
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5. For the beginning, we click the ‘run’ button without changing any value in order to
know what graph will be produce. Then, we can see that only straight lines are produced for
both hares and lynx. We need to note that the lynx birth rate depends upon the food supply
available, which is the hares and the death rate of the lynx is not dependent on the hares’
density.
This graph shows that the amount of the prey and predator are constant along the
years. This does not mean that no interaction is occurred, but this is meant that the condition
for this interaction is stable. The amount of hares is the same as the amount of lynx dead. As
the lynx dead, so the amount of hares will not be reduced because they are not being eaten.
This step is to demonstrate to the student on how to use this simulation and see the
relationship among the variables on the graph. This simulation enables them to know the way
scientists do their work. This simulation can make the students more interested to conduct an
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6. experiment because they are able to change the values to any value that they want and see
what the result is.
Students should predict and explain the outcomes that they expect the simulation to
generate. From that, the students will not stay passively in the class experiment. Every effort
should be make it difficult for them to become passive. Each student must submit timely
input and not rely on classmates to play for them. So, everyone will have the experience of
using the simulation.
After changing the value of size of one time lynx harvest to 160, the graph has shown
fluctuation. Here, it shows that the amount of the lynx is depending on the amount of the
hares. If the amount of hares is increase, the amount of the lynx will also increase. If the
hares decrease, the lynx also decrease. But, the graph shows straight line at the beginning. At
this point, there is no interaction yet.
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7. This simulation has the potential to engage students in deep learning that empowers
understanding compared to the surface learning that requires only memorization. From this
simulation, students will more understand as they conduct the experiment by themselves and
find the relationship between the variables in order to get the conclusion of the interaction. If
they did not use this simulation, they maybe not understand, but they only memorize what the
teacher has taught them.
According to the pattern of the graph, the students are able to predict what will
happen on the next years as they know already what the pattern is. If the rate of prey is
decreasing, the rate of predator is also decreasing. And if the rate of prey is increasing, the
rate of predator is also increase.
Then, we change the value of the size of one time lynx harvest to 380. This amount is
doubled to the value for the first trial, which is 160. So, the fluctuation of this graph also
shows doubled height of the first trial. Here, the students can see how the graph changes
when the value is changed. The students can understand and predict the graph along the years
as the pattern of the fluctuation is just the same from the beginning to the end.
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8. By using this simulation, the students can think more about what will happen next and
what are the factors that can cause the pattern of the graph. The students also can develop a
feel for what variables are important and the significance of magnitude changes in
parameters. If the magnitude is change, the graph will also change. There is no such thing
that the value is change, but the graph still the same.
This simulation also can help the students to understand the probability and sampling
theory. The teachers not have to worry the validity of this simulation theory because
instructional simulations have proven their worth many times in the statistics based fields. So,
it can be said that simulation is one of the best method for the teachers to give their student
more understanding in the abstract topics.
When we change the value of the size of one time lynx harvest to the maximum value,
which is 750, this graph is shown. Specifically, increasing in the prey population will cause
the predator birth rate to rise and thus increase their population. Then, the prey death rate will
rise. This graph shows a typical plot produced from that situation. Here we can see the
characteristics of cyclical fluctuations between the hares and the lynx.
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9. When we look at the pattern of the graph, we noticed that the lynx’s pattern is closely
follows the hares’ pattern but the lynx’s peaks and valleys happen a bit after the hares’ peaks
and valley. This interaction is complex. Disease, food supply and other predators are
variables in this complex interaction. The flux in this cyclic relationship is what allows for
the ecosystem dynamic to work.
Every ten years or so, the hares’ reproduction rate increases. As more hares are born,
they eat more of their food supply. The lynx population size also begins to increase because
hares are their food.
As this graph is more complex to be interpreted by the students, it can cause actively
engaging in student. They are actively participating to formulate new questions to be asked
and also anticipating the outcomes. Social processes and social interactions in action are also
occurred. They are also able to transfer knowledge to new problems and situations. A well
done simulation should be constructed to include an extension to a new problem or new set
parameters that requires student to extend what they have learned in an earlier content.
3.0 Conclusion
Post simulation discussion with the students leads to deeper learning. So, the
instructor should:
1. Provide sufficient time for students to reflect on and discuss what they learned
from the simulation.
2. Integrate the course goals into the post simulation discussion.
3. Ask the students explicitly such as ask how the simulation helped them to
understand the course goals or how it may have made the goals more confusing.
Simulation is suitable to be used in the school because it can motivate students in
learning. Simulation motivate students by keeping them actively engaged in the learning
process through requiring that problem solving and decision making skills be used to make
the simulation run. As the simulation runs, it is modelling a dynamic system in which the
learner is involved. Thus, participation in simulations enables students to engage in systems
thinking and enhances their understanding of systems as well as of science concepts.
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10. Simulation can be considered as a powerful tool in active learning experiences. It can
provide a kind of lab-like experiences. So, the students will become more exciting and
inspiring in study because most of the students like to do something rather than just hearing
to something. Finding a good simulation in teaching is a challenge for the teachers in order to
integrate them into the content and objectives of the course chosen. However, if the teachers
know what their students need, it is easier for them to choose a suitable simulation.
STELLA is suitable to be launched in Malaysia as it is one of the simulations which
give benefits to the users whether the user is a student or a teacher. Some of STELLA
benefits are:
1. The language increases the accuracy and clarity of verbal descriptions,
ambiguities diminish and communication becomes much more efficient and
efficient.
2. The software provides a check on intuition.
3. This software provides a vehicle for building an understanding of why.
4. The tools enable an easier operation and demonstration
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11. References
A. A. Berryman (1992). The Origins and Evolution of Predator-Prey Theory. Ecology. 73 (5).
Retrieved from http://www.jstor.org/discover/10.2307/1940005?uid=373867
2&uid=21 29& uid=2&uid=70&uid=4&sid=21101509219257
Peter Chesson (1978). Predator-prey Theory and Variability. Annual Revolution Ecology
System. 9:323 (47). Retrieved from http://eebweb.arizona.edu/faculty/
chesson/Pete/ Reprints/ 1978_Predator-Prey%20Theory%20and%20Variability.pdf
Anonymous (2002). Lynx-Hares Cycles. Retrieved November 25, 2012 from
http://pzweb.harvard.edu/ucp/curriculum/ecosystems/s6_res_lynxhare.pdf
Anonymous (1996). Effective Use of Simulations In The Classroom. Retrieved November 25,
2012 from http://www.clexchange.org/ftp/documents/Implementation/IM1996-
01EffectiveUseOfSims.pdf
Barbara L. Peckarsky (2006). Predator-Prey Interaction. Retrieved November 25, 2012 from
http://www.zoology.wisc.edu/faculty/peckarsky/pdf/CH24predprey.pdf
Marshall W. Johnson (2000). Prey / Predator Interaction Models. Retrieved November 27,
2012 from http://nature.berkeley.edu/biocon/BC%20Class%20Notes/73-77%20
Predator%20Models.pdf
Mike Scott (2004). Data Modelling. Retrieved November 27, 2012 from
http://www.liberty.edu/media/1414/[6330]ERDDataModeling.pdf
Isee system (2012). STELLA System Thinking for Education and Research. Retrieved
November 20, 2012 from http://www.iseesystems.com/softwares/Education/
StellaSoftware.aspx
Peter Vescuso (2008). Using STELLA to Create Learning Laboratories: An Example From
Physics. Retrieved November 26, 2012 from http://www.systemdynamics.org
/conferences/1985/proceed/vescu964.pdf
William W. Murdoch (1971). The Developmental Response of Predators to Changes in Prey
Density. Ecology. 52 (1) Retrieved from http://www.jstor.org/discover/10.2307/1
934744?uid=3738672&uid=2129&uid=2& ui d=70&uid=4&sid=21101509437847
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