STELLA

This is an individual assignment. I had choose the title of predator-prey dynamics. In this assignment, we have to apply the model and simulation.

This is the result.

1.0        INTRODUCTION OF MODELING AND SIMULATION

Model and simulation has become part and parcel of advanced learning environment, performance technologies and knowledge management systems. Model and simulation can provide a foundation of an effective integration of teaching and learning. Modeling and simulation is a discipline for developing a level of understanding of the interaction of the parts of a system, and of the system as a whole. The level of understanding which may be developed via this discipline is seldom achievable via any other discipline. A system is understood to be an entity which maintains its existence through the interaction of its parts.

          Modeling and simulation is a discipline, it is also very much an art form. One can learn about riding a bicycle from reading a book. To really learn to ride a bicycle, one must become actively engaged with the bicycle itself. Modeling and simulation follows much the same reality. You can learn much about modeling and simulation from reading books and talking with other people. Skill and talent in developing models and performing simulations is only developed through the building of models and simulating them. It is very much a learn as you go process. From the interaction of the developer and the models emerges an understanding of what makes sense and what does not.

1.1     WHAT IS MODELING?

Modeling is the process of producing a model. A model is a representation of the construction and working of some system of interest. A model is similar to but simpler than the system it represents. One purpose of a model is to enable the analyst to predict the effect of changes to the system. On the one hand, a model should be a close approximation to the real system and incorporate most of its salient features. On the other hand, it should not be so complex that it is impossible to understand and experiment with it. A good model is a judicious trade off between realism and simplicity. Simulation practitioners recommend increasing the complexity of a model iteratively. An important issue in modeling is the model validity. Model validation techniques include simulating the model under known input conditions and comparing model output with system output.

          Generally, a model intended for a simulation study is a mathematical model developed with the help of simulation software. Mathematical model classifications include deterministic (input and output variables are fixed values) or stochastic (at least one of the input or output variables is probabilistic), static (time is not taken into account) or dynamic (time-varying interactions among variables are taken into account). Typically, simulation models are stochastic and dynamic.

          A model is a simplified representation of the actual system intended to promote better understanding. Whether a model is a good model or not depends on the extent to which it promotes understanding. Since all models are simplifications of reality there is always a trade-off as to what level of detail is included in the model. If too little detail is included in the model one runs the risk of missing relevant interactions and the resultant model does not promote understanding. If too much detail is included in the model, the model may become overly complicated and actually preclude the development of understanding. One simply cannot develop all models in the context of the entire universe.

1.2     WHAT IS SIMULATION?

A simulation of a system is the operation of a model of the system. The model can be reconfigured and experimented with, usually, this is impossible, too expensive or impractical to do in the system it represents. The operation of the model can be studied, and hence, and properties concerning the behaviour of the actual system or its subsystem can be inferred. In its broadest sense, simulation is a tool to evaluate the performance of a system, existing or proposed, under different configurations of interest and over long periods of real time.

          Simulation is used before an existing system is altered or a new system built, to reduce the chances of failure to meet specifications, to eliminate unforeseen bottlenecks, to optimize system performance. For instance, simulation can be used to answer several questions like, what is the best design for a new telecommunication network?. A simulation generally refers to a computerized version of the model which is run over time to study the implications of the defined interactions. Simulations are generally iterative in the development. One develops a model, simulates it, learns from the simulation, revises the model, and continues the iterations until an adequate level of understanding is developed.

2.0     ADVANTAGES OF SIMULATION

Even when it’s practical to place students in real-life situations so that they can learn by doing, it’s not always preferable. Simulations offer many key advantages over real life. One of them is that simulation can boost student motivation. This is because the students are able to explore the experiment by themselves. So that, it can help them to learnt more through this kind of simulation. The students can carried out the experiment by their own and this situation can let them to easily change and adjust the parameter given for more understanding. They also can repeat the experiment for more than once. Students had the advantage of the simulation tools, animations, and learning modules to get more insight into the theoretical contents of the course. Students will have the opportunity to put a number of theoretical concepts into practice by simply using the simulation. Besides that, learning through simulation can bring them to deep learning too.

Students are able to make further prediction for certain cases by using simulation. Sometimes, certain topics to be learnt by students cannot be done for real because of certain reasons, so that, by using simulation they are able to make prediction for that topic easily. Thus, learning by using simulation give many benefit for students such as the  students will feel happy to learnt something and the process of teaching and learning become more meaningful. The students become very well motivated and interested in the course.

Simulations allow students to play with time in ways the real world does not permit. Often, the real world moves so quickly that students do not have time to think things over as much as they would like. However, in a simulation, if a student wishes to sit and ponder his course of action, he can freeze the simulation, and perhaps even ask an expert some questions. If a student is unclear as to why things turned out the way they did, we can allow him to loop back in time and review the course of events. If events are moving too quickly, the student can slow them down. Students can even decide to back time up so that can try a different approach.

Simulation can be used as an effective means for teaching or demonstrating concepts to students. This is particularly true of simulation that make intelligent use of computer graphics and animation. Such simulation dynamically show the behavioural and relationship of all the simulated system’s components, thereby providing the user with a meaningful understanding of the system’s nature. Consider again, for example, a circuit simulation. By showing the path taken by signals as inputs are consumed by components and outputs are produced over their respective fanout, the students can actually see what is happening within the circuit and is therefore left with a better understanding for the dynamics of the circuit. Such a stimulation should also permit students to speed up, slow down, stop, or even reverse a simulation as a means of aiding understanding. This is particularly true when simulating circuits which contain feedback loops or other operations which are not immediately intuitive upon an initial investigation.

Lastly, simulation also provide teachers with  better access to students. Simulations can be instrumented so that teachers can monitor students, waiting until students get into a jam that indicates that they are ready to hear something the teacher wants to convey. In computer-based simulations, the teachers themselves can automated, thereby making one teacher’s knowledge available as needed to many individual students. In the full implementation of this idea, the entire corporate memory of an organization, or all the experts in a various field, can come to the fore, ready to tell their stories, in response to a situation that has occurred in practice within a simulation.

3.0     SAMPLE MODEL OF PREDATOR-PREY DYNAMICS

Below in Figure 1 is very simple map of hare population dynamics. The box represents the number of hare in the population at any point in time. This stock accumulates the flow of births, net of the flow of deaths. The logic shown here says that hares beget more hares. In other words, hares breed like rabbits. The larger the population, the greater the birth flow. The little circle called hare birth fraction. This circle represents the number of offspring produced on average, per hares in the population, per year.

          Lynx eat hare. This one component of the predator/prey interactions that is the consuming of prey by the predators. The number of hares killed per lynx per year is assumed to depend on hare density. The greater the density of hares in the ecosystem, the larger the number of hares consumed per lynx per year.

          This linkage from hare, to density, to hares killed per lynx, to hare deaths, and back to hare again, forms a counteracting feedback loop. An increase in the number of hare in the system propagates around the loop to lead to an increase in the hare death flow, and thus brings the number of hare back down again. This show us that the counteracting loops counteract the change.

          Lets move on to the lynx birth process. As we can see, this process parallel to the birth process for hares. There is a connection from the population to its inflow, and a birth fraction. Lynx beget lynx. After that, lynx die. More precisely, some fraction dies each year. That fraction s determined by the density of the hare population in the ecosystem. A higher density of hares will contribute to the long-lived lynx. On the other hand, as the population density of hares declines, a large portion of the lynx population will die due to malnutrition and starvation

Figure 1

4.0     DISCUSSION ON SAMPLE OF PREDATOR-PREY DYNAMICS

Figure 2

Figure 3

Figure 4

Figure 5

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. In this model and simulation, I had choose the topic  from the discipline of biology which is the predator-prey dynamics and the predator-prey oscillations are common in many simple ecosystems. 

          Within this simple predator-prey dynamics, I had run 4 simulation which is differ in the value of the parameter. That parameter in this experiment is the size of 1 time lynx harvest. In the first experiment that I had run, I set the size of 1 time lynx harvest to zero. As the result, I can see that there are only a straight line graph showing that the lynx and hare population is still the same through years. So that, I can say that this first run as the control.

          Then, I had run second experiment which I increased the size of 1 time lynx harvest to 230. From this run, I noticed that when the lynx population decrease, the hare start to increase in their size of population. But,  after several years, since the hares keep increasing, the lynx also start to increase in their population’s size. It might be because of the lynx have enough supply of food which they eat on hare. Due to this situation, the hares’ size of hares start to decline. The effect of decreasing of hares also affect the size of lynx because the lynx depends on hares for the food. When the lynx decrease, the hare are able to increase back. This cycle will start over again.

          The same situation goes to the third run and fourth run. In the third run, I increase the size of 1 time lynx harvest to 480 while in the fourth run I had increased it to 700. We can see the different in the form of the size of both populations involved the occurrence of the flux in the graph. The flux that occur in this cyclic relationship is what allows for the ecosystem dynamic to work. Without flux, vegetation would not have a chance to recover from the hare population’s continuous eating, and without vegetation, the hare population could no longer exist in its habitat. The most important thing is that, the concept of the cycle is remain the same which is when the population’s size of the lynx increase, the size of population of the hares decrease. Therefore, we can say that the size of lynx depends on the size of hare.

In the dynamics of a single population, we typically take into consideration of some factor such as natural growth rate and the carrying capacity of the environment. Mathematical ecology require the study of the populations that interact, thereby affecting each other’s growth rates. In this model and simulation, I had study about an interaction, in which there are exactly two species, one of which  we called a predator that eats the other prey. Such pairs exist throughout nature such as lynx and hares.

          There are four graph of simulation above named Figure 2, Figure 3, Figure 4, and Figure 5. When we look at the graph of the simulation, it illustrate the relationship between the size of the hare population and the size of the lynx population. Notice that how each population has a boom (when there are too many lynxes or hares for the available resources) and a bust (when many hares or lynxes die and very few are left) pattern. We can look at the pattern in the graph of simulation.

          We are able to see that how the lynxes pattern closely follows the hares pattern, but that the lynxes peaks and valleys happen a bit after the hares peaks and valleys. We know that the lynx and hare populations have a predator-prey relationship. Factors such as disease, food supply, and other predators are variables in this complex relationship. The flux that occur in this cyclic relationship is what allows for the ecosystem dynamic to work. Without flux, vegetation would not have a chance to recover from the hare population’s continuous eating, and without vegetation, the hare population could no longer exist in its habitat. Therefore, this situation neither could the lynx population that depends upon the hare population for food.

          Every certain years, or so, the hares’ reproduction rate increases. As more hares are born, they eat more of their food supply. They eat so much food that they are forced to supplement their diet with less desirable and nutritious food. As the hare population size grows, the lynx population size begins to increase in response. Because they are so many hares, other predators opportunistically begin to hunt them along with the lynxes. The hares’ less nutritious and varied diet begins to have an effect, the hares begin to die due illness and disease. Fewer hare are born because there is less food. The hare population size begins to go into a steep declines. Therefore, the lynx population also begins to decline. Some lynxes starve and others die due to diseases. Both the lynx and the hare populations have fewer babies and this decrease in population gives the vegetation a chance to recover. Once there is enough vegetation for the hares to begin to increase their population the whole cycle begins again.

5.0     CONCLUSION

Modeling and simulation give many benefit for our life. It help us to visualize the data and able to see the pattern and draw a conclusions that would otherwise be difficult to discern. Since the amount of real-world data that can be collected in domain such this may be massive, computers are essential for storing, and analyzing the patterns inherent in the data. Within this model and simulation, the discipline that I consider is biology, specifically the study of population growth in a predator-prey relationship on the Canada lynx and the snowshoe hare.

          When studying complex system, such as an ecosystem involving predator and prey species, simply collecting and analyzing real-world data is sometimes not enough. To further study about certain desired system and perhaps to test hypotheses about its behaviour, modeling and simulation can be the best choice. This is because, computer models allow us to alter the parameters of the system and observe the resulting changes. Since the computers are fast, long-range developments in the system can be simulated at incredible speeds, at a fraction of the cost of field observation.

          Even though, there are some disadvantage of simulation such as it can be expensive to measure how one thing affects another, to take the initial measurements, to create the model itself (such as aerodynamic wind tunnel), but still simulation and modeling provide us with many advantages. Thus, in my opinion, learning by using simulation and modeling can increase the students performance in our Malaysian schools. It should be implemented in every schools with the help of school management and teachers.

  

6.0     REFERENCES

Advantages and disadvantages of simulation (2012). Retrieved on October 25, 2012 from http://www.bbc.co.uk/schools/gcsebitesize/ict/modelling/1computersimulationrev3.shtml

Donald Craig (1996). Advantages of Simulation. Retrieved on October 22, 2012 from  http://www.cs.mun.ca/~donald/msc/node6.html  

Gene Bellinger (2004). Modeling & Simulation. Retrieved on October 27, 2012 from http://www.systems-thinking.org/modsim/modsim.htm

Simulation Leads to More Motivated Students and Improved Teaching and Learning (2009). Retrieved on October 22, 2012 from http://nanohub.org/newsletter/articles/simulation-leads-to-more-motivated-students-and-improved-teaching-and-learning\