The models we will use come from Northwestern University's Center for Connected Learning and Computer Based Modelling and run in a program called Netlogo. The program and models are available for downloading, so you can continue to explore them on your own computers if you're so inclined.
The models from this site that we will be exploring in class are:
Whichever model you choose to explore, think of it as a process of making observations in order to try and come up with a "story" of how the system behaves. Report your observations and story in the course forum area.
Our hypothesis was that if we put everything exactly in the middle on the bars---if the sheep and wolves, for example, had the same reproduction rate and nutrition intake--the ecosysem would be balanced.
We were wrong. Yay for us.
After scrupulous experimentation with differing levels of variables, we discovered a model in which the ecosystem sustained itself. In this system, while the wolves got more nutrition from their food, the sheep reproduced faster. We kept the grass rate at around 100 (if we took away the primary nutrition source of the sheep, they died off and the wolves followd them), and eventually the screen flashed, alternately, full-sheep and full-wolves. Then the mac crashed, because macs are evil.
In conclusion, we suggest a new hypothesis. Wheras wolves, as predators, will deplete the sheep population if they are allowed to reproduce equally, if they simply gain more from their food (as actually happens in real life, considering they're eating meat, which has a higher nutritional quotient anyway) and reproduce less than the sheep, the sheep will be able to maintain a stable population. To test this hypothesis, we could run the simulation several more times.
Initially, we attempted to achieve homeostasis by setting all rates at the same level. In doing so, we found inverse relationships between the sheep/grass levels and the sheep/wolf levels.
In revision, we increased wolf gains from food. This resulted in the inherent death of sheep.
Our optimal level, yet not consistently sustained, was when when the sheep population levels were slightly higher than wolf, yet the wolf gain from consumption was considerable higher. While the model began with a direct relationship between the species, it ended in the inverse fluctuations of population levels.
In conclusion, death is inherent. While we are dealing with only two to three variables, it is possible that other external variables not introduced into the model aid in the consistency of survivorship curves.
The factors that can be changed with this program include probability of having a sexual relationship, condom use, length of relationship, and frequency of testing.
We kept these factors constant:
-5 average coupling tendency
-20 week duration of relationship
-observed over 30 years
**we altered the condom use and frequency of testing.
Our hypothesis was that condom use would be the most important factor in preventing the spread of HIV.
Condom use: 3/10
Testing: 0 times a year
Percent infected: 99%
Testing: 1 time a year
Percent infected: 9.33%
Testing: 2 times a year
Testing: 0 times a year
Testing: 1 time a year
Testing: 2 times a year
Final Observations: Condom use was important; but test frequency had a greater effect on percent infected. We were shocked at how drastic the difference was, particularly between scenario 4 and 6, because we set them up to simulate what we estimate is closest to real life in our generation.
Conclusion: get tested. twice a year.
We wanted to make the sheep, wolves and grass all survive for a long period of time. We figured out since the sheep are lower on the food chain you need a lot more of them. You also need more grass than sheep fr the same reason. We found that it was easier to have the grass on, so that would be a variable as well, because when there was a never-ending supply of grass the populations never stayed stable. By letting everything depend on the other variables, everything stayed more stable.
Also, we played with how much energry wolves can derive from eating a sheep compared to how much energy sheep got from grass. We ended up succeeding in making a stable environment.
We used the sheep and wolf model. We kept all of the variables the same, the results were always random. When we tried changing the number of sheep and wolves, while still keeping the other variables the same, the results were either one or both would die. Our observations were inconsistent with our hyothesis. We then reduced alll variables for the sheep and the esults showed (surprisingly) that the wolves died first and the sheep reproduced continously.
When examining with grass as a changing factor, we followed the same procedures as the first trial. The results we had were always random with one or both dying.
5- food gain
Grass at 30 reproduction rate
It was at this point that we found equilibrium.
We played around with the termite model. We found that changing the density determined how well the termites clustered the wood chips. When we changed the population, the only thing that changed was how fast or slow the termites clustered the wood chips.
A bigger density resulted in huge irregular looking clumps, almost like bands. A smaller density caused termites to make a lot of really small piles before eventually building up into few large clusters.
Since they move randomly, the clusters are always of different shapes and patterns. There is no predictability.
We tried to create a system which ensured that no species would become extinct by lack of food or by becoming food for predators.
We assumed that in creating a balance of wolf, sheep, and grass, it was important to begin with the same number of wolves and sheep, including the gain from food and reproduction rate.
Having attempted to begin with equal numbers, we found that an equilibrium of species could not be maintained. The wolves ate the sheep too quickly, so we decreased their number, assuming that the sheep population would be maintained due to a decreased number of predators. However, we soon came to see that the wolves would eventually become extinct, whereas the sheep would not become extinct and exist with the grass. Something else that we noticed was that the relative gain from food for sheep was quicker than that of the wolves, even with less number of wolves. If we had kept the gain from food equal, the sheep would have had a better advantage. We decided to lower the gain from food for sheep, so that the wolves had a better chance of remaining part of the ecosystem.
We then came to understand that in order to maintain equilibrium, we had to start out with a smaller number of wolves and sheep in general. We kept the proportion of wolves and sheep the same as the previous experiments, but lowered the number from 100 sheep to 44 and 80 wolves to 32.
This produced an equilibrium of species, that is, all were able to survive together.
For this lab we studied the Wolf/Sheet Predation model. We went into experiment expecting to be able to find a harmonious balance between wolves and sheep. We first increased the sheep population to 250 and increased the wolf population to 120. This lead to the extinction of wolves. We changed reprodution rates of both animals, and yet the wolves stiff suffered from extinction. Differnces in the wolf population were also made, but failed to yeild positive results. After these many changes in variables we decided that balance could not be reached with this vast number of sheep.
We then added grass as another variable, again starting with 250 sheep and 120 wolves. However, the wolves still became extinct.
At this point, we decided to use the initial populations given by the computer program -- 49 wolves and 82 sheep. We kept the grass as a variable, decreasing the regrowth rate to 25. With these factors in place, we found a stable environment for an infinate number of time. The sheep were dominate at most points in time, however, neither species became extinct.
At these setting the sheep and wolf populations expanded indefinitely. The rate of expansion of the sheep population was very high, and for the wolves very low. Yet, somehow a balance was achieved because both populations survived until our computer ran out of memory, and terminated netlogo. The sheep population at the time of termination was 28,774 and the wolf population a mere 188.
We had the grass option turned off in our first couple of trials. We hypothesize that the grass option, while complicating the experiment, will ultimately serve to limit the expansion of the sheep population.
After setting the grass option to on, and changing the rate of grass regrowth time to 50 (all other values were constant), we found a repeating, self-perpetuating pattern that continued indefinitely. The number of sheep was still greater than the number of wolves, however unlike our previous trials the number of sheep was closer to the number of wolves (about three times the number of wolves).
The pattern gained stability, with the values fluctuating around a point, with no net gain or loss. Our data supports our original hypothesis, that the use of the grass option will limit the expansion of the sheep population. This limitation is what allowed the values to become stable (because the sheep did not increase indefinitely as before).
There was not a regular pattern in the increase of the number of clusters, but the number of clusters did increase as the population increased. We think this is because the cells don't have to go as far to form clumps when there are lots of cells present. If there are too few cells, the green chemical evaporates before any other cells happen upon it, so they do not form clumps. (We think they might eventually, given a long time, but we did not observe any clumps below a population of 150.)
In dealing with the wolf-sheep predation model, we quickly discovered that the key to creating a stable ecosystem was to, without changing any of the other settings, "turn on" the grass. So we decided to change several of the other settings. We found that this ecosystem has a tendency to stabilize at a point where there are approximately twice as many sheep as there are wolves, even if the starting numbers of both are equal or even if the starting number of wolves is greater. We also found that altering the "sheep/wolf reproduce" numbers (the probabilities of each group reproducing at each timestep) did not really destabilize the ecosystem by that much. We found, however, that altering the "sheep/wolf gain from food" numbers had very significant effects on the ecosystem - if we increased the sheep gain-from-food, both the sheep and wolves became extinct very quickly. We then decided to increase proportionally the wolves' gain from food, and found once again that both species quickly became extinct.
Why did this happen? We're not really sure. However, we can hazard a guess:
When, for example, the sheep gain from food was increased, the number of sheep that showed up on the field greatly increased. This would suggest that the probability of their reproducing at each timestep had increased, but we knew that we controlled that number, so we had to discard that idea. What we believe was happening can be explained as follows: Sheep can die in two ways, according to this model: starvation and being eaten by a wolf. Having a low gain from food entails a greater likelihood of dying from starvation (if the grass function is turned on, of course). So, when the gain from food was increased, the sheep were much less likely to starve, causing there to be more of them over the course of time....
as stated above, we're not really sure. at all.
We attempted to achieve a stable environment in which both sheep and wolf populations coexisted for a long duration.
We observed the effect of altering one variable at a time while keeping the others constant. This confirmed for us that the relationship between all of the variables is highly important.
We noticed that different combinations of variables; inital number of sheep/wolves, gain from food, and reproductive rate, not only produced different results, but the time until extinction also changed.
We hypothesized that the number of sheep had to be greater than the number of wolves, that the wolves had to gain more from their food than the sheep, and that the rate of reproduction for wolves had to be slightly greater than that of sheep.
The closest we got to achieving a long duration of existence was:
# of sheep: 102 # of wolves: 60
gain from food: 11 gain from food: 25
reproduction: 6% reproduction: 7%
Init.sheep Init. Wolves SheepgainFood W.G.F S. repro W. repro
100 40 5% 15% 5% 5%
Thus, sheep Up, wolves Up--> sheep Down, wolves Down--> sheep Up
The one we did that worked:
I. Sheep I. Wolves S.gainFood W.gainFood S. repro W. repro
100 40 29 60 19 6
After 53 time units there were
The sheep were continuing upward, while the wolves increased at a steady, but slower rate. In conclusion, although our model works, we believe that there is no real solution to this problem: the key is moderation and balance, and diversity. Things are dependent upon one another, in order to create something new, something must first be destroyed---if a model could give us a solution to this problem, then life would be very easy.
We thought it would be intersting to test the spread of HIV observing two main variables: Weeks of commitment between partners and condom use. There was a constant 300 person population and 2.67 % was infectd to start.
An extremely brief conclusion: (we will explain further)
with 50 weeks commitment, 0 condom use
65.67% infected by 10 years
with 10 weeks commitment, 0 condom use
100% infected in 10 years
with 50 weeks commitment, 10 condom use (full condom use)
32.88% infected in ten years
10 week commitment, 10 condom use
We determined from this that we need to know several other factors. What changes once the people know they are infected? Based on the experiment, we can still see them coupling rapidly. This would not happen in real life. We also wanted to know if 10 condom use stood for 100% of the population using condoms, because that seemed unlikely and high for the scores we got.
Basically we can conclude that if no condoms are used, and commitment to one partner is extreamly short, than the entire population of 300 would contract HIV in 10 years. With comparitive observations of our data, we can say that condom use is a more important factor in stopping the spread (or slowing the spread) of HIV than lengthening the weeks commitment.
We hypothesize that when the density of the simulation is higher, there will be none or fewer piles, on the contrary to that when the density of the simulation is lower there will be more piles.
Number of Termites- 110 (number used in all test)
@ 2 mins. 4 piles
@5 mins. 4 piles
@7 mins. 4 piles
@2 mins..- 0 piles
@ 5 mins.- 0 piles
@ 7 mins- 0 piles
@2 mins. 2 piles
@5mins- 2 piles (one extremely large and 1 tiny)
@ 5mins- 2 piles
We feel that to get a proper set we will need to do more trials.
I tried many different combinations to match the level of growth of all 3 species. The final one I came up with kept an environmental balance, each of the 3, grass, sheep, and wolves, would increase and decrease interchangeably. None of the species died out, and they continuously overlapped each other in population. I ran this trial for 350 ticks.
Initial number: 75
Initial number: 50
Gain : 25
Grass growth time: 25
My observations from the graph were that as each species population increased, so did the other, and as each decreased, the same occurred. Since the wolves did have a limited food source, the sheep also had to have a limited food source, or their population would skyrocket within seconds. The 25 extra sheep in the beginning were enough of a buffer to let the wolves catch up, then for the two to grow and decline together.
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