2012 HiMCM A題特等獎(jiǎng)學(xué)生論文下載3652

2012 HiMCM A題特等獎(jiǎng)學(xué)生論文下載3652

 

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論文摘要如下：

15th Annual High School Mathematical Contest in Modeling (HiMCM)

Summary Sheet (Please attach a copy of this page to each copy of your Solution Paper.)

Team Control Number: 3652

Problem Chosen: A

Summary

 

The final goal of our model is to simulate the number of Manitoban elks at the end of a period of time and evaluate if the Manitoban elks can adapt to the environmental conditions in eastern America, more specifically the GSMNP (Great Smokey Mountain National Park). In going about this problem, we constructed a model that predicts the change in the elk population over time.

 

Our model calculated the change in population by first calculating the birth rate and death rate, then calculating the limit to the elk population in GSMNP: The carrying capacity.

 

We calculated the birth rate of elks by averaging the elk births in the given data to obtain the arithmetic mean, and calculated the death rate in a slightly more complicated manner of splitting it into two sub-models: An accidental death rate model and a natural death rate model. The former accidental death rate model takes the arithmetic mean of the poaching rate, accident rate, predator attack rate, sickness rate, and an unknown factor rate based on the data given to obtain the probability of an elk dying from environmental factors in any given year. The natural death rate model, on the other hand, simply models the deaths of elks that reach their natural age limit.

 

We then estimated the carrying capacity of the elk population by rearranging the main function and calculating the arithmetic mean of all data inputted into it, and combined the above models to form our final elk population iterated model.

 

Next, we constructed a Monte Carlo Simulation Program to test our function for us. The program simulates the elk population’s interaction with Nature based on the functions derived in the iterated model for a large number of trials and outputs a statistical average of final population for comparison to our given data. We optimize the program by tweaking input rates and the sickness rate function in order to accurately portray the population growth function.

 

The original figures were derived by using data from 2001- 2007. By applying the calculated rates to the Monte Carlo simulations, a stunning accuracy of elks was achieved. After optimization and modification of the constant rates into functions, the absolute uncertainty of elks was reduced to for any set of given statistics (including total poached, total killed by predators, total killed by accidents, total killed by sickness etc.)

 

The model predicts that the number of elks will increase steadily in the future until it peaks at a limit of 1101, then fluctuate and oscillate slightly around this limit.

 

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