Monte Carlo simulations provide a valuable tool for understanding complex phenomena. In class we have analyzed a collection of population models using differential equations. However, there are clearly significant stochastic effects when you consider real populations, and they are especially apparent for smaller populations. You will examine probabilistic models for the growth of populations, starting with a basic Malthusian growth model and extending it to the more complicated predator-prey (or Lotka-Volterra) model. Develop the appropriate growth and death terms for these models using a probabilistic derivation. (You can find information on this approach in the text below by Haberman.) Monte Carlo simulations are simply a means of testing a probabilistic models by selecting random numbers to determine whether a particular event such as a birth or death happens in a given interval. By performing a large number of Monte Carlo simulations, you should be able to average your simulations and obtain results very similar to the deterministic models.
Below are a collection of websites that will help you learn more about Monte Carlo techniques:
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