Environmental Decisionmaking

Problem Set #3:

1) (10 pts) Take your two schematics from Problem Set #2 (the water in the pond and the colonization of a new island), and set them up as Excel models. For the pond problem, assume that there are 100,000 gallons of water in the pond, and that 500 gallons of water flow into the pond every hour. What must the rate coefficient be for the water flowing out of the pond, to keep the level of water from changing? Run the model with those parameters. Now, assume that the amount of incoming water increased (perhaps somebody began irrigation upstream), and so 600 gallons/hour began to flow into the pond. After about a month, would the pond reach a new steady-state (does the graph roughly level off?). For the island problem, set up the stock and flow model. Put in numbers just to make sure that it runs and makes sense, but don't worry if they aren't meaningful (though feel free to try to think about how to make them meaningful). You can e-mail me your Stella programs.

2) (5 pts) Set up the Rabbit and Foxes model that we went through in class (i.e. stocks of rabbits and foxes, where fox population affects rabbit deaths, and rabbit populations affect fox deaths and births). See if you can find a way to get the rabbit and fox populations relatively stable for a long period of time at some natural level (i.e. it has to be above the level that you force with a "max" function). You may not do this by simply cutting down the birth and death rates to very low values, but other than that you may use any reasonable combination of rates and you may add in any other feature in your model that you want (for example, food, disease, alternative prey species, multiple sites, different sorts of mathematical representations of the interactions as long as you can justify them, and so on). If you use explicit immigration, then I want the steady-state population to be at least twice the immigrating population (i.e., you can't just say "I have 300 rabbits immigrating every period, and my rabbit population is stable at 300!"). Explain what you have done.

3) (5 pts) Briefly explain the arguments that Meadows et al. make in the reading. What are your thoughts on the connection between exponential growth and sustainability, and how compelling do you find the discussion of this connection in the reading? Explain.