CASE STUDY: Kaibab Plateau

Overview:

The Year is 1900. The place is the Kaibab Plateau, on the rim of the Grand Canyon in Arizona. You have been given the responsibility of managing the wildlife on the Kaibab Plateau in a manner that satisfies the major interest groups of the area. There are many groups whose concerns you will need to balance as you play the game.

The ranchers of the plateau region are concerned about the large number of predators that exist on the plateau. The predators feed primarily on the rodents and deer of the plateau, but are beginning to make raids on cattle herds. The economic losses to ranchers are growing. To combat the problem, ranchers encourage you to set a high bounty on predators. A high bounty, they argue, will encourage hunting of predators and thereby keep cattle losses to a minimum. Ranchers are also beginning to graze their cattle on the plateau. Ranchers want you to ensure that the forage on the range remains healthy. Because ranchers exert political clout, you have been counseled to heed their advice.

Deer hunting is growing in popularity in this region. Pressure is now growing for you to increase the annual deer tag allotment. Deer tags, of course, are the major source of funding for your resource management department.

Conservationists are concerned about the "purity" of the plateau region. They have told you that they think you can be a good manager for the plateau. They have also warned you not to let the system get "out of control."

Building the Model:

For purposes of this model, we're only going to concern ourselves with three main components:

Deer population
Predators
Available food supply

Food is grown and consumed. We will measure food in generic "food units" and begin in the year 1900 with 98,750 food units. Food regeneration is calculated using this equation:

regeneration = (100000 - current food supply) / regeneration time

Food is regenerated (grown) based on the current supply of food, based on this schedule:

Food Units	Regeneration time
0	50
10000	42.8
20000	36.8
30000	1.25
40000	1.00
50000	0.5
60000	0.5
70000	0.25
80000	0.25
90000	0.25
100000	0.25

Food is consumed only by the deer population (predators live from eating deer). Each deer consumes an amount of food dependent on the accumulated food supply. A table that shows this relationship is as follows:

Food Units	Consumption /deer (food units/year)
0	0
10000	0.015
20000	0.115
30000	0.38
40000	0.725
50000	0.875
60000	0.95
70000	0.98
80000	1.0
90000	1.0
100000	1.0

Deer population is influenced by number of births and deaths. Initially (in 1990), there are 5,000 healthy deer. The deer birth rate is affected by consumption of food per deer, based on this table:

Deer birth rate	Consumption per deer (food units per year)
0.015	0
0.065	0.1
0.145	0.2
0.345	0.3
0.675	0.4
0.86	0.5
0.97	0.6
0.985	0.7
0.995	0.8
0.995	0.9
1.0	1.0

Deer can die in one of two ways: through predation or starvation. The starvation rate is dependent, of course, on the number of deer and the amount of food consumed per deer. A table showing this relationship is as follows:

Deer death rate	Consumption per deer (food units per year)
0.81	0
0.79	0.1
0.74	0.2
0.68	0.3
0.55	0.4
0.47	0.5
0.44	0.6
0.4	0.7
0.4	0.8
0.4	0.9
0.4	1.0

Deer can also die through predation. Predation depends on the number of predators, the number of kills per predators, AND the number of deer killed by hunters every year. A generic rule for calculating number of deer killed by hunters is 1/3 of a deer for every deer hunting tag issued. A table equating kills per predator as a function of deer density is as follows:

Deer density	Kills per predator
0	0
1	0.04
2	0.1
3	0.275
4	0.625
5	1
6	1.5
7	2.08
8	2.6
9	3
10	3

Deer density is affected by the number of deer and the area. The area of the Kaibab Plateau is estimated at 1,000 acres. Deer density also influences the predator birth rate, as described in this table:

Deer density	Predator birth rate
0	0
10	0.05
20	0.1
30	0.15
40	0.2
50	0.25
60	0.3
70	0.35
80	0.4
90	0.45
100	0.5

The predator birth rate is a function of the number of predators currently alive and the predator birth rate. Initially (in 1990), there are 3,000 predators living on the Kaibab Plateau. There is also the situation that an influx of 100 additional predators occurs in 1942

Predator deaths are influenced by the predator mortality rate and the number of living predators. The predator mortality rate is a function of the bounty paid to hunters for killing predators. The government has, however, put a limit on the bounty to be offed at $100. The relationship between predator bounty and predator death rate is shown in this table:

Predator bounty	Predator death rate( in dollars)
0	0.025
10	0.035
20	0.06
30	0.11
40	0.255
50	0.325
60	0.37
70	0.495
80	0.675
90	0.815
100	0.995

Once you have designed your model, run the model from the year 1900 to the year 1940. NOTE: some of your inputs have not been explicitly stated. You will need to decide on some initial values. Similarly, the step time (dt) and the numerical method have not been identified...they are for you to decide!

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