## Third Modeling Exercise

In class presentation due on Feb 13

## Predator-Prey Relations and EcoSystem Management

Ground Rules:

While there are exact ways to do these calculations, they are extremely tedious and even a bit complicated. We are never interested in an exact answer, just an approximate model answer. Keep that in mind! Items to calculate and report on are in red This assignment is not as bad as it seems. Simple modeling will give the approximate solutions.

Preserving the Zindernoodle:

Our company has been hired to come up with a plan to preserve a rare, yet curiously charming and seductive wild weed known as the Zindernoodle or Zinder-noodle if your Canadian. We are charged with coming up with a sustainable method so that visitors to Zindernoodle-land (or Zindernoodleland-o-rama if your American) can always be charmed by nature. We must work out a strategy.

Solution phase 1: Let the things grow ...

The Zinderbald wilderness area is a unique and very fragile ecosystem embedded in an otherwise hostile and forbidding environment. It is a small 1000 acre oasis in the wasteland in which the Zinder-noodle plant grows. Zinder-noodles grow quite fast and they require 1 nutrient unit to consume in order to grow to maturity in one day. However, if the Zinder-noodle density exceeds more than 1000 per acre, a catastrophic failure occurs and it is the demise of the Zinder-noodle.

The average lifetime of a Zinder-noodle is 1000 days. When the Zinder-noodle dies after 1000 days it gives 4 units of nutrients back to the soil which it has stored up from processing sunlight. In addition, the atmosphere adds an extra 0.2 units of nutrients per day due to the combined action of the zinderbites, a small bacterial unit with an annoying smell when unearthed coupled with annual rainfall. The average rainfall in the wilderness area is only 10 inches a year.

1. Let's assume initial conditions of 1000 Zinder-noodle plants scattered over these 1000 acres. Under the conditions, specificed above when will the demise of the Zinder-noodle occur? - They key here is that everytime a new unit of nutrient is available, a Zindernoodle grows (in 1 day).

2. What happens in the case where there is a long term drought and the average rainfall is only 4 inches a year?

3. Is rainfall an important parameter?

Solution phase 2: Introducing a Predator

We return back to the initial conditions of 1000 Zinder-noodle plants on 1000 acres.

We now introduce a new parameter: The blade-muncher.

These are nasty beasties that just love to munch away on the zinder-noodle plants. One blade-muncher eats 1 zinder-noodle every 10 days. Blade-munchers also spend a lot of time together and give birth to a pair of blade-munchettes every 15 days. The maturation period of a blade-munchette is 30 days after which time they become a blade-muncher and then eat zinder-noodles. At the moment there is no predator that eats the blade-muncher.

4. If we introduce 100 blade-munchers into the system is this catastrophic or not? That is, will the Zinder-noodles survive for very long?

5. If we want to use the blade-munchers as some form of control for the Zindernoodle growth, how many should we introduce initially?

Solution phase 3: Controlling the Blade-Muncher.

Again, go back to the initial conditions but now we introduce the Zardhogs. These are fierce, smelly creatures that just love to eat blade-munchers but hate the taste of blade-munchettes so they have to wait until the little ones mature. A zardhog spends most of its time sleeping and generally consumes 1 blade-muncher every 5 days. They generally have 1 off spring every 6 months (they would have more but they spend most of their time fighting since there are all married to one another). In addition, if the Zindernoodle density exceeds 20 per acre, that creates a toxic environment for the Zardhogs and they explode upon contact with a Zindernoodle. Of course, if the Zardhogs eat all the blade-munchers, they die of starvation.

Ah, now it looks like its possible to achieve an equilibrium solution if we open the wilderness area to Zardhog hunting to control that population.

6. For a blade-muncher initial population of 40, how many Zardhogs must be present in the system in order to maintain system equilibrium (equilibrium is defined as the state which keeps the Zinder-noodle population constant). Given this, how many Zardhogs per year need to be hunted.

7. Sunshine Moonbeam, the President of the Sierra Club has declared that Zardhogs are national treasures and all hunting must cease. Following Sunshine Moonbeam's edict, describe the evolution of the system if we start with 1000 zindernoodles on 1000 acres, an initial population of 10 blade-munchers and 2 Zardhogs. That is, will the Zardhogs die of starvation or explosion or will they actually survive?