Ecosystem Modeling Assignment
Predator-Prey Relations and EcoSystem Management:
The Fate of the Zindernoodles
Note: This assignment is due on Tuesday evening, May 19
so you have a full week to do it. The "zoom"-session on Monday May 18 will not contain any "lecture" style material; instead that session will be devoted to answering questions about this particular assignment, if there are any.
This is a simple modeling assignment that is designed all to be done by counting various things in a spreadsheet. No application of equations are needed, you just need to keep track of various things in the ecosystem and you need to determine what the relevant timescale (i.e. number of days) is for each part of the asked questions. Believe it or not, you have all the tools to do this, you just need to think logically about the problem as you go through it.
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 and system behavior which will be
reported via tables and graphs that are constructed from you counting numbers.
An example graph you might construct would look like this:
Preserving the Zindernoodle:
Your 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. You 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. You must work out a strategy.
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 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 nutrient war occurs cluminating in the release
of Zindernoodle toxic venom. That causes the demise of the Zinder-noodle, the end of our tourist trap,
and the termination of your contract.
Solution phase 1: Let the things grow ...
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 0.4 units of nutrients per day due to the combined action of the
zinderbites, a small bacterial unit with an annoying smell. The zinderbite process is catalyzed by rainfall.
A study done at the Instutite of Scientists That Do Studies has shown that the
actual rate of zinderbite nutrient return is very sensitive to the annual
rainfall, scaling as 0.4 units per day x (annual rain/10)2.5, where
annual rain is measured in inches. The average rainfall in the wilderness area is
only 10 inches a year, but in rare seasons, the rainfall can be quite
a bit higher. Under these average conditions, 1 nutrient of soil is then returned every 2.5 days so if you start out with say 100 zindernoodles than 2.5 days later you would have 101 and 2.5 days after that you would have 102 - this is how you being to count the system in your spreadsheet or every 10 days there are 4 new Zindernoodles.
Hence an intial counting table would look something like this:
1. Let's assume initial conditions of 1000 Zinder-noodle
plants scattered over these 1000 acres. Remember, when the Zindernoodle population grows to 1000 Zinders per acre (total population of 1 million) they all die.
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). Nutrients come both from the action of the zinderbiters and the death of a Zindernoodle.
2. What happens in the case of wet year where the rainfall is 30 inches
per year?
3. Is rainfall potentially 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?
6. If we genetically breed blade-munchers to eat faster, say 1 zinder-noodel every 5 days, does that help with controlling the population?
Solution phase 3: Controlling the Blade-Muncher.
Again, go back to the generic conditions (where the blade-muncher consumes
1 zinder-noodle every 10 days) 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.
Zardhogs 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. Life is tough as a Zardhog.
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.
7. 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.
8. 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?
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