Trial 1 - Messing Around with Populations
-
As you may
have discovered while thinking about deer,
there are a great number of factors that
affect the size of a population. We can
often only guess what their influence really
is. To explore how these systems work, you
will use a simplified population model with
only a few factors.
-
Picture yourself as a rancher
with a large field of sheep. You start with
an equal number of males (horns) and females
(no horns). They live for six years. The
sheep move around the field and eat grass,
which grows back at a certain rate. The
patch is green if there is grass there, and
brown if there is no grass. In the model,
the sheep move and eat during the year. They
use up energy as they move, and gain energy
from eating grass. If their energy goes to
zero, they die.
-
Once a year, from age 3 to age 6,
each female gives birth to a baby. How many
babies could a female produce in its lifetime?
-
Open
the model. See Technical Hints to run
and save the evolution model.
[model: sheep-populationA
]
-
To run
the model, always first hit SETUP. Hit
GO-ONCE to run the model for one year. Hit
GO-FOREVER to run the model continuously. To
stop, hit the same button again. The graph
shows the amount of grass (green) and the
total population (black) as time goes
by.
-
Run the model for about 50 years.
What do you observe about the relationship
between the grass and the population?
-
Use GO-ONCE instead of GO-FOREVER,
and run one year at a time. Look more
carefully at the relationship between sheep
and grass. If you drag the cursor onto the
graph, you can read values at the location
of the cursor. Before you run the next
year, try to predict whether the sheep and
grass will go up or down. Describe
what you observe.
-
What causes this pattern?
-
Using the GO-FOREVER button, run the
model for 100 years. Even though the
population always goes up and down, what is
the "average" value that is
roughly at the center of these fluctuations?
Average long-term value =
-
Look at the last 30 years (year 70
to year 100). How big are the fluctuations?
Maximum
population |
|
Minimum population |
|
Size of fluctuation |
|
-
Suppose you had thousands of sheep,
in a much larger field, instead of a few
hundred. Do you think the population would
be steadier?
| a. Yes,
fluctuations not so big. |
| b. No, larger fluctuations. |
| c. It would make
no difference. |
-
Why do you think so?
-
The
model allows you to adjust several factors.
Try changing them one at a
time, following the steps below.
After that, you can do other experiments on
your own. Here are the starting values:
-
INITIAL-NUMBER
= starting number of sheep = 100
-
GRASS-REGROWTH-RATE =
how fast the grass grows back = 80
-
GAIN-FROM-FOOD = amount
of food they gain from eating a square of
grass = 2.0
-
BIRTHRATE-% = chance
that a female will have a baby once a year =
100%
-
Suppose the starting number was 200,
in the same field. What would happen to the
average population after a period of time,
compared to a starting number of 100?
| c. It would be
about the same |
-
Now try it. You must hit SETUP each
time you change INITIAL-NUMBER.
- Set
INITIAL-NUMBER = 200. Hit SETUP, then
GO-FOREVER. Run it for 50 years. Notice the
average long-term population.
Fill in the table.
- Set
INITIAL-NUMBER = 100 and again notice the
average long-term population
after 50 years. Fill in the table.
- Set INITIAL-NUMBER = 50. Fill in the
table.
INITIAL-NUMBER
|
Average long-term population
|
200 |
|
100 |
|
50 |
|
-
Is there a pattern in the long-term population?
| a. It is greater
if the initial number is greater |
| b. It is less if
the initial number is greater |
| d. It changes but
there is no pattern |
-
How can you explain this result?
-
What would happen to the average
population if you decreased
GRASS-REGROWTH-RATE? This might be caused by
a decrease in rainfall.
| c. It would stay
the same |
-
Now try it. Set INITIAL-NUMBER back
to 100. Run the model and try different
values of GRASS-REGROWTH-RATE. You can
change GRASS-REGROWTH-RATE while the model
is running. Fill in the table.
GRASS-REGROWTH-RATE
|
Average long-term population
|
95 |
|
80 |
|
50 |
|
-
What happens to the population?
| a. It is greater
if the grass growth rate is greater |
| b. It is less if
the grass growth rate is greater |
-
How can you explain this result?
-
What would happen to the average
population if GAIN-FROM-FOOD (the energy
sheep get from eating grass) were reduced?
This might correspond to a grass that was
less nutritious.
| c. It would stay
the same |
-
Now try it. Set GRASS-REGROWTH-RATE
back to 80. Run the model and try different
values of GAIN-FROM-FOOD. You can change
GAIN-FROM-FOOD while the model is running.
Fill in the table.
GAIN-FROM-FOOD
|
Average long-term population
|
3 |
|
2.5 |
|
2 |
|
1.5 |
|
1 |
|
Describe the pattern you
observe and explain why you think this happens.
inc.
Copyright 2005 The Concord Consortium, All
rights reserved.
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