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sheep-populationA

by Ed Hazzard (Submitted: 02/07/2005)

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Evolution: Sheep-populationA
This is a model of a flock of sheep whose survival depends on eating grass. One can study the effect on the population of initial number, grass regrowth rate, and birthrate.

Here are are some explorations:

1. 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.

2. Once a year, from age 3 to age 6, each female gives birth to a baby.

3. 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.

4. Run the model for about 50 years. What do you observe about the relationship between the grass and the population?
5.
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.

6. What causes this pattern?

7. 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?

8. Look at the last 30 years (year 70 to year 100). How big are the fluctuations?
Maximum population
Minimum population
Size of fluctuation

9. 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.

10. Why do you think so?

11. 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%

12. 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?
a. [ ] It would be greater
b. [ ] It would be less
c. [ ] It would be about the same

13. Now try it. You must hit SETUP each time you change INITIAL-NUMBER.
a. Set INITIAL-NUMBER = 200. Hit SETUP, then GO-FOREVER. Run it for 50 years. Notice the average long-term population. Fill in the table.
b. Set INITIAL-NUMBER = 100 and again notice the average long-term population after 50 years. Fill in the table.
c. Set INITIAL-NUMBER = 50. Fill in the table.

INITIAL-NUMBER Average long-term population
200
100
50

14. 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
c. [ ] It is about the same
d. [ ] It changes but there is no pattern

15. How can you explain this result?

16. What would happen to the average population if you decreased GRASS-REGROWTH-RATE? This might be caused by a decrease in rainfall.
a. [ ] It would decrease
b. [ ] It would increase
c. [ ] It would stay the same

17. 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

18. 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
c. [ ] It is about the same
d. [ ] There is no pattern

19. How can you explain this result?

20. 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.
e. [ ] It would decrease
f. [ ] It would increase
g. [ ] It would stay the same

21. 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.

To explore other features of this population, go on to sheep-populationB.

To explore evolutionary adaptation, go on to sheep-selection.

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