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Evolution: SheeppopulationA
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 GOONCE to run the model for one year. Hit GOFOREVER 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?
6. What causes this pattern?
7. Using the GOFOREVER button, run the model for 100 years. Even though the population always goes up and down, what is the ÒaverageÓ 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?
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?
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:
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?
13. Now try it. You must hit SETUP each time you change INITIALNUMBER.
INITIALNUMBER Average longterm population
14. Is there a pattern in the longterm population?
15. How can you explain this result?
16. What would happen to the average population if you decreased GRASSREGROWTHRATE? This might be caused by a decrease in rainfall.
17. Now try it. Set INITIALNUMBER back to 100. Run the model and try different values of GRASSREGROWTHRATE. You can change GRASSREGROWTHRATE while the model is running. Fill in the table.
GRASSREGROWTHRATE Average longterm population
18. What happens to the population?
19. How can you explain this result?
20. What would happen to the average population if GAINFROMFOOD (the energy sheep get from eating grass) were reduced? This might correspond to a grass that was less nutritious.
21. Now try it. Set GRASSREGROWTHRATE back to 80. Run the model and try different values of GAINFROMFOOD. You can change GAINFROMFOOD while the model is running. Fill in the table.
GAINFROMFOOD Average longterm population
Describe the pattern you observe and explain why you think this happens.
To explore other features of this population, go on to sheeppopulationB.
To explore evolutionary adaptation, go on to sheepselection.

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