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

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Evolution: Sheep-populationB
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. PopulationB focuses on uncontrolled growth.

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. What would happen to the population if the sheep had as much grass as they wanted?

5. Try this with the model. Change the LIMITED-GRASS? Switch to OFF. Then there is unlimited grass for the sheep to eat. Click on SETUP. Click on GO-ONCE five times. As the number of sheep gets very large, the model will run more slowly! What happens to the population?

6. Start again by clicking on SETUP. Try using the REAPER button, which reduces the herd at the end of each year. The NUMBER-REMOVED slider sets how many sheep are removed by the REAPER button. Run the model with the GO-FOREVER button. Can you keep the population under control? How?

7. What you just did with the REAPER button is what must happen in nature to keep a population stable. Many animals die every year!

8. Now try changing the variable BIRTHRATE-%. This is the chance that a female will have a baby once a year. Try to keep the population stable even when the GO-FOREVER button is on. If the population gets out of control, stop, hit SETUP, and start again. What is a value of BIRTHRATE-% that keeps the population roughly steady when the grass growth is unlimited?

9. Notice that the effect of changing the birthrate is delayed. Why is this?

10. What is the lowest value of BIRTHRATE-% for which the herd doesn’t die off?

11. If the sheep only died of old age, the birthrate for a constant population – called the “replacement rate” – should be about 50%. Here’s why.
a. For a 100% birthrate, each female has one baby a year for four years – a total of 4 babies in her lifetime.
b. For a 50% birthrate, each female has 2 babies in her lifetime.
c. Since the male doesn’t have babies, the 2 babies just replace the mother and the father.
Is your minimum birthrate greater or less than 50%?

12. Many animals – for example, mosquitoes and fish – may lay thousands of eggs in one year. Why might this be a good survival strategy. Why don’t they take over the world?

To explore extinction, go on to sheep-populationC.

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