Easter Island Population Model – Answer Sheet

Part 1 – System Dynamics Model

Population Structure

How should we use these in an equation to calculate a value for the birth rate per year?

Q1. Write your answer in the box below, including the calculation and final value (and round your answer to nearest thousandth). Make sure to include the units. (1 mark)

Q2. Write the equation for the ‘Births’ flow in the model in the box below. Make sure to include the units. (1 mark)

Q3. Write the equation for the ‘Deaths’ flow in the model in the box below. Make sure to include the units. (1 mark)

Tree Structure

For now we will consider trees to be a non-renewable resource, since the natives did not replant the trees they used. We want to keep track of the number of trees over time, so should trees be modelled using a stock or a flow?

Q4.

Write your answer in the box below. Explain your answer. (1 mark)

Given that trees are only decreasing, how would you model this, using an inflow or an outflow?

Q5.

Write your answer in the box below. Explain the reasoning behind this model structure. (1 mark) Call this flow ‘Consumption’.

Define the Death Rate Converter

How should we use these in an equation to calculate the death rate per year?

Q6.

Write your answer in the box below. Make sure to include the units. (1 mark)

Q7. Write the equation for the ‘Effect of Tree Supply on Death Rate’ in the box below. Explain the units. (1 mark)

Q8. Paste a copy of your graphical function into the box below. (2 marks)

Connect Population and Trees

As the population increases, what do you think will happen to the consumption of trees? Would it increase, decrease or remain the same? Why?

Q9.

Write your answer in the box below. Explain your answer. (2 marks)

Q10. Write the equation for the ‘Actual Tree Consumption per Person per Year’ in the box below. Make sure to include the units. (1 mark)

Q11. Write the equation for the ‘Consumption’ in the box below. Make sure to include the units.
(1 mark)

Q12. Write the equation for the ‘Available Trees per Person’ in the box below. Make sure to include the units. (1 mark)

Simulate the Model

Q13. Looking at the first graph, explain the observed trends in the population and trees over time. Include a copy of your first graph in your answer. (2 marks)

Q14. Looking at the second graph, why do you think the population started to decline? Include a copy of your second graph in your answer. (2 marks)

Q15. How many years does it take the population to double? (1 mark)

Q16. Is the doubling time the same for different time periods? Why, or why not? (2 marks)

Q17. What was the largest value for the population? (1 mark)

Q18.

What year did the population start to decline? (1 mark)

Q19. How many people are left in 1900? (1 mark)

Q20. How many trees are left in 1900? (1 mark)

Tree Replanting Structure

Q21.

Looking at your graph, explain the observed trends in population and trees over time. Include a copy of your graph in your answer. (2 marks)

Q22. How many people are left in 1900? (1 mark)

Q23.

How many trees are left in 1900? (1 mark)

Q24. Looking at your graph, explain the observed trends in population and trees over time. Include a copy of your graph in your answer. (2 marks)

Q25. How many people are now left in 1900? (1 mark)

Q26. How many trees are now left in 1900? (1 mark)

Step 6 – Completed Model

Q27. Insert a picture of your completed model that shows: tree replanting, sapling deaths, tree maturation and cyclone loss.

Insert two graph outputs:

- First graph: mature tree numbers and human population between 400-2000 AD without tree replanting, sapling death, tree maturation and cyclone loss.

- Second graph: mature tree numbers and human population between 400-2000 AD with tree replanting, sapling death, tree maturation and cyclone loss. (5 marks)

Note: to copy a model from Stella, drag a box around the model using your mouse and press
Ctrl + C on your keypad, then go to your document and press Ctrl + V. To copy a graph from Stella, right click on the graph, select copy, then go to your document and press Ctrl + V on your keypad.

Part 2 – Causal Loop Diagrams

Q28.

Draw a feedback loop that relates the population with the number of trees. Make sure to include all polarities and a loop label to your feedback loop. Explain your feedback loop. (2 marks)

Q29. In the Easter Island Population Model, what common mode of system behaviour does human population represent?

a) Draw the generic CLD that explains this behaviour and then

b) Draw a second CLD that replaces the variables in the generic CLD with those relevant to Easter Island.

Make sure to include all polarities and loop labels in your CLDs. (5 marks)

Q30. What system archetype best represents the Easter Island situation?

a) Draw the generic CLD that explains this system archetype and then

b) Draw a second CLD that replaces the variables in the generic CLD with those relevant to Easter Island.

Make sure to include all polarities and loop labels in your CLDs. (5 marks)