1. The POPULUS modelling software Download your copy from the following website (the authors of the program are also cited there). This primer is best used with a running POPULUS program. http://www.cbs.umn.edu/populus/ The opening screen is shown below. This primer is based on Java Version 5.4. Run the POPULUS program first before opening this primer. You can shift from program to primer and back using Alt-Tab. Main Menu bar – gives access to major program features

2. The POPULUS modelling software Depending on your screen size, you may need to adjust the POPULUS program windows. Each of them can be scaled by clicking-and-dragging on any edge (just like any other window). POPULUS windows may be scaled by clicking-and- dragging on any edge. POPULUS windows may be repositioned by clicking- and-dragging on their heading.

3. The POPULUS modelling software A Help document can be accessed by clicking on the Help button in the menu bar. The help document is a pdf file and will require a pdf reader.

4. The POPULUS modelling software Access the models by clicking on the Model button. We’ll discuss Density-Independent growth in this section.

5. The POPULUS modelling software: Density-Independent Growth This refers to the starting population size you wish to define (we will be using the default value of 10) This refers to the number of generations you wish the model to run. We will be using 100 throughout our simulations. (Change this setting to 100).

6. The POPULUS modelling software: Density-Independent Growth There are several plot types available by which one can view the results of a model. N vs t is the plot of the population abundance (y- axis) over time (x-axis).

7. The POPULUS modelling software: Density-Independent Growth The ‘View’ button instructs the program to run the simulation and make the graph of the dynamic.

8. The POPULUS modelling software: Density-Independent Growth the population dynamic of density- independent species is defined by the factor rN (N refers to population size) r refers to the balance between birth and death rates (r = b – d) such that: if r = 0, then birth balances death (the population is stable) if r > 0, then there are more births than deaths (the population is increasing) if r < 0, then there are more deaths than births (the population is shrinking towards extinction)

9. The POPULUS modelling software: Density-Independent Growth The growth of the Density-Independent population relies only on r (the balance of its birth and death rates). The environment cannot limit its growth hence its population rapidly reaches huge numbers. This is known as exponential growth. Set the parameters as shown below and click the ‘View’ button. Read Core Case Study 1 (page 5) of our textbook for more on exponential growth and its attendant problems. For more on J-curve population models, read pages 109-111 of our text.

10. The POPULUS modelling software: Density-Independent Growth This is a J-curve model or the exponential growth curve of a Density-Independent population. Such populations are typical or r-selected species. Lag phase – population is at low numbers; adjusting to the environmental conditions Log phase – population has achieved maximium growth rate (exponential)

11. The POPULUS modelling software: Density-Independent Growth Now let’s simulate several populations with increasing r. (You may now close the graph by clicking on the ‘Close’ button.) Change the r parameter to 0.2 and view the N vs t graph. Generate another graph for a population with r = 0.3. Can you see how the model changes? Click here to close the active graph. Generate 3 graphs with increasing r by changing the r parameter (0.1, 0.2, and 0.3). Click ‘View’ to plot the graph.

12. The POPULUS modelling software: Density-Independent Growth If you were able to change the r parameter successfully, then you should have seen the following graphs (click anywhere on the slide to see the graphs in animation):

13. The POPULUS modelling software: Density-Independent Growth One of the aspects that changes is the curve. It becomes steeper as r increases. (See circled area in the animation below- click anywhere on the slide to begin). This means that the population is growing more explosively as r increases.

14. The POPULUS modelling software: Density-Independent Growth Another change can be seen in the abundance of the population. The population reaches a higher abundance as r increases. This can be seen in the y-axis scale. (See circled area in the animation below- click anywhere on the slide to begin). The model uses an exponential scale in the y-axis. To understand what this means, click here.

15. The POPULUS modelling software: Density-Independent Growth The following websites will be able to give you a broader and deeper knowledge of population growth models. http://www.nature.com/scitable/knowledge/library/an-introduction-to-population-growth- 84225544 http://www.nature.com/scitable/knowledge/library/how-populations-grow-the-exponential- and-logistic-13240157 End of primer. Press any keyboard button to exit.

16. Reviewer on exponential notation Exponents are used when huge numbers need to be written in shorthand. Consider the number 1,000,000,000,000. It would be tiresome to keep writing this number by itself but it becomes next to impossible to use it on a graphical scale as shown below: The solution is to use the exponential notation. Go HOMENEXT 1,000,000,000,000 2,000,000,000,000 3,000,000,000,000 4,000,000,000,000 5,000,000,000,000 6,000,000,000,000 7,000,000,000,000 8,000,000,000,000 9,000,000,000,000

17. Reviewer on exponential notation By default, exponential notation uses a base number of 10 which is represented as capital E. The number 1,000,000,000,000 can be written in scientific notation as 1 x 10 12. This is read as 1 times ten raised to the power of 12. 10 is the base number, 12 is the exponent. We got 12 by counting the digits to the right of 1 (the number being displayed). The displayed number may also have any number of decimals as you deem fit. Hence, 1,000,000,000,000 can also be written as 1.00 x 10 12. In POPULUS, scientific notation is written even shorter using capital E. So the number above is written by POPULUS as 1E12. If two decimals are used, then POPULUS writes it as 1.00E12. Study the following examples: NEXT RawScientific NotationPOPULUS notation 9,000,000,0009 x 10 12 9E12 10,000,000,000,0001.0 x 10 13 1.0E13 150,000,000,000,0001.50 x 10 14 1.50E14 Go BACK

18. So our cumbersome graph can now be written more conveniently. See below: Go HOMENEXT 1,000,000,000,000 2,000,000,000,000 3,000,000,000,000 4,000,000,000,000 5,000,000,000,000 6,000,000,000,000 7,000,000,000,000 8,000,000,000,000 9,000,000,000,000 1 x 10 12 2 x 10 12 3 x 10 12 4 x 10 12 5 x 10 12 6 x 10 12 7 x 10 12 8 x 10 12 9 x 10 12 1E12 2E12 3E12 4E12 5E12 6E12 7E12 8E12 9E12 This is the notation you will see in POPULUS graphs.