POPULUS Modelling Software: Lotka-Volterra Competition & Co-Existence

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) 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 repositioned by clicking-and-dragging on their heading. POPULUS windows may be scaled by clicking-and-dragging on any edge.

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 Lotka-Volterra competition models in this section. • NOTE: This primer assumes that you have mastered the lesson(s) on: • Density-Independent growth models • Density-Dependent growth models • Lotka-Volterra competition (co-existence model)

5. The POPULUS modelling software: Lotka-Volterra Competition (Either species may win; co-existence is not possible.) We have seen from the previous models that if two species are equally competitive, they will co-exist. Now we look at the scenario in which they are not equally competitive but in such a way that each species has a good chance of winning the competitive interaction and driving the other species to extinction. Let’s start from the situation in which Species 2 has an overwhelming K2. Input the following parameters and generate the N2 vs N1 plot. Recall that 1E3 is scientific notation for 1,000.

6. The POPULUS modelling software: Lotka-Volterra Competition (Either species may win; co-existence is not possible.) The resulting graph is shown below. To give Species1 a better chance of winning, let’s increase β (effect of Species 1 on Species 2). Biologically speaking, we are making Species1 better able to find food, water and shelter at the expense of Species2. The following graphs show the changes in the competition dynamics. As expected, Species 2 will always win in this scenario because of its overwhelming K2. It can maximize its environment better than Species 1. But what will happen as β increases?

7. The POPULUS modelling software: Lotka-Volterra Competition (Either species may win; co-existence is not possible.) β = 1.0

8. The POPULUS modelling software: Lotka-Volterra Competition (Either species may win; co-existence is not possible.) β = 2.0

9. The POPULUS modelling software: Lotka-Volterra Competition (Either species may win; co-existence is not possible.) β = 4.0

10. The POPULUS modelling software: Lotka-Volterra Competition (Either species may win; co-existence is not possible.) β = 8.0 The area (encircled) in which Species 1 grows while Species 2 dies increases as β increases. This is as expected since Species 1 is becoming a more able competitor.

11. The POPULUS modelling software: Lotka-Volterra Competition (Either species may win; co-existence is not possible.) By doing a vector analysis, one can see that the outcome of the competitive interaction depends on the initial abundance of the competitors. The following graphs show these.

12. The POPULUS modelling software: Lotka-Volterra Competition (Either species may win; co-existence is not possible.) Plot these graphs in your POPULUS program by changing the initial abundance of the two species. N1(0) = 50 N2(0) = 600

13. The POPULUS modelling software: Lotka-Volterra Competition (Either species may win; co-existence is not possible.) Plot these graphs in your POPULUS program by changing the initial abundance of the two species. N1(0) = 70 N2(0) = 700

14. The POPULUS modelling software: Lotka-Volterra Competition (Either species may win; co-existence is not possible.) Plot these graphs in your POPULUS program by changing the initial abundance of the two species. N1(0) = 200 N2(0) = 800

15. The POPULUS modelling software: Lotka-Volterra Competition (Either species may win; co-existence is not possible.) Plot these graphs in your POPULUS program by changing the initial abundance of the two species. N1(0) = 100 N2(0) = 400

16. The POPULUS modelling software: Lotka-Volterra Competition (Either species may win; co-existence is not possible.) Plot these graphs in your POPULUS program by changing the initial abundance of the two species. N1(0) = 50 N2(0) = 100

17. The POPULUS modelling software: Lotka-Volterra Competition (Either species may win; co-existence is not possible.) Plot these graphs in your POPULUS program by changing the initial abundance of the two species. N1(0) = 10 N2(0) = 200

18. The POPULUS modelling software: Lotka-Volterra Competition (Either species may win; co-existence is not possible.) Now let’s take a look at the N vs t plot for N1(0) = 10 and N2(0) = 200. This plot shows a very clear win for Species 2. We can see its growth curve reaching a resultant K2 of ~1000 while that of Species 1 hit zero (recall concept of x-intercept).

19. The POPULUS modelling software: Lotka-Volterra Competition (Either species may win; co-existence is not possible.) The N vs t plot for N1(0) = 50 and N2(0) = 100 however, has a different story. This plot predicts a win for Species 1 with Species 2 putting up a good fight in the beginning. Now, if you were a conservationist intent on preserving Species2, one option open to you would be to cull (trim as in ‘kill the excess’) the Species 1 population before they can outcompete Species2. Culling can be done at Time 10 as the model predicts (see dashed line).

20. The POPULUS modelling software: Lotka-Volterra Competition We end our discussion of the Lotka-Volterra Competition models where either species may win and co-existence is not possible. To continue, you must download the other models from the ESIII blog.