WLF 448: Fish & Wildlife Population Ecology
Lab Notes 11, Fall 2004

In-class Exercise #11: Competition

Scenario #1: Green sunfish and bluegill competition

You have both green sunfish (Lepomis cyanellus) and bluegill (L. macrochirus) available for stocking in a 10 ha impoundment. These two species compete to some degree; pertinent population data are:

Green sunfish Bluegill
K1 = 600 K2 = 600
r1 = 0.10 r2 = 0.10
a12 = 1.50 a21 = 0.90

  1. Is there some level of competition between these 2 species? How do you know?

  2. Would you classify these species as weak, moderate, or strong competitors?  Think about population density.

  3. Which species appears to be the stronger competitor? Why?

  4. What would the phase-plane diagram look like for this situation?

  5. What outcome would you predict if we started with 100 of each species?

  6. How would we "test" if there is really competition between these 2 species? Hint: Think about Emlen's definition of competition.

  7. Use program POPULUS to simulate the population growth of 100 green sunfish growing alone (i.e., without bluegills present). Was the projected growth what you expected (i.e, logistic growth)? Did the population reach carrying capacity? If so, what was it and how many years did it take to reach K?   To answer these questions follow the steps below:    1.  Open POPULUS which you should have on your zip or H: drive from Lab #10 on limited population growth.  2.  Go to the Model drop down menu, Multi-species dynamics, and Lotka-Volterra Competition.  3.  An input window should appear.  Input the data for species #1 and #2 (i.e., K1, K2, N1, N2, r1, r2, etc.)  Note: In POPULUS a21 = α and a12 = β.  4.  Choose N vs. t for plot type.  5.  Choose 'Run until steady' for Termination conditions.  6. Click on View to see graph and answer the questions.

  8. Use program POPULUS to simulate the population growth of 100 bluegill growing alone (i.e., without sunfish present). Was the projected growth what you expected (i.e, logistic growth)? Did the population reach carrying capacity? If so, what was it and how many years did it take to reach K?  Follow the same steps described above in question #7.

  9. If you initially stocked 100 sunfish and 100 bluegill, what is the projected population size of each species in 5 years? 10 years? 40 years? Was your predicted outcome (question #5) correct?  To answer these questions follow steps 1-4 in question #7, but for step 5 under Termination conditions choose 5 under 'Run until time'.  And then click on View to see graph.  To determine the population size of each species after 5 years, click on File and then 'Save output to text file'.  Save the file to your zip or H: drive.  Your TA will explain the output file and how to find the population size value for each species.  Next change the 'Run until time' to 10 and repeat the same steps for saving your output file.  Do the same for 40 years also.  Then answer the above questions.

  10. Compare the population projections of each species when grown alone and together. How did "competition" affect the growth of each species? Was your guess about which species was the stronger competitor correct?

  11. What would happen if you used the same initial population sizes but changed the following data:

    Note:  Be sure to look at both plot types (i.e., N vs t and N2 vs N1).  And choose 'Run until steady' for your Termination conditions.  You can also output the population sizes over time using the instructions above regarding saving output to a text file.

  12. What would happen if we took the input parameters from question #11 and changed the initial population sizes to N1=10 and N2=100?

  13. Are these projections realistic? Why or why not? (Hint: Think about the assumptions of the model).

Note:  You can save *.jpg files of your output graphs from POPULUS.  In the 'Output' window, click on 'File' and then select 'Save output graph to file'.  Be sure to save your graph to your zip or H: drive. 

Scenario #2: Competition between 2 species of yeast (Gause 1934)

Gause (1934) used these data to verify the mathematical theory behind the Lotka-Volterra competition model.  Two species of yeast: Saccharomyces cerevisiae and Schizosaccharomyces kephir are both pure lines of yeast.  In the MS Excel file called Gause_yeast.xls (file:///K:/WLF/448/2004/Lab2004/Competition/Gause_yeast.xls) are the data of population growth for each species when grown alone over time.  Population growth for yeast is measured by volume. So each line in the file at a specific time t represents the volume of yeast. 

Plot these data as N vs t on separate graphs using MS Excel and determine the value for K1 and K2.  When creating your graph use the 'XY scatter plot with data points using a smoothed line'.  This will make it easier for you to see the population trend and determine carrying capacity.  Your TA will show you how this can be done.  You will need these values of K1 and K2 for your problem set.

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Revised: 09 November 2004