# HW Exercise: Competition and the Lotka Volterra Equation

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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
Is there some level of competition between these 2 species? How do you know?
Would you classify these species as weak, moderate, or strong competitors?  Think about population density.
Which species appears to be the stronger competitor? Why?
What would the phase-plane diagram look like for this situation?
What outcome would you predict if we started with 100 of each species?
How would we “test” if there is really competition between these 2 species?
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’.  Save graphs that will help answer the following questions, and insert them into the word file with your answers where appropriate.
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?
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?
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?
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?
What would happen if you used the same initial population sizes but changed the following data:
Green sunfish: K1 = 600, r1=0.10, a12=1.45
Bluegill: K2=700, r2=0.30, a21=0.95

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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.
What would happen if we took the input parameters from question #11 and changed the initial population sizes to N1=10 and N2=100?
Are these projections realistic? Why or why not? (Hint: Think about the assumptions of the model).
Submit your answers to these questions before class on Thursday, October 24

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