exercises lotka volterra competition 1a 1 pt in lecture we introduced to you the concept of zero

1a. A zero-growth isocline in the Lotka-Volterra competition model is a line on a graph that rep

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Exercises: Lotka-Volterra Competition 1a. [1 pt] In the lecture, we were introduced to the concept of zero-growth isoclines. Use your own words to explain what a zero-growth isocline is, as used in the Lotka-Volterra competition model. 1b. [3 pts] The figure below is an N2 vs. N1 phase plot for a Lotka-Volterra Competition model. The two lines are the zero-growth isoclines for Species 1 (dash line) and Species 2 (solid line). Determine if the abundance of each species will increase, decrease, or stay the same at each of the six points on the phase plot (represented as open circles, from A to F). 1c. [2 pts] Open Populus, click "Model," and choose "Lotka-Volterra Competition" from the "Multi-Species Dynamics" menu. Using the default parameters, algebraically derive equations for the isoclines of Species 1 and Species 2. If you cannot remember the Lotka-Volterra Competition equations, they are here for your reference: 2a. [1 pt] Keeping the default parameters, click N2 vs. N1 plot. You should see the isoclines of the two species as well as a green curve with a closed and an open circle on each end. The green curve is the time trajectory of the two populations. The open circle represents the population sizes at time zero, and the closed circle represents the population sizes at the end of the run time. From this phase plot, what is the outcome of the competition between the two species? (You may need to click "Run until steady state" if the abundances have not yet reached an equilibrium point.) 2b. [2 pts] While keeping all the other parameters at their defaults, click the N vs. t plot again. Can you change K1 so that Species 1 outcompetes Species 2 (i.e., so that Species 1 has a higher steady-state abundance than Species 2)? If so, what value of K1 achieves this? If you return K1 to its original default value (K1 = 500), can you achieve the same effect by changing only Î±? If so, what value of Î± did you use?

          Exercises:
Lotka-Volterra Competition
1a. [1 pt] In the lecture, we were introduced to the concept of zero-growth isoclines. Use your own words to explain what a zero-growth isocline is, as used in the Lotka-Volterra competition model.
1b. [3 pts] The figure below is an N2 vs. N1 phase plot for a Lotka-Volterra Competition model. The two lines are the zero-growth isoclines for Species 1 (dash line) and Species 2 (solid line). Determine if the abundance of each species will increase, decrease, or stay the same at each of the six points on the phase plot (represented as open circles, from A to F).
1c. [2 pts] Open Populus, click "Model," and choose "Lotka-Volterra Competition" from the "Multi-Species Dynamics" menu. Using the default parameters, algebraically derive equations for the isoclines of Species 1 and Species 2. If you cannot remember the Lotka-Volterra Competition equations, they are here for your reference:
2a. [1 pt] Keeping the default parameters, click N2 vs. N1 plot. You should see the isoclines of the two species as well as a green curve with a closed and an open circle on each end. The green curve is the time trajectory of the two populations. The open circle represents the population sizes at time zero, and the closed circle represents the population sizes at the end of the run time. From this phase plot, what is the outcome of the competition between the two species? (You may need to click "Run until steady state" if the abundances have not yet reached an equilibrium point.)
2b. [2 pts] While keeping all the other parameters at their defaults, click the N vs. t plot again. Can you change K1 so that Species 1 outcompetes Species 2 (i.e., so that Species 1 has a higher steady-state abundance than Species 2)? If so, what value of K1 achieves this? If you return K1 to its original default value (K1 = 500), can you achieve the same effect by changing only Î±? If so, what value of Î± did you use?

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