Use Inequalities Generated by the Lotka-Volterra Competition Model to Determine $\alpha$

question 27

Essay

Use inequalities generated by the Lotka-Volterra competition model to determine whether two species of Paramecium (P. caudatum is "species 1" and P. aurelia is "species 2") will coexist or drive each other to extinction in the three scenarios below. In these examples, N₁ = N₂, and K₁ = K₂ = 50.
Scenario 1: Determine the outcome of the competitive interaction between P. caudatum and P. aurelia if $\alpha$ = 0.3, and $\beta$ = 0.6.
Scenario 2: Determine the outcome of the competitive interaction between P. caudatum and P. aurelia if $\alpha$ = 1.5, and $\beta$ = 0.6.
Based on conditions in scenario 1, answer the following questions:
a) What does K₁/K₂ equal?
b) Is $\alpha$ greater than (>) or less than (<) K₁/K₂?
c) Is $\beta$ > or < K₁/K₂?

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