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

question 23

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.
Determine the outcomes of competition between the two species under scenario 1.Answer the following questions:
a) Do species 1 and species 2 coexist?
b) Does one species drive the other to extinction? If so, which goes extinct?

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Definitions:

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A culinary practice of preserving oranges in a brine or vinegar solution, often with spices, to extend their shelf life and enhance flavor.