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

question 25

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.
For scenarios 1 and 2, sketch the outcome of the competitive interaction using N₁ and N₂ isoclines. Put species 1 on the x-axis and species 2 on the y-axis. Label the points at which your isoclines intersect the axes as K₁, K₂, K₁/? and K₂/?. Using your calculations from the questions above, indicate the stable equilibrium point with a star. The units on your graphs should range from 0 to 200, in increments of 40.

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Definitions:

Entire Burden

The total impact or effect of something, often related to the full cost or responsibility borne by an entity.

After-Tax Equilibrium

The balance or condition of a market after the effects of taxes have been considered, reflecting the impact on prices and quantities of goods and services.

Supply Curve

A graph showing the relationship between the price of a good and the quantity of that good supplied.

Effective Price

The final price after accounting for rebates, discounts, or other financial adjustments.