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

question 68

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 how each species affects the other under Scenario 2. Answer the following questions:
a) Each individual of species 2 has the same effect on species 1 as how many individuals of species 1?
b) Each individual of species 1 has the same effect on species 2 as how many individuals of species 2?

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Definitions:

Testosterone

is a steroid hormone primarily produced in the testes of males and the ovaries of females, responsible for the development of male secondary sexual characteristics.

Y Chromosome

One of the two chromosomes that determine sex; in males, one member of the 23rd pair of chromosomes is Y.

Male or Female Genitalia

The sexual and reproductive organs specific to males (penis, scrotum, etc.) and females (vagina, ovaries, etc.).

Y Chromosome

A sex chromosome found in mammals, including humans, that is typically associated with male characteristics and is paired with an X chromosome in males.