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# Eat or be eaten

## Question

We have three separate environments where X and Y are unique species to each environment.  Decide and justify what type of relationship the two respective species have in each environment.

Environment 1

x' = 2x - 3xy

y' = -3y + 4xy

Environment 2

x' = xy - 2x

y' = y - 2x

Environment 3

x' = y

y' = 1/x

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sry i can't understand in this ques

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Environment 3

x' = y

y' = 1/x = 1/y

only have y in environment 3?

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We have three separate environments where X and Y are unique species to each environment.  Decide and justify what type of relationship the two respective species have in each environment.

Environment 1

x' = 2x - 3xy

y' = -3y + 4xy

Environment 2

x' = xy - 2x

y' = y - 2x

Environment 3

x' = y

y' = 1/x

So in environment one

The rate of change of x is determined by both 2x and the interaction of -3xy

What does this mean? Well it means that the species has a natural growth rate (i.e. the 2x represents the mating and therefore growth of the population)  However the interaction of -3xy shows that as there are more y's, the overall growth of the species begins to go down.  Hence this would imply that either the species y in this case is living off of the animal x or that y out competes x for the same food source.

Looking at y's rate of change in this environment should clarify which of these two concepts are occurring.

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