Question

For the system below identify the parameters as growth rates, carrying capacities, and measure of interactions between species. Determine if the species compete or cooperate..
x'=2x - (x^2)/16 + 2xy
y'=3y - (y^2)/20 - 7xy

(a) Growth rate constant:
(b) Interaction constant:

Answer 1

Answer:

• 2 and 3 are the the growth rates parameter for x and y respectively
• 16 and 20 are the carrying capacities for x and y respectively
• 2 and 7 measures the benefit to x and y of the interaction of the two species.

The species compete each other.

Step-by-step explanation:

When we have a population model for two species as we have here, the differential equations looks like this:

$\frac{dx}{dt}=a*x+b\frac{x^{2}}{N}+c*xy$

$\frac{dy}{dt}=d*x+e\frac{y^{2}}{M}+f*xy)$

Here:

a and d are the the growth rates parameter for x and y respectively

N and M are the carrying capacities for x and y respectively

c and f measures the benefit to x and y of the interaction of the two species.

So in our case we have:

$\frac{dx}{dt}=2*x+\frac{x^{2}}{16}+2*xy$

$\frac{dy}{dt}=3*x-\frac{x^{2}}{20}-7*xy$

Therefore:

• 2 and 3 are the the growth rates parameter for x and y respectively
• 16 and 20 are the carrying capacities for x and y respectively
• 2 and 7 measures the benefit to x and y of the interaction of the two species.

The term xy determine the if the species are cooperating of competing, so in this case have negative xy term in the second equation, it means the presence of either species decreases the rate of change of the other, so the species compete each other.

I hope it helps you!