Understanding the Lotka Volterra Equations: Explained in Simple Terms

[Tom Segal]

Homework Statement

Hello everyone.
I'm trying to figure out the meaning of the multiplier N in the following equations, called the Lotka Volterra equations. They describe the growth rate of predators (P) which grow by eating prey and die from ageing, and the growth rate of their prey (N), which grows "magically" (doesn't need food) and also dies from ageing.

Homework Equations

dP/dt = -qP +caPN
dN/dt = rN -aPN

The Attempt at a Solution

a is the amount of prey killed by each predator per unit of time, and multiplied by P we get the total amount of prey killed by all the predators per unit of time. Why then do we multiply by N? (In other words why in the second equation we have -aPN instead of just -aP?)

Same about the second expression in the first equation.. c is the amount of prey (food) that is required in order to create a predator, so caP is the total amount of predators that are created per unit of time. Why then multiply by N?

After I finished writing this post I figured I should use the search engine first, so I did, and I found many topics about this subject, but none dealt with this specific problem, so my question remains.


Thanks!
Great forum by the way, I've been stalking it for a while.

 

[Dick]

I think, and I'm not an expert, that the factors of PN account for the probability of predator meeting prey. The number of encounters should depend on both P and N.