3 species Predator Prey Model: dP1/dt = P1( a - bP1) - cP1P2, dP2/dt = dP1P2 - ...

Can anyone help explain the relationship of the followingmodel to me?

I need to understand it so I can manipulate it in a computerprogramme, but I'm having difficulty as I haven't done any sort of math oralgebra or differential equations in over 10 years!

An equation for a 3 species predator prey model:

dP1/dt = P1( a - bP1) - cP1P2

dP2/dt = dP1P2 - eP2 - fP2P3

dP3/dt = gP2P3 - hP3

- P1, P2, P3 represent the number of animals in the threespecies
-a is the birth rate of the first species
-b is the natural death rate of the first species
-c is the death rate of the first species due to predationby the second
-d is the birth rate of the second species due to thenumbers of the first
-e is the natural death rate of the second species
-f is the death rate of the second species due to predationby the third
-g is the birth rate of the third species due to numbers ofthe second
-h is the natural death rate of the third species

I do not have values for birth rates or death rates. I justneed the relationship of this equation explained to me. death and birth ratesright now can be off the top of the head.

Ive been at this all day. my head is jumbled


3 eats 2 and 2 eats 1

so in theory, if there is no first species the 2nd and 3rddies, if there is no 3rd species 2nd species increases, if there is no 2ndspecies the 1st increases and the 3rd dies.

I have no idea on numerical values to try for my birth ratesand death rates

lovely_laura67 said:

dP1/dt = P1( a - bP1) - cP1P2

Click to expand...

The first part of this is a little cloudy. If it were written \(\displaystyle aP_{1} - bP_{1}^{2}\), it may be more clear. That "a" sitting there by itself isn't very helpful. These are separate but simultaneous proportionalities. The change in the population depends on three factors.

aP1 -- Increase due to birth Related directly to the population. This is a little dubious, as a more complete model might examine females who can bear offspring. That's a lot less than then entire population. Maybe the "a" takes care of that. Anyway...

-bP1^2 is a lot harder to explain. This may be an overcrowding idea. As the population grows, more deaths occur, but this population is particularly sensitive to death as the population grows. That's what the ^2 does. It just makes the population influence death MUCH faster than it would if it were just -bP1

-cP1P2 Pretty clear, here. If either population shrinks a lot, this just stops happening unless the other population still manages to grow, even if they can't find food - which would be pretty unlikely.

You can talk your way through the other pieces.