bunnyLet’s suppose we have bunch of cute fluffy rabbits and a bunch of tough sheep hanging out in an enclosed field. If there were only one of these species, their population would grow logistically. We also know that rabbits, well, reproduce much faster than the sheep and we know that sheep eat way more than our fluffy bunnies.

So, the question is: if these two species are hanging out together and are fighting for the same tasty grass, who wins??

Our equations that model rabbit and sheep behavior:
Rabbits: x’=3x-x^2-2xy
Sheep: y’=2y-y^2-xy

These are basically modified logistic equations and a bit of bunny or sheep loss to competition. Have you ever seen a rabbit go hungry? It’s not a pretty sight.

We can do a whole lot of cool analysis to this system of equations. My other question–do you want to read about it? Maybe not.

In the end, we learn that there are two stable situations: one where the bunnies win out and one where the sheep win out. And who wins all depends on how many of each you start with. Pretty nifty.

And all of this talk boils down to the Principle of Competitive Exclusion from good ol’ biology. That is, two species competing for the same limited resources can’t coexist. So, our bunnies will probably slip under the wire fence and head for greener pastures.