Section 5 - Interpretation

Do these equilibria make sense?

When there's no sort of mutualism in effect (b and d are both zero), it's pretty easy to tell what's going on. The two species grow independently from each other: species x doesn't care how big (or small) species y gets because it won't affect the rate at which species x grows.

There are two relevant parameters: a (birth) and e (death). Obviously, the larger a is, the bigger the population will be able to get before death brings it to a halt at the equilibrium, and the larger e gets, the faster death will be able to decimate the population. These two competing factors are very straight-forwardly reflected in the formulas for the equilibria: a/e and c/f.

Unfortunately, when mutualism is in effect (b and d are both greater than or equal to zero) the formulas for the equilibria are a little less straight forward. However, we are able to see from the formulas that when b and d are equal to zero the formulas simplify to: a/e and c/f which are the nonmutualistic equilibria that we found in section 2.

Also, as the mutualism parameters (b and d) increase, the x and y equilibria increase above their nonmutualistic levels, which is what we would expect, because the more the species benefit from the other's existance, the higher their populations are able to rise.

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