# 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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