Consider the equations describing the interactions of robins $r$ and worms $w$, $$\frac{dw}{dt} = w-wr,\qquad\mbox{and}\qquad \frac{dr}{dt} = -r+rw.$$ (a) What are the (non-zero) nullclines for this system?
$w =$
$r =$

(b) Your nullclines divide the phase plane into four regions. Give a sample point in each region, and indicate for that point whether each of the populations is increasing or decreasing (by entering the word increasing or decreasing appropriate blank):

(i) $(w, r) =$ (, ) is in one region, where
the population of worms, $w$ is
and the population of robins, $r$ is .

(ii) $(w, r) =$ (, ) is in a second region, where
the population of worms, $w$ is
and the population of robins, $r$ is .

(iii) $(w, r) =$ (, ) is in a third region, where
the population of worms, $w$ is
and the population of robins, $r$ is .

(iv) $(w, r) =$ (, ) is in the fourth region, where
the population of worms, $w$ is
and the population of robins, $r$ is .

Notice what your conclusions about these four regions say about how the populations change with time.