Ah, ok, looked some stuff up. So r can be negative - in which case the only stable level of population is 0, while there is also an unstable equilibrium at K. Just putting that in would help clarify things. Of course r<0 has some very unrealistic implications if N(0)>K.

Question - is there some maximization of fitness going on here which determines {r,K} - the wording of the text sort of implies it?