  We determine the impact of resource renewal on the lifetime of a forager that
depletes its environment and starves if it wanders too long without eating. In
the framework of the minimal starving random walk model with resource renewal,
there are three universal classes of behavior as a function of the renewal
time. For sufficiently rapid renewal, foragers are immortal, while foragers
have a finite lifetime otherwise. In one dimension, there is a third regime,
for sufficiently slow renewal, in which the lifetime of the forager is
independent of the renewal time. We outline an enumeration method to determine
the mean lifetime of the forager in the mortal regime.
