Universality classes of foraging with resource renewal

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.