Lecturer: Prof. Sidney Redner
Affiliation: Santa Fe Institute
Abstract:
What is the fate of a forager that depletes its
environment as it wanders?
We investigate this question within the
framework of the "starving" random walk
model. Here, a random walk can travel S steps
without eating before starving. Each lattice
site initially contains food and a walker
consumes the food whenever it is found.
When the walker hits an empty site, the time
until the walker starves decreases by 1. We
determine the lifetime of the walker,
analytically in one dimension and numerically
in higher dimensions.
In two dimensions, long-lived walks explore a
highly ramified region so they always remain
close to sources of food.
We also determine the impact of resource
renewal on forager lifetimes. We find three
universal regimes 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.
Finally, we investigate the role of forager
reproduction in a more general model in which
hungry foragers do not reproduce and die at
some rate, while full foragers do not die but
reproduce. Foragers convert from hungry to
full depending on whether or not they have
eaten recently. We outline the rich
phenomenology of this ecologically inspired
model.