new SwarmFest talk

[Marcus G. Daniels]

An Agent-Based Model of Fish Behavior: Part III
Jim Anderson & Nick Beer
Columbia Basin Research, University of Washington

This is the third round of modeling the migration of juvenile salmon
through the Columbia River with agent-based models.  In the first
round, reported at SwarmFest 2000¹, we successfully modeled the
hydrological and topographical features of Little Goose Reservoir in
the Snake River.  Using a simple algorithm, where fish swam with a
downstream velocity plus a random velocity dependent on habitat
preference, we were able to fit observations of fish travel time and
survival through the reservoir.  However, when we altered hydrological
conditions to represent the reservoir drawdown proposed as a salmon
recovery action, the model failed spectacularly.  The little smolts
were speed demons swimming at many times the water velocity.  In the
second round, presented at the Ecological Society Annual meeting in
August 2000, we made the fish a little smarter with their movements
depending on a memory factor that altered their motivations to swim,
feed and avoid predators.  The model produced little black dots that
moved around the computer screen eating little pink dots while
avoiding big red ones.  It had some elements representing how
biologists think fish think (!)  but it lacked a coherent structure
and set of unifying principles.  As a consequence, it was difficult to
relate the dots to observations of fish in nature or controlled
experiments.

Hoping the third time's a charm, we started from scratch, defining
fish interactions in a game-theoretic approach where the choice of
behavior is defined by the expected utility of the behavior, which in
turn is defined by the intrinsic utility and the probability of
obtaining the it.  All pretty standard game-theory stuff so far: which
behavior is selected at any moment depends on its utility.  It became
interesting though, when we devised a formal structure of agents and
associated behaviors.  The agents a fish encounters are prey,
predator, boundary and habitat.  Behaviors are defined in terms of
swimming speed and direction.  For a fish/agent interaction we define
two classes of behavior: tactical when the fish is in contact with an
agent and strategic when it is not.  Tactical behaviors optimize the
encounter outcome and strategic behaviors alter the chance of future
encounters.  Tactical probabilities are defined in terms of fish
distances to the agents, while strategic probabilities are defined in
terms of the history of tactical probabilities as weighted by fish
memory coefficients.  Utilities have one part dependent on the agent
and another part dependent on the fish.  Laboratory experiments on
predator-prey interactions and patch selection, interpreted within
this structure, provide a plethora of data with which to calibrate our
model.  This approach simplifies how we characterize behavior and it
is our hope that it is extensible to larger more complex systems.

¹ http://www.cbr.washington.edu/papers/swarmfest.html


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