SwarmFest talk: Doug Donalson

[Marcus G. Daniels]

[http://www.swarm.org/community-swarmfest-program.html#Donalson]

Modeling in Continuous Space and Time: When Being Discrete just isn't enough 

Doug Donalson <address@hidden>
Center for Environmental Analysis, Department of Biology
Cal State LA

Most individual based models are constructed using a discrete
time/discrete space engine.  While, for many applications, this causes
no model artifacts, there can be effects introduced by the fine grain
quantization of time and space. In discrete time model, the artifacts
can occur two ways. The first is from the assumption that the average
behavior during a time interval is equivalent to the starting value of
the state variables. The second can occur when the different
mechanisms that cause state changes within the time interval are not
executed randomly. One potential discrete space artifact I call
implicit competition.  An individual that colonizes a cell, no matter
its size, immediately excludes all other individuals from the entire
area of the cell.

An alternate method for handling space and time in individual based
models is the use of continuous time and space. A continuous time
engine is also called an event driven schedule and works from the
assumption that no two events (or state changes) ever occur
simultaneously. Because of this, time can be advanced state change by
state change. In a continuous space model, an individual can occupy
any coordinate within the spatial arena, as opposed to being
constrained to the center of a cell. I give an overview of
implementations of a continuous time/continuous space model vs. a
discrete time/discrete space model.  I then discuss some of the
advantages and disadvantages of each type of model.


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