ABSTRACT: Understanding and predicting stochastic spatial models
using local structure theory
by David Hiebeler
Center for Applied Math, Cornell University
Presented at the annual meeting of the
Ecological Society of America, August 12, 1996 in Providence, RI.
Many of the so-called spatial models in ecology (e.g. metapopulation
or patch-occupancy models) actually involve little or no detailed
spatial structure, and perhaps may be more accurately referred to as
pseudo-spatial models. However, models which incorporate detailed
spatial structure (such as cellular automata models, e.g. Caswell and
Etter 1993) are notoriously hard to analyze except via simulation; at
best one can usually resort to a mean field theory approximation,
which incorporates the very minimum of spatial structure by assuming
that no spatial correlations develop over time in the lattice. I will
discuss a generalization of mean field theory, called local structure
theory, and apply it to a stochastic cellular automaton patch-based
model. This generalization allows one to incoporate more of the
detailed spatial structure of the model into what is still essentially
a mean field approximation, by assuming that only local (short-range)
correlations develop over time. By using local structure theory we
obtain dramatically more accurate predictions of state frequencies
(e.g. patch occupancy probabilities) in the original detailed spatial
model, even where there is significant clustering in the spatial
system, i.e. where the mean field theory performs poorly.
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Last modified: Wed May 19 20:38:33 1999