#
Stochastic and deterministic spatial modeling in population dynamics

May 4 to May 8, 2009
at the

American Institute of Mathematics,
San Jose, California

organized by

Zhilan Feng and Priscilla Greenwood

## Original Announcement

This workshop has the objective of generating new ideas about how to model
spatial problems arising in epidemiology, ecology, evolution, and other areas
involving population dynamics. There will be people who are expert in
stochastic modeling, others in deterministic modeling, and a few people
already combining these approaches. Some specific techniques that will be
examined include patch models, or metapopulations, interacting particle
systems and their diffusion limits, graphical models, agent based models,
branching diffusions, "small world" models.
Some typical problems which require explicitly spatial modeling are: How fast
and in what patterns does an epidemic spread? How does the spatial form of
local communities effect the coexistence of species which may be competing for
resources, or involved in other kinds of ecological interactions?

An hypothesis that underlies much spatial modeling is that individuals
interact only with their neighbors, or occasionally over a distance, but not
uniformly with all other individuals. This hypothesis allows us to model
evolution of interacting populations living in spatially explicit habitats or
moving. In several examples, critical values are raised above their values for
analogous uniformly mixed populations. Whereas stochasticity may not change
critical values, focus on probability distributions broadens our decision
space to include the variety of possible behaviors of a population system and
the likelihoods associated with these possibilities.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.