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VIGRE seminar, summer 2001: Ecological Modeling
- Instructors
- Jay Walton, Paulo Lima-Filho
- Students enrolled
- Scott Pickens (undergraduate mathematics student); Dylan
Copeland, Robert Main, John Ryan, Yanqiu Wang (graduate mathematics
students); Meagan Clement — Washington and Lee, William
Koppelman — University of Wyoming, Brandon Lindley —
University of Central Arkansas REU students
- Description
- The subject was ecological modeling; the mathematics utilized
was very diverse including pointset topology, differential
geometry, continuum mechanics, dynamical systems and partial
differential equations. The overarching problem was predicting the
impact upon an ecological environment of changes in the habitat
size and structure, for example adding roads to a national park for
the purpose of gaining access to natural resources. Ideas from
topology and differential geometry were used to describe the
topology and topography of habitats from the perspective of
individual species. The interactions of species living within the
habitat were modeled using ideas from continuum mechanics developed
for that purpose by Walton and C. Turner for Turner's Ph.D.
dissertation. The problems considered in this course are part of
the activities supported by an NSF Biocomplexity Incubator grant
(co-PI's: T. Lacher (Wildlife Ecology), Lima-Filho, Pilant,
Stiller, and Walton). Previous models in this area frequently do
not take into account the varied topology and topography and, in
addition, make use of ODE's and spatially averaged competition
parameters. These tend to predict one species completely wiping out
the other. However, the PDE models that incorporate spatial effects
give a much richer range of possible outcomes.
- Impact
- The modeling approaches that the students investigated in the
VIGRE course are the subject of an upcoming science news report to
be aired on the National Public Radio program Earth
and Sky sometime in the future. In addition, one of the (then)
first year graduate students who took the VIGRE course (supported
as a VIGRE Fellow), Dylan Copeland, is now working on a problem
coming from the class. The work is joint with B. Popov, J. Walton
and M. Ziane, and Dylan is being supported on the NSF Biocomplexity
grant mentioned above. This work will certainly lead to the first
of many papers in this problem area.
One of the REU students, Bill Koppelman, has applied to the Texas
A&M graduate math program (as well as others) to study
mathematics applied to ecology. The lone Texas A&M
undergraduate student in the course, Scott Pickens, was a sophomore
at the time of the course. He now intends to pursue a mathematical
career, and enthusiastically volunteered to be a member of our
first ever COMAP Interdisciplinary Contest in Modeling team that
competed in this year's competition in late January when he heard
that the topic was wildlife and resource management. The contest
problem turned out to involve species survival in a fragmented
habitat to which Scott applied many of the ideas from last summer's
VIGRE course.