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.