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12.517 G(2) 309 Spring 2001
The theme for Spring 2001 will be Ecological Theory.
Ecological theory attempts to explain the interaction of individual organisms and their resulting collective dynamics mathematically and, more recently, computationally. The latter developments offer the appealing possibility of creating artificial ecologies to motivate theory and test its predictions.
In this class we will critically review both classical works and recent literature. Emphasis will be on providing a theoretical and phenomenological foundation for the study of computational models. We will meet twice weekly for roundtable discussions. No background in ecology will be presumed; however mathematics at the level of 18.03 is essential.
Revised schedule: Mondays and Wednesdays from 4:00-5:30 pm in Rm. 54-313.
Contacts: Prof. Daniel Rothman and Joshua Weitz
Syllabus:
- I. Complexity, stability, and the struggle for existence
-
Predator-prey models.
(Lotka, 1925;
Volterra, 1926)
-
Ecological experiments.
(Gause, 1934a;
Gause, 1934b)
-
Niche theory.
(Hutchinson, 1957;
Hutchinson, 1959)
-
Stability of complex systems.
(May, 1973;
Kerner, 1974)
-
Competitive exclusion.
(Armstrong and McGehee, 1980)
-
Chaotic dynamics.
(Cushing et al., 2001)
-
Network theory.
(Krapivsky and Redner, 2000;
Strogatz, 2001)
- II. Spatial interactions
-
Population dispersal.
(Skellam, 1951)
-
Patchiness.
(MacArthur and Pianka, 1966)
-
Pattern and scale.
(Levin, 1992)
-
Spatial models and interacting particle systems.
(Durrett, 1994)
-
Lattice-gas models.
(Satulovsky and Tome, 1994)
-
Plankton patchiness.
(Flierl et al., 1999)
-
Scaling from trees to forests.
(Plotkin et al., 2000)
- III. Co-evolution with the environment
-
Evolution of biodiversity.
(Signor, 1985;
Signor, 1990)
-
Adaptation and diversification.
(Lenski and Travisano, 1994)
-
Artificial life and biological complexity.
(Adami et al., 2000)
-
Cycles.
(Kauffman, 1969)
- IV. Student presentations
-
Reactivity, stability, and plankton (2 presentations).
-
Theory of productivity - diversity relationships.
-
Evolution of virulence in host - pathogen systems.
-
Renormalization approach to biological systems.
-
Directed motion in Lotka - Volterra models.
-
``Highly Optimized Tolerance'' and ecology.
-
Theory of vegetation patterns.