Dynamics of Complex Systems: Ecological Theory

Readings

Lec #	Topics	Readings
Complexity, Stability, and the Struggle for Existence
1	Predator-prey Models	Lotka, A. Elements of Mathematical Biology. New York, NY: Dover Publications, Inc. 1925, Reprinted 1957. ISBN: 9780486603469. Volterra, V. “Fluctuations in the Abundance of a Species Considered Mathematically.” Nature 118 (1926): 558-560.
2	Supplemental Information Ecological Experiments	Gause, G. F. “The Struggle for Existence.” Baltimore, MD: Williams and Wilkins, 1934a. (Full text). ———. “Experimental Analysis of Vito Volterra’s Mathematical Theory of the Struggle for Existence.” Science 79 (1934b): 16-17.
3	Supplemental Information Niche Theory	Hutchinson, G. E. Concluding Remarks. Cold Spring Harbor Symp. Quan Biol 22 (1957): 415-427. ———. “Homage to Santa Rosalia, Or Why Are There So Many Kinds of Animals?” American Naturalist 93 (1959): 254-259.
4	Stability of Complex Systems	May, R. M. Stability and Complexity in Model Ecosystems . Princeton, NJ: Princeton University Press, 2001. ISBN: 9780691088617. Kerner, E. H. “Why Are There So Many Species?” Bull Math Biol 36 (1974): 477-488.
5	Supplemental Information Competitive Exclusion	Armstrong, R. A., and R. McGehee. “Competitive Exclusion.” American Naturalist 115 (1980): 151-170.
6	Chaotic Dynamics	Cushing, J. M., et al. “A Chaotic Attractor in Ecology: Theory and Experimental Data.” Chaos Solitons and Fractals 12 (2001): 219-234.
7	Network Theory	Krapivsky, P. L., and S. Redner. “Organization of Growing Random Networks.” Cond-mat/0011094, 2000. Strogatz, S. H. “Exploring Complex Networks.” Nature 410 (2001): 268-276.
Spatial Interactions
8	Population Dispersal	Skellam, J. G. “Random Dispersal in Theoretical Populations.” Biometrika 38 (1951): 196-216.
9	Patchiness	MacArthur, R. H., and E. R. Pianka. “On Optimal Use of a Patchy Environment.” American Naturalist 100 (1966): 603-609.
10	Pattern and Scale	Levin, S. A. “The Problem of Pattern and Scale in Ecology.” Ecology 73 (1992): 1943-1967.
11	Spatial Models and Interacting Particle Systems	Durrett, R. “Stochastic Spatial Models.” SIAM Review 41 (1994): 677-718.
12	Lattice-gas Models	Satulovsky, J. E., and T. Tome. “Stochastic Lattice Gas Model for a Predator-prey System.” Phys Rev E 49 (1994): 5073-5079.
13	Plankton Patchiness	Flierl, G., D. Grunbaum, S. Levin, and D. Olson. “From Individuals to Aggregations: The Interplay Between Behavior and Physics.” Journal of Theoretical Biology 196 (1999): 397-454.
14	Supplemental Information Scaling from Trees to Forests	Plotkin, J. B., et al. “Predicting Species Diversity in Tropical Forests.” Proc Natl Acad Sci 97 (2000): 10850-10854.
Co-evolution with the Environment
15	Evolution of Biodiversity	Signor, P. W., III. “Real and Apparent Trends in Species Richness Through Time.” In Phanerozoic Diversity Patterns. Edited by J. W. Valentine. Princeton, NJ: Princeton University Press, 1986, pp. 129-150. ISBN: 9780691083742. ———. “The Geologic History of Diversity.” Annu Rev Ecol Syst 21 (1990): 509-539.
16	Supplemental Information Adaptation and Diversification	Lenski, R. E., and M. Travisano. “Dynamics of Adapatation and Diversification: A 10,000-generation Experiment with Bacterial Populations.” Proc Natl Acad Sci 91 (1994): 6808-6814.
17	Artificial Life and Biological Complexity	Adami, C., C. Ofria, and T. C. Collier. “Evolution of Biological Complexity.” Proc Natl Acad Sci 97 (2000): 4463-4468.
18	Cycles	Kauffman, S. “Metabolic Stability and Epigenesis in Randomly Constructed Genetic Nets.” Journal of Theoretical Biology 22 (1969): 437-467.
Student Presentations
19	Reactivity, Stability, and Plankton (2 Presentations)
20	Theory of Productivity-Diversity Relationships
21	Evolution of Virulence in Host-Pathogen Systems
22	Renormalization Approach to Biological Systems
23	Directed Motion in Lotka-Volterra Models
24	Supplemental Information “Highly Optimized Tolerance” and Ecology
25	Theory of Vegetation Patterns