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Dr. William M. Schaffer, Professor

Positions and Education
Professor, Ecology and Evolutionary Biology, University of Arizona, 1982-present
Associate Professor, Ecology and Evolutionary Biology, University of Arizona, 1977-82
Assistant Professor, Ecology and Evolutionary Biology, University of Arizona, 1975-77 Assistant Professor, University of Utah, 1972-75
Ph.D., Biology, Princeton University, 1972
M.S., Biology, Princeton University, 1970
B.S., Biology, Yale University, 1967
Honors and Awards
Guggenheim Fellowship, 1984-1985
Member Intl. Adv. Committee, Wagenengin Univ. 75 Anniver. Jubilee, 1992-1993

Research Interests
W. M. Schaffer's principal interests involve the application of nonlinear dynamics to biology at a variety of levels. At the biochemical level, he has collaborated with T. V. Bronnikova and others on the the peroxidase-oxidase reaction, which has become a model system for the study of complex dynamical behavior in a biochemical contexts. This work has resulted in the production of the first detailed model which is able to reproduce complicated bifurcation sequences observed in careful laboratory experiments. At the physiological level, he is interested in dynamical scenarios which might account for the natural history of diseases such as epilepsy in which the (overt manifestations) of the pathology are intermittent. This work is still preliminary. At the ecological level, he is concerned with complex population dynamics and with the ups and downs of human epidemics. His work on chaos in childhood diseases, in particular, sparked considerable interest in this topic. Presently, he is studying predator-prey dynamics in the presence of seasonality. This work has interesting mathematical content as well as implications for the control of insect pest species in agroecosystems.

Visit Bill Schaffer's website.

PubMed list of publications for Bill Schaffer
Selected Publications
  1. Schaffer, W. M., Bronnikova, T. V. and L. F. Olsen. 2001. Nonlinear dynamics of the peroxidase-oxidase reaction: II. Compatibility of an extended mechanistic model with previously reported model-data correspondences. J. Phys. Chem. In press.

  2. Schaffer, W. M., Pederson, B., Moore, B. K., Skarpaas, O., King, A. A. and T. V. Bronnikova. 2001. Subharmonic resonance and multi-annual oscillations in northern mammal cycles: A nonlinear dynamics perspective. Chaos, Solitons and Fractals. 12:251-264.

  3. King, A. A. and W. M. Schaffer. 2001. The geometry of a population cycle: A mechanistic model of snowshoe hare demography. Ecology 82: 814-830.

  4. King, A. A. and W. M. Schaffer. 1999. The rainbow bridge: Hamiltonian limits and harmonic resonance in predator-prey dynamics. J. Math. Biol. 39: 439-469.

  5. Bronnikova, T. V., Schaffer, W. M., Hauser, M. J. B. and L. F. Olsen. 1998. Routes to chaos in the peroxidase-oxidase reaction: II. The fat torus scenario. J. Phys. Chem. B. 102:632-640.

  6. King, A., Schaffer,W. M., Gordon,C., Treat,J., and M. Kot. 1996. Weakly dissipative predator-prey systems. Bull. Math. Biol. 58:835-860.

  7. Rosko, D. J., Schaffer, W. M. and J. C. Allen. 1994. Chaos and metapopulation persistence. Pp. 115-144. In, Yamaguti, M. (ed.) Towards the Harnessing of Chaos. Elsevier.

  8. Kendall, B., Schaffer, W. M., Olsen, L. F., Tidd, C. W. and B. L. Jorgensen. 1994. Using chaos to understand biological dynamics. Pp. 184-203. In, Grassman, J. and G. van Straten (eds.) Predictability and nonlinear modelling in natural sciences and Economics. Kluwer Academic Publ. Dordrecht.

  9. Schaffer, W. M. 1968b. Intraspecific combat and the evolution of the Caprini. Evolution. 22: 812-825.

  10. Schaffer, W. M. 1974a. The evolution of optimal reproductive strategies: The effects of age structure. Ecology. 55: 291-303.

  11. Schaffer, W. M., and M. V. Schaffer. 1979. The adaptive significance f variation in reproductive habit in Agavaceae. II: Pollinator foraging behavior and selection for increased reproductive effort. Ecology. 60: 976-987.

  12. Schaffer, W. M. 1985b. Can nonlinear dynamics help us infer mechanisms in ecology and epidemiology? IMA J. Math. Appl. Med. Biol. 2: 221-252.

  13. Schaffer, W. M. and M. Kot. 1985a. Nearly one dimensional dynamics in an epidemic. J. Theor. Biol. 112: 403-427.

  14. Schaffer, W. M. and M. Kot. 1986b. The coals that Newcastle forgot: Chaos in ecological systems. Trends in Ecology and Evolution. 1: 58-63.

  15. Olsen, L. F. and W. M. Schaffer. 1990. Chaos vs. noisy periodicity: Alternative hypotheses for childhood epidemics. Science. 249:499-504.

  16. Allen J. C., Schaffer, W. M. and D. Rosko. 1993. Chaos reduces species extinction by amplifying local population noise. Nature. 364: 229-232.

  17. Bronnikova, T. V., Fed'kina, V. R., Schaffer, W. M. and L. F. Olsen. 1995. Period-doubling bifurcations in a detailed model of the peroxidase-oxidase reaction. J. Phys. Chem. 99: 9309-9312.

  18. King, A., W. M. Schaffer, C. Gordon, J. Treat and M. Kot. 1996. Weakly dissipative predator-prey systems. Bull. Math. Biol. 58:835-860.

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