William Schaffer

Professor Emeritus

Positions and Education: 

  • Professor Emeritus, Ecology and Evolutionary Biology, University of Arizona, 2019-present 
  • Professor, Ecology and Evolutionary Biology, University of Arizona, 1982-2019 
  • Visiting Professor. Odense University, Odense, DK. 1994 
  • President. Dynamical Systems, Inc. 1986-94 
  • 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. Magna cum Laude; Phi Beta Kappa; High Honors in Biology; Silliman Cup for Scholarship. 

Honors and Awards: 

  • 1967-1970. NSF Pre-doctoral Fellow; Princeton National Fellow. 
  • 1975. Elected Sigma Xi
  • Guggenheim Fellowship, 1984-1985. 
  • Member Intl. Adv. Committee, Wageningen Univ. 75 Anniversary Jubilee, 1992-1993. 
  • Invited contributor to various anthologies (commentaries, original papers, reprinted publications) and symposia. Most recently, 
  1. Curtin, C. and Allen, T. (eds.). 2017. Complex Ecology: Foundational Perspectives on a Dynamic View of Ecology and Conservation. Cambridge University Press.  
  2. Invited presentation at M. L. Rosenzweig Festschrift Symposium, 7 March, 2017. 

Editorial Work: 

  • 2001. Guest Editor (invited) of Special Issue on "Chaos in Ecology," Chaos, Solitons and Fractals
  • 2002. Organizer. Ecological Society of America Workshop on Chaos in Ecology. Tucson, AZ.  

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.

Selected Publications: 

  1. Olsen, L. F. and W. M. Schaffer. 1990. Chaos vs. noisy periodicity: Alternative hypotheses for childhood epidemics. Science. 249:499-504.
  2. Allen J. C., Schaffer, W. M. and D. Rosko. 1993. Chaos reduces species extinction by amplifying local population noise. Nature. 364: 229-232.
  3. 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.
  4. King, A. A. and W. M. Schaffer. 1999. The rainbow bridge: Hamiltonian limits and resonance in predator-prey dynamics. J. Math. Biol. 39: 439-469.
  5. Schaffer, W. M. and T. V. Bronnikova. 2012. Peroxidase-ROS interactions. Nonlinear Dynamcs. 68: 413-430