structures and feedback properties, expose them to perturbations, observe their recovery, and then—in the same way that one might “train” a chess-playing program—modify these systems until they become more tolerant of the disturbances to which they are exposed. Doyle and Carlson’s strategy offers a way to improve the structure of systems when the mathematics cannot be solved. Nevertheless, as the authors themselves point out, their approach does have a drawback: Systems that are engineered or have evolved to be tolerant of a particular set of disturbances often do so at the expense of their response to other classes of disturbances. Such systems are at once robust and fragile—an outcome that policymakers and researchers might wish to guard against as they seek better ways to manage risk and avert systemic failures.12


Amin, M. 2002. “Restructuring the Electric Enterprise: Simulating the Evolution of the Electric Power Industry with Intelligent Adaptive Agents.” In A. Faruqui and K. Eakin, eds., Electricity Pricing in Transition, 27-50. Boston: Kluwer Academic Publishers.

Asbeck, E., and Y. Y. Haimes. 1984. “The Partitioned Multiobjective Risk Method.” Large Scale Systems 6, no. 1: 13-38.

Bascompte, J., P. Jordano, and J. M. Olesen. 2006. “Asymmetric Coevolutionary Networks Facilitate Biodiversity Maintenance.” Science 312, no. 5772 (April 21): 431-3.

Baumbach, R., A. Knoll, and J. Sepkowski, Jr. 2002. “Anatomical and Ecological Constraints on Phanerzoic Animal Diversity in the Marine Realm.” Proceedings of the National Academy of Sciences 99: 6854-9.

Bernanke, B., M. Gertler, and S. Gilchrist. 1996. “The Financial Accelerator and the Flight to Quality.” Review of Economics and Statistics 78, no. 1 (February): 1-15.

Carlson, J. M., and J. Doyle. 2002. “Complexity and Robustness.” Proceedings of the National Academy of Sciences 99, suppl. 1: 2538-45.

Couzin, I. D., J. Krause, N. R. Franks, and S. A. Levin. 2005. “Effective Leadership and Decision-Making in Animal Groups on the Move.” Nature 433, no. 7025 (February 3): 513-6.

Keeling, M. J., M. E. J. Woolhouse, R. M. May, G. Davies, and B. T. Grenfell. 2003. “Modelling Vaccination Strategies Against Foot-and-Mouth Disease.” Nature 421, no. 6919 (January 9): 136-42.

Levin, S. 2000. Fragile Dominion. New York: Perseus.

Lux, T., and M. Marchesi. 1999. “Scaling and Criticality in a Stochastic Multi-Agent Model of a Financial Market.” Nature 397, no. 6719 (February 11): 498-500.

May, R. M. 2004. “Uses and Abuses of Mathematics in Biology.” Science 303, no. 5659 (February 6): 790-3.

National Research Council. 2005. Mathematics and 21st Century Biology. Washington, D.C.: The National Academies Press.

Zhou, T., J. M. Carlson, and J. Doyle. 2002. “Mutation, Specialization, and Hypersensitivity in Highly Optimized Tolerance.” Proceedings of the National Academy of Sciences 99: 2049-54.


See, for example, Zhou, Carlson, and Doyle (2002) and Carlson and Doyle (2002).

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