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Chaos is rare

New study reveals the evolution of oscillatory behavior in age-structured species

University of Chicago Press Journals

Classical ecological theory suggests that simple models can display a range of population behavior: from equilibrium to chaos. However, in real populations, stable and oscillatory behavior is common but chaotic dynamics are not. Although models may allow many different forms of dynamical behavior, evolution perhaps constrains the dynamics that occur. As selection on life-history traits (e.g. investment in fecundity vs. survival) is likely to have population dynamical consequences, models investigating the evolution of dynamics should be undertaken in a life-history framework.

In this study, to appear in the July 2005 issue of The American Naturalist, researchers used an adaptive dynamics approach to investigate the evolution of dynamics in a family of age-structured models, where fecundity was density-dependent and where there were trade-offs between survival and reproduction. They found that the evolutionarily stable population dynamics occurred in an area of parameter space outside, but close to, the bifurcation from stable to oscillatory dynamics.

The evolved dynamics were typically cyclic with a period of 2-3 times the maturation time of the model; this is common in nature, and such cycles are typically called "delayed feedback cycles." Furthermore, at the evolutionarily stable state (ESS), small changes in life-history traits could create marked increases in periodicity, making the dynamics responsive to changes in the system. The study reveals why chaos is rare in nature: it is not evolutionarily stable for the models we consider.


Sponsored by the American Society of Naturalists, The American Naturalist is a leading journal in the fields of ecology and evolutionary biology and animal behavior. For more information, please see our website:

J. V. Greenman, T. G. Benton, M. Boots, and A. R. White, "The evolution of oscillatory behavior in age-structured species" 166:1 July 2005.

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