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Stabilization of Chaotic and Non-Permanent Food Web Dynamics

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  • Richard J. Williams
  • Neo D. Martinez

Abstract

A long history of dynamical analyses of food-web networks has led to important insights into the effects of complexity, omnivory and interaction strength on food-web stability. Some recent insights are based on nonlinear bioenergetic consumer-resource models that display chaotic behavior in three species food chains which can be stabilized by omnivory and weak interaction of a fourth species. By altering these models to slightly relax predation on low-density prey (changing from type II to weak type III functional response), we drastically alter the dynamics of systems containing up to ten species. Our model stabilizes chaotic dynamics in three species systems and reduces or eliminates extinctions and non-persistent chaos in ten species systems. This increased stability allows analysis of systems with greater biodiversity than in earlier work and suggests that dynamic stability is not as severe a constraint on the structure of large food webs as previously thought. The sensitivity of dynamical models to small changes in the predator- prey functional response suggests that this response is a crucial aspect of species interactions that must be more precisely addressed in empirical studies.

Suggested Citation

  • Richard J. Williams & Neo D. Martinez, 2001. "Stabilization of Chaotic and Non-Permanent Food Web Dynamics," Working Papers 01-07-037, Santa Fe Institute.
  • Handle: RePEc:wop:safiwp:01-07-037
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    References listed on IDEAS

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    1. J. Doyne Farmer, 2002. "Market force, ecology and evolution," Industrial and Corporate Change, Oxford University Press, pages 895-953.
    2. Challet, Damien & Stinchcombe, Robin, 2001. "Analyzing and modeling 1+1d markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 300(1), pages 285-299.
    3. Gode, Dhananjay K & Sunder, Shyam, 1993. "Allocative Efficiency of Markets with Zero-Intelligence Traders: Market as a Partial Substitute for Individual Rationality," Journal of Political Economy, University of Chicago Press, vol. 101(1), pages 119-137, February.
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    Keywords

    Ecology; food web; dynamics; stability; chaos; functional response;

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