Persistence in Food Webs. I. Lotka-Volterra Food Chains,

Abstract

Of numerous ecosystem stability considerations, none probably affects ecosystem structure as drastically as the extinction of a biological species. As demonstrated by public concern about projects such as the TVA Tellico Dam Project where the persistence of the snail darter Percina tanasi is vascillating, extinction of a biotic component of a food chain is topical as well as ecologically fundamental. Viewing the importance of persistence-extinction phenomena, it is somewhat surprising that the modelling and analysis of ecosystems have not concentrated foremost upon species survival. The influence of stability eventuation in the engineering and mathematical communities was, undoubtedly, initially too inviting and overwhelming. The qualitative approach employed here introduces the concept of a persistence or extinction function which is essentially an appropriate system transformation in the Lyapunov tradition. This technique yields (global) persistence or extinction results from the system structure without a priori information of the asymptotic character of the model solutions. The conclusions are sharp and depend only upon the model parameter and food chain length.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1978
Accession Number
ADA081125

Entities

People

  • Thomas C. Gard
  • Thomas G. Hallam

Organizations

  • University of Tennessee system

Tags

DTIC Thesaurus Topics

  • Coefficients
  • Differential Equations
  • Dynamics
  • Ecosystems
  • Endangered Species
  • Engineering
  • Equations
  • Extinction
  • Fish
  • Food Chains
  • Inequalities
  • Intervals
  • Mathematical Analysis
  • Payload
  • Plastic Explosives
  • Real Numbers
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Aquatic Ecology
  • Military History of the United States in the 20th Century.