Bulletin of Mathematical Biology

, Volume 36, Issue 5–6, pp 527–533 | Cite as

Necessary and sufficient condition for a model insect population to go to extinction

  • David H. Staley
  • William R. Holt
  • William N. CannonJr.
Article
  • 33 Downloads

Abstract

A necessary and sufficient condition on the parameters for a model population to become extinct is presented. The mathematical model describes an insect population with overlapping generations where the females are polyandrous and the males are subject to autosterilization. The relationship between the values of the parameters of the model and the time to extinction is illustrated.

Keywords

Population Model Female Population Immature Stage Population Number Insect Population 

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Literature

  1. Cole, L. C. 1954. “The Population Consequences of Life History Phenomena”.Quant. Rev. Biol.,29, 103–137.CrossRefGoogle Scholar
  2. Staley, D. H., W. N. Cannon, Jr. and W. R. Holt. 1971. “A Mathematical Model of an Insect Population with Overlapping Generations where the Females are Polyandrous and the Males are Subject to Auto-Sterilization”.Ann. Entromol. Soc. Am.,62 (2), 325–330.Google Scholar
  3. Thompson, W. R. 1931. “On the Reproduction of Organisms with Overlapping Generations”.Bull. Entomol. Res. 22, 147–172.CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 1974

Authors and Affiliations

  • David H. Staley
    • 1
  • William R. Holt
    • 2
  • William N. CannonJr.
    • 2
  1. 1.Department of MathematicsOhio Wesleyan UniversityDelaware
  2. 2.Northeastern Forest Experiment Station, Forest ServiceUSDADelaware

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