Skip to main content
SpringerLink
Log in

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

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature

  • Cole, L. C. 1954. “The Population Consequences of Life History Phenomena”.Quant. Rev. Biol.,29, 103–137.

    Article  Google Scholar 

  • 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 

  • Thompson, W. R. 1931. “On the Reproduction of Organisms with Overlapping Generations”.Bull. Entomol. Res. 22, 147–172.

    Article  Google Scholar 

Download references

Author information

Author notes

  1. William R. Holt

    Present address: Boehringer Ingelhim Ltd., 10523, Elmsford, New York

Authors and Affiliations

  1. Department of Mathematics, Ohio Wesleyan University, Delaware, Ohio

    David H. Staley

  2. Northeastern Forest Experiment Station, Forest Service, USDA, Delaware, Ohio

    William R. Holt & William N. Cannon Jr.

Authors
  1. David H. Staley
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. William R. Holt
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. William N. Cannon Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Staley, D.H., Holt, W.R. & Cannon, W.N. Necessary and sufficient condition for a model insect population to go to extinction. Bltn Mathcal Biology 36, 527–533 (1974). https://doi.org/10.1007/BF02463264

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02463264

Keywords

Search

Navigation