A predator prey model with age structure

Jim M Cushing, M. Saleem

Research output: Contribution to journalArticle

60 Citations (Scopus)

Abstract

A general predator-prey model is considered in which the predator population is assumed to have an age structure which significantly affects its fecundity. The model equations are derived from the general McKendrick equations for age structured populations. The existence, stability and destabilization of equilibria are studied as they depend on the prey's natural carrying capacity and the maturation period m of the predator. The main result of the paper is that for a broad class of maturation functions positive equilibria are either unstable for small m or are destabilized as m decreases to zero. This is in contrast to the usual rule of thumb that increasing (not decreasing) delays in growth rate responses cause instabilities.

Original languageEnglish (US)
Pages (from-to)231-250
Number of pages20
JournalJournal of Mathematical Biology
Volume14
Issue number2
DOIs
StatePublished - 1982

Fingerprint

Age Structure
Predator-prey Model
Predator
age structure
Age-structured Population
predators
Carrying Capacity
Conservation of Natural Resources
Prey
Population
Fertility
Unstable
carrying capacity
Decrease
Zero
fecundity
Growth
Model
Class

Keywords

  • Age structure
  • Predator-prey
  • Stability

ASJC Scopus subject areas

  • Agricultural and Biological Sciences (miscellaneous)
  • Mathematics (miscellaneous)

Cite this

A predator prey model with age structure. / Cushing, Jim M; Saleem, M.

In: Journal of Mathematical Biology, Vol. 14, No. 2, 1982, p. 231-250.

Research output: Contribution to journalArticle

Cushing, Jim M ; Saleem, M. / A predator prey model with age structure. In: Journal of Mathematical Biology. 1982 ; Vol. 14, No. 2. pp. 231-250.
@article{f83a01497da5406e9f182147e2ed6940,
title = "A predator prey model with age structure",
abstract = "A general predator-prey model is considered in which the predator population is assumed to have an age structure which significantly affects its fecundity. The model equations are derived from the general McKendrick equations for age structured populations. The existence, stability and destabilization of equilibria are studied as they depend on the prey's natural carrying capacity and the maturation period m of the predator. The main result of the paper is that for a broad class of maturation functions positive equilibria are either unstable for small m or are destabilized as m decreases to zero. This is in contrast to the usual rule of thumb that increasing (not decreasing) delays in growth rate responses cause instabilities.",
keywords = "Age structure, Predator-prey, Stability",
author = "Cushing, {Jim M} and M. Saleem",
year = "1982",
doi = "10.1007/BF01832847",
language = "English (US)",
volume = "14",
pages = "231--250",
journal = "Journal of Mathematical Biology",
issn = "0303-6812",
publisher = "Springer Verlag",
number = "2",

}

TY - JOUR

T1 - A predator prey model with age structure

AU - Cushing, Jim M

AU - Saleem, M.

PY - 1982

Y1 - 1982

N2 - A general predator-prey model is considered in which the predator population is assumed to have an age structure which significantly affects its fecundity. The model equations are derived from the general McKendrick equations for age structured populations. The existence, stability and destabilization of equilibria are studied as they depend on the prey's natural carrying capacity and the maturation period m of the predator. The main result of the paper is that for a broad class of maturation functions positive equilibria are either unstable for small m or are destabilized as m decreases to zero. This is in contrast to the usual rule of thumb that increasing (not decreasing) delays in growth rate responses cause instabilities.

AB - A general predator-prey model is considered in which the predator population is assumed to have an age structure which significantly affects its fecundity. The model equations are derived from the general McKendrick equations for age structured populations. The existence, stability and destabilization of equilibria are studied as they depend on the prey's natural carrying capacity and the maturation period m of the predator. The main result of the paper is that for a broad class of maturation functions positive equilibria are either unstable for small m or are destabilized as m decreases to zero. This is in contrast to the usual rule of thumb that increasing (not decreasing) delays in growth rate responses cause instabilities.

KW - Age structure

KW - Predator-prey

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=0019993839&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0019993839&partnerID=8YFLogxK

U2 - 10.1007/BF01832847

DO - 10.1007/BF01832847

M3 - Article

C2 - 7119585

AN - SCOPUS:0019993839

VL - 14

SP - 231

EP - 250

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 2

ER -