The stability of internal equilibria in predator-prey models with breeding suppression

Graeme D. Ruxton, Q. J A Khan, Mohamed Al-Lawatia

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We present two models that represent the suppression of breeding by prey in response to short-term increases in predation pressure. For both of these models, we have been able to produce analytic conditions for the local stability of the interior steady state, in terms of the values of combinations of these parameters. Although our models are as simple as possible to capture the effect of breeding suppression, the expression for local stability, even in their simplest form, are complex. Thus, we come to the important conclusion that there is no simple and general rule for the effect of the behaviours described here (anti-predatory breeding suppression and prey switching by predators) on the stability of population dynamics. Rather, effects will be system specific. However, we hope that the results and methodological framework outlined here will provide a useful tool for others to investigate the consequences for particular real systems.

Original languageEnglish
Pages (from-to)207-219
Number of pages13
JournalIMA Journal of Mathematics Applied in Medicine and Biology
Volume19
Issue number3
Publication statusPublished - Sep 2002

Fingerprint

Predator-prey Model
Breeding
breeding
Local Stability
predator
Prey
Internal
predators
Population dynamics
Population Dynamics
Predator
population dynamics
Interior
predation
Model
Pressure
effect

Keywords

  • Equilibria
  • Local stability
  • Ordinary differential equations
  • Steady state

ASJC Scopus subject areas

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

Cite this

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AU - Al-Lawatia, Mohamed

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AB - We present two models that represent the suppression of breeding by prey in response to short-term increases in predation pressure. For both of these models, we have been able to produce analytic conditions for the local stability of the interior steady state, in terms of the values of combinations of these parameters. Although our models are as simple as possible to capture the effect of breeding suppression, the expression for local stability, even in their simplest form, are complex. Thus, we come to the important conclusion that there is no simple and general rule for the effect of the behaviours described here (anti-predatory breeding suppression and prey switching by predators) on the stability of population dynamics. Rather, effects will be system specific. However, we hope that the results and methodological framework outlined here will provide a useful tool for others to investigate the consequences for particular real systems.

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