The impact of a predator on the outcome of competition in the three-trophic food web

PS Dutta, B.W. Kooi, U Feudel

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

We study the effects of predation on the competition of prey populations for two resources in a chemostat. Weinvestigate a variety of small food web compositions: the bi-trophic food web (two resources—two competing prey) and the three-trophic food web (two resources—two prey—generalist predator) comparing different model formulations: substitutable resources and essential resources, namely Liebig's minimum law model (perfect essential resources) and complementary resources formulations. The prediction of the outcome of competition is solely based on bifurcation analysis in which the inflow of resources into the chemostat is used as the bifurcation parameter. We show that the results for different bi-trophic food webs are very similar, as only equilibria are involved in the long-term dynamics. In the three-trophic food web, the outcome of competition is manifested largely by non-equilibrium dynamics, i.e., in oscillatory behavior. The emergence of predator–prey cycles leads to strong deviations between the predictions of the outcome of competition based on Liebig's minimum law and the complementary resources. We show that the complementary resources formulation yields a stabilization of the three-trophic food web by decreasing the existence interval of oscillations. Furthermore, we
find an exchange of a region of oscillatory co-existence of all three species in Liebig's formulation by a region of bistability of two limit cycles containing only one prey and the predator in the complementary formulation.
Original languageEnglish
Pages (from-to)28-42
JournalJournal of Theoretical Biology
Volume417
DOIs
Publication statusPublished - 21 Mar 2017

Fingerprint

Food Web
Food Chain
Predator
food webs
predators
Resources
Chemostats
Prey
Formulation
Chemostat
prediction
Nonequilibrium Dynamics
Predator-prey
oscillation
Bistability
Prediction
Bifurcation Analysis
Stabilization
Coexistence
Limit Cycle

Keywords

  • Bifurcation analysis Chemostat Competition Food web reduction Mass balance model

Cite this

@article{68bca1348c1e446196d3aec1d8cbe263,
title = "The impact of a predator on the outcome of competition in the three-trophic food web",
abstract = "We study the effects of predation on the competition of prey populations for two resources in a chemostat. Weinvestigate a variety of small food web compositions: the bi-trophic food web (two resources—two competing prey) and the three-trophic food web (two resources—two prey—generalist predator) comparing different model formulations: substitutable resources and essential resources, namely Liebig's minimum law model (perfect essential resources) and complementary resources formulations. The prediction of the outcome of competition is solely based on bifurcation analysis in which the inflow of resources into the chemostat is used as the bifurcation parameter. We show that the results for different bi-trophic food webs are very similar, as only equilibria are involved in the long-term dynamics. In the three-trophic food web, the outcome of competition is manifested largely by non-equilibrium dynamics, i.e., in oscillatory behavior. The emergence of predator–prey cycles leads to strong deviations between the predictions of the outcome of competition based on Liebig's minimum law and the complementary resources. We show that the complementary resources formulation yields a stabilization of the three-trophic food web by decreasing the existence interval of oscillations. Furthermore, wefind an exchange of a region of oscillatory co-existence of all three species in Liebig's formulation by a region of bistability of two limit cycles containing only one prey and the predator in the complementary formulation.",
keywords = "Bifurcation analysis Chemostat Competition Food web reduction Mass balance model",
author = "PS Dutta and B.W. Kooi and U Feudel",
year = "2017",
month = "3",
day = "21",
doi = "10.1016/j.jtbi.2017.01.020",
language = "English",
volume = "417",
pages = "28--42",
journal = "Journal of Theoretical Biology",
issn = "0022-5193",
publisher = "Academic Press Inc.",

}

The impact of a predator on the outcome of competition in the three-trophic food web. / Dutta, PS; Kooi, B.W.; Feudel, U.

In: Journal of Theoretical Biology, Vol. 417, 21.03.2017, p. 28-42.

Research output: Contribution to JournalArticleAcademicpeer-review

TY - JOUR

T1 - The impact of a predator on the outcome of competition in the three-trophic food web

AU - Dutta, PS

AU - Kooi, B.W.

AU - Feudel, U

PY - 2017/3/21

Y1 - 2017/3/21

N2 - We study the effects of predation on the competition of prey populations for two resources in a chemostat. Weinvestigate a variety of small food web compositions: the bi-trophic food web (two resources—two competing prey) and the three-trophic food web (two resources—two prey—generalist predator) comparing different model formulations: substitutable resources and essential resources, namely Liebig's minimum law model (perfect essential resources) and complementary resources formulations. The prediction of the outcome of competition is solely based on bifurcation analysis in which the inflow of resources into the chemostat is used as the bifurcation parameter. We show that the results for different bi-trophic food webs are very similar, as only equilibria are involved in the long-term dynamics. In the three-trophic food web, the outcome of competition is manifested largely by non-equilibrium dynamics, i.e., in oscillatory behavior. The emergence of predator–prey cycles leads to strong deviations between the predictions of the outcome of competition based on Liebig's minimum law and the complementary resources. We show that the complementary resources formulation yields a stabilization of the three-trophic food web by decreasing the existence interval of oscillations. Furthermore, wefind an exchange of a region of oscillatory co-existence of all three species in Liebig's formulation by a region of bistability of two limit cycles containing only one prey and the predator in the complementary formulation.

AB - We study the effects of predation on the competition of prey populations for two resources in a chemostat. Weinvestigate a variety of small food web compositions: the bi-trophic food web (two resources—two competing prey) and the three-trophic food web (two resources—two prey—generalist predator) comparing different model formulations: substitutable resources and essential resources, namely Liebig's minimum law model (perfect essential resources) and complementary resources formulations. The prediction of the outcome of competition is solely based on bifurcation analysis in which the inflow of resources into the chemostat is used as the bifurcation parameter. We show that the results for different bi-trophic food webs are very similar, as only equilibria are involved in the long-term dynamics. In the three-trophic food web, the outcome of competition is manifested largely by non-equilibrium dynamics, i.e., in oscillatory behavior. The emergence of predator–prey cycles leads to strong deviations between the predictions of the outcome of competition based on Liebig's minimum law and the complementary resources. We show that the complementary resources formulation yields a stabilization of the three-trophic food web by decreasing the existence interval of oscillations. Furthermore, wefind an exchange of a region of oscillatory co-existence of all three species in Liebig's formulation by a region of bistability of two limit cycles containing only one prey and the predator in the complementary formulation.

KW - Bifurcation analysis Chemostat Competition Food web reduction Mass balance model

U2 - 10.1016/j.jtbi.2017.01.020

DO - 10.1016/j.jtbi.2017.01.020

M3 - Article

VL - 417

SP - 28

EP - 42

JO - Journal of Theoretical Biology

JF - Journal of Theoretical Biology

SN - 0022-5193

ER -