Competitive coexistence in stoichiometric chaos

Bo Deng, Irakli Loladze

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

Classical predator-prey models, such as Lotka-Volterra, track the abundance of prey, but ignore its quality. Yet, in the past decade, some new and occasionally counterintuitive effects of prey quality on food web dynamics emerged from both experiments and mathematical modeling. The underpinning of this work is the theory of ecological stoichiometry that is centered on the fact that each organism is a mixture of multiple chemical elements such as carbon (C), nitrogen (N), and phosphorus (P). The ratios of these elements can vary within and among species, providing simple ways to represent prey quality as its C:N or C:P ratios. When these ratios modeled to vary, as they frequently do in nature, seemingly paradoxical results can arise such as the extinction of a predator that has an abundant and accessible prey. Here, for the first time, we show analytically that the reduction in prey quality can give rise to chaotic oscillations. In particular, when competing predators differ in their sensitivity to prey quality then all species can coexist via chaotic fluctuations. The chaos generating mechanism is based on the existence of a junction-fold point on the nullcline surfaces of the species. Conditions on parameters are found for such a point, and the singular perturbation method and the kneading sequence analysis are used to demonstrate the existence of a period-doubling cascade to chaos as a result of the point.

Original languageEnglish (US)
Article number033108
JournalChaos
Volume17
Issue number3
DOIs
StatePublished - Jan 1 2007

Fingerprint

Prey
Coexistence
Chaos theory
Chemical elements
chaos
Chaos
predators
Stoichiometry
Phosphorus
Predator
Nitrogen
Carbon
chemical elements
Vary
period doubling
Food Web
Singular Perturbation Method
Lotka-Volterra
organisms
food

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

Competitive coexistence in stoichiometric chaos. / Deng, Bo; Loladze, Irakli.

In: Chaos, Vol. 17, No. 3, 033108, 01.01.2007.

Research output: Contribution to journalArticle

Deng, Bo ; Loladze, Irakli. / Competitive coexistence in stoichiometric chaos. In: Chaos. 2007 ; Vol. 17, No. 3.
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