A mutualism-parasitism system modeling host and parasite with mutualism at low density

Yuanshi Wang, Donald L. DeAngelis

Research output: Contribution to journalArticle

7 Scopus citations


A mutualism-parasitism system of two species is considered, where mutualism is the dominant interaction when the predators (parasites) are at low density while parasitism is dominant when the predators are at high den- sity. Our aim is to show that mutualism at low density promotes coexistence of the species and leads to high production of the prey (host). The mutualism- parasitism system presented here is a combination of the Lotka-Volterra co- operative model and Lotka-Volterra predator-prey model. By comparing dy- namics of this system with those of the Lotka-Volterra predator-prey model, we present the mechanisms by which the mutualism improves the coexistence of the species and production of the prey. Then the parameter space is di- vided into six regions, which correspond to the four outcomes of mutualism, commensalism, predation/parasitism and neutralism, respectively. When the parameters are varied continuously among the six regions, it is shown that the interaction outcomes of the system transition smoothly among the four out- comes. By comparing the dynamics of the specic system with those of the Lotka-Volterra cooperative model, we show that the parasitism at high density promotes stability of the system. A novel aspect of this paper is the simplicity of the model, which allows rigorous and thorough analysis and transparency of the results.

Original languageEnglish (US)
Pages (from-to)431-444
Number of pages14
JournalMathematical Biosciences and Engineering
Issue number2
StatePublished - Apr 1 2012



  • Coexistence
  • Lotka-Volterra
  • Mutualism
  • Parasitism
  • Population dynamics

ASJC Scopus subject areas

  • Applied Mathematics
  • Modeling and Simulation
  • Computational Mathematics
  • Agricultural and Biological Sciences(all)
  • Medicine(all)

Cite this