Mathematical modeling on obligate mutualism

Interactions between leaf-cutter ants and their fungus garden

Yun Kang, Rebecca Clark, Michael Makiyama, Jennifer Fewell

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

We propose a simple mathematical model by applying Michaelis-Menton equations of enzyme kinetics to study the mutualistic interaction between the leaf cutter ant and its fungus garden at the early stage of colony expansion. We derive sufficient conditions on the extinction and coexistence of these two species. In addition, we give a region of initial condition that leads to the extinction of two species when the model has an interior attractor. Our global analysis indicates that the division of labor by worker ants and initial conditions are two important factors that determine whether leaf cutter ants' colonies and their fungus garden can survive and grow or not. We validate the model by comparing model simulations and data on fungal and ant colony growth rates under laboratory conditions. We perform sensitive analysis of the model based on the experimental data to gain more biological insights on ecological interactions between leaf-cutter ants and their fungus garden. Finally, we give conclusions and discuss potential future work.

Original languageEnglish (US)
Pages (from-to)116-127
Number of pages12
JournalJournal of Theoretical Biology
Volume289
Issue number1
DOIs
StatePublished - Nov 21 2011

Fingerprint

Mutualism
cutters
Symbiosis
Ants
mutualism
Fungi
Mathematical Modeling
Formicidae
Leaves
mathematical models
Ant Colony
Extinction
Initial conditions
extinction
Interaction
Enzyme Kinetics
leaves
polyethism
enzyme kinetics
Global Analysis

Keywords

  • Coexistence
  • Extinction
  • Functional/numerical response
  • Multiple attractors
  • Population dynamics

ASJC Scopus subject areas

  • Medicine(all)
  • Immunology and Microbiology(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Agricultural and Biological Sciences(all)
  • Modeling and Simulation
  • Statistics and Probability
  • Applied Mathematics

Cite this

Mathematical modeling on obligate mutualism : Interactions between leaf-cutter ants and their fungus garden. / Kang, Yun; Clark, Rebecca; Makiyama, Michael; Fewell, Jennifer.

In: Journal of Theoretical Biology, Vol. 289, No. 1, 21.11.2011, p. 116-127.

Research output: Contribution to journalArticle

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