title: Mathematical modeling on obligate mutualism: Interactions between leaf-cutter ants and their fungus garden.
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.
authors: Applied Sciences and Mathematics, Arizona State University, Mesa, AZ 85212, USA. yun.kang@asu.edu
authors: Yun
authors: Y
authors: Kang
authors: Rebecca
authors: R
authors: Clark
authors: Michael
authors: M
authors: Makiyama
authors: Jennifer
authors: J
authors: Fewell
mesh_terms: D000818:Animals; D001000:Ants / Q000254:growth & development*; D018533:Biomass; D005658:Fungi / Q000254:growth & development*; D008954:Models, Biological; D018515:Plant Leaves / Q000382:microbiology; D011157:Population Dynamics; D013559:Symbiosis / Q000502:physiology*