Mathematical modeling on obligate mutualism: Interactions between leaf-cutter ants and their fungus garden

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.

► We model obligate mutualistic interactions between leaf-cutter ants and their fungus garden at the early colony expansion.
► We do global math analysis of model.
► Our results indicate that the division of labor and initial conditions determine whether both species can coexist or not.
► Our model has been validated by data.