Task Allocation of Wasps Governed by Common Stomach: A Model Based on Electric Circuits

Simple regulatory mechanisms based on the idea of the saturable 'common stomach' can control the regulation of construction behavior and colony-level responses to environmental perturbations in Metapolybia wasp societies. We mapped the different task groups to mutual inductance electrical circuits and used Kirchoff's basic voltage laws to build a model that uses master equations from physics, yet is able to provide strong predictions for this complex biological phenomenon. Similar to real colonies, independently of the initial conditions, the system shortly sets into an equilibrium, which provides optimal task allocation for a steady construction, depending on the influx of accessible water. The system is very flexible and in the case of perturbations, it reallocates its workforce and adapts to the new situation with different equilibrium levels. Similar to the finding of field studies, decreasing any task groups caused decrease of construction; increasing or decreasing water inflow stimulated or reduced the work of other task groups while triggering compensatory behavior in water foragers. We also showed that only well connected circuits are able to produce adequate construction and this agrees with the finding that this type of task partitioning only exists in larger colonies. Studying the buffer properties of the common stomach and its effect on the foragers revealed that it provides stronger negative feedback to the water foragers, while the connection between the pulp foragers and the common stomach has a strong fixed-point attractor, as evidenced by the dissipative trajectory.