Homeostatic self-regulation is a fundamental aspect of open dissipative systems. Integral feedback has been found to be important for homeostatic control on both the cellular and molecular levels of biological organization and in engineered systems. Analyzing the task allocation mechanisms of three insect societies, we identified a model of integral control residing at colony level. We characterized a general functional core mechanism, called the “common stomach,” where a crucial shared substance for colony function self-regulates its own quantity via reallocating the colony’s workforce, which collects and uses this substance. The central component in a redundant feedback network is the saturation level of this substance in the colony. An interaction network of positive and negative feedback loops ensures the homeostatic state of this substance and the workforce involved in processing this substance. Extensive sensitivity and stability analyses of the core model revealed that the system is very resilient against perturbations and compensates for specific types of stress that real colonies face in their ecosystems. The core regulation system is highly scalable, and due to its buffer function, it can filter noise and find a new equilibrium quickly after environmental (supply) or colony-state (demand) changes. The common stomach regulation system is an example of convergent evolution among the three different societies, and we predict that similar integral control regulation mechanisms have evolved frequently within natural complex systems.

Task allocation, and task switching have an important effect on the efficiency of distributed, locally controlled systems such as social insect colonies. Both efficiency and workload distribution are global features of the system which are not directly accessible to workers and can only be sampled locally by an individual in a distributed system. To investigate how the cost of task switching affects global performance we use social wasp societies as a metaphor to construct a simple model system with four interconnected tasks. Our goal is not the accurate description of the behavior of a given species, but to seek general conclusions on the effect of noise and time delay on a behavior that is partitioned into subtasks. In our model a nest structure needs to be constructed by the cooperation of individuals that carry out different tasks: builders, pulp and water foragers, and individuals storing water. We report a simulation study based on a model using delay-differential equations to analyze the trade-off between task switching costs and keeping a high degree of adaptivity in a dynamic, noisy environment. Combining the methods of time-delayed equations and stochastic processes we are able to represent the influence of swarm size and task switching sensitivity. We find that the system is stable for reasonable choices of parameters but shows oscillations for extreme choices of parameters and we find that the system is resilient to perturbations. We identify a trade-off between reaching equilibria of high performance and having short transients.

Task allocation, and task switching have an important effect on the efficiency of distributed, locally controlled systems such as social insect colonies. Both efficiency and workload distribution are global features of the system which are not directly accessible to workers and can only be sampled locally by an individual in a distributed system. To investigate how the cost of task switching affects global performance we use social wasp societies as a metaphor to construct a simple model system with four interconnected tasks. Our goal is not the accurate description of the behavior of a given species, but to seek general conclusions on the effect of noise and time delay on a behavior that is partitioned into subtasks. In our model a nest structure needs to be constructed by the cooperation of individuals that carry out different tasks: builders, pulp and water foragers, and individuals storing water. We report a simulation study based on a model using delay-differential equations to analyze the trade-off between task switching costs and keeping a high degree of adaptivity in a dynamic, noisy environment. Combining the methods of time-delayed equations and stochastic processes we are able to represent the influence of swarm size and task switching sensitivity. We find that the system is stable for reasonable choices of parameters but shows oscillations for extreme choices of parameters and we find that the system is resilient to perturbations. We identify a trade-off between reaching equilibria of high performance and having short transients.

Metapolybia wasps live in small societies (around one hundred adults) and rear their young in nests they construct on flat surfaces from plant materials. For processing nest paper, they must gather plant materials and process it into pulp with water. The water is collected by water foragers and is transferred to pulp foragers indirectly via a "common stomach." The common stomach, or social crop, is formed by generalist wasps called laborers. These wasps can engage in water exchange, store water in their crops, and may become specialist foragers or builders. We provide an alternative model for regulating task partitioning in construction behavior by using an agent based modeling framework parameterized by our field observations. Our model predicts that assessing colony needs via individual interactions with the common stomach leads to a robust regulation of task partitioning in construction behavior. By using perturbation experiments in our simulations, we show that this emergent task allocation is able to dynamically adapt to perturbations of the environment and to changes in colony-level demands or population structure. The robustness of our model stems from the fact that the common stomach is both a strong buffer and a source of several feedback mechanisms that affect the individual wasps. We show that both the efficiency and the task fidelity of these colonies are dependent upon colony size. We also demonstrate that the emergence of specialist wasps (individuals with high task fidelity) does not require any special initial conditions or reinforcement at the individual level, but it is rather a consequence of colony-level workflow stability. Our model closely mimics the behavior of Metapolybia wasps, demonstrating that a regulation mechanism based on simple pair-wise interactions through a common stomach is a plausible hypothesis for the organization of collective behavior.

Metapolybia wasps construct their nests on flat surfaces using plant materials, which they process into paper. For processing the pulp wasps need water, which is collected by water foragers, and it is transferred to pulp foragers indirectly via a "common stomach." The common stomach is formed by generalist wasps that can engage in water exchange and can store water in their crops. Our goal is to provide an alternative model for regulating task partitioning in construction behavior, focusing on worker connectivity instead of using threshold curves to model mechanisms of colony-level regulation. We propose that the existence of an information center and of a network of worker interactions, which establish sets of positive and negative feedbacks, allow collective regulation of colony-wide behaviors. Using a Stock and Flow modeling framework, we illustrate that the common stomach could serve both as a temporal storage for water and also as a source of information about the colony's current demands related to nest construction tasks. Our model predicts that assessing colony needs via individual interactions with the common stomach leads to a robust regulation of task partitioning in construction behavior. Using perturbation experiments in our simulations, we show that this emergent task allocation is able to dynamically adapt to perturbations of the environment and to changes in colony-level demands or population structure. Our model closely mimics and predicts the behavior of Metapolybia wasps, demonstrating that the regulation mechanism based on worker connectivity through a common stomach is a plausible hypothesis for the organization of collective behavior.