Time delay implies cost on task switching: a model to investigate the efficiency of task partitioning

Self-complexification through integral feedback in eusocial paper wasps of various levels of sociality

We investigate how simple physical interactions can generate remarkable diversity in the life history of social agents using data of social wasps, yielding complex scalable task partitioning. We built and analyzed a computational model to investigate how diverse task allocation patterns found in nature can emerge from the same behavioral blueprint. Self-organizing mechanisms of interwoven behavioral feedback loops, task-dependent time delays and simple material flows between interacting individuals yield an emergent homeostatic self-regulation while keeping the global colony performance scalable. Task allocation mechanisms based on implicitly honest signaling via material flows are not only very robust but are also highly evolvable due to their simplicity and reliability. We find that task partitioning has evolved to be scalable and adaptable to life history traits, such as expected colony size or temporal bottlenecks in the available workforce or materials. By tuning solely the total number of agents and a social connectivity-related parameter in the model, our simulations yield the whole range of emergent patterns in task allocation and task fidelity akin to observed field data. Our model suggests that the material exchange ("common stomach mechanism") found in many paper wasps provides a common functional "core" across these genera, which not only provides self-regulation of the colony, but also provides a scalable mechanism allowing natural selection to yield complex social integration in larger colonies over the course of their evolutionary trajectory.

When being flexible matters: Ecological underpinnings for the evolution of collective flexibility and task allocation

A central problem in evolutionary biology is explaining variation in the organization of task allocation across collective systems. Why do human cells irreversibly adopt a task during development (e.g., kidney vs. liver cell), while sponge cells switch between different cell types? And why have only some ant species evolved specialized castes of workers for particular tasks? Although it seems reasonable to suppose that such differences reflect, at least partially, the different ecological pressures that systems face, there is no general understanding of how a system’s dynamic environment shapes its task allocation. To this end, we develop a general mathematical framework that reveals how simple ecological considerations could potentially explain cross-system variation in task allocation—including in flexibility, specialization, and (in)activity.

Task allocation is a central feature of collective organization. Living collective systems, such as multicellular organisms or social insect colonies, have evolved diverse ways to allocate individuals to different tasks, ranging from rigid, inflexible task allocation that is not adjusted to changing circumstances to more fluid, flexible task allocation that is rapidly adjusted to the external environment. While the mechanisms underlying task allocation have been intensely studied, it remains poorly understood whether differences in the flexibility of task allocation can be viewed as adaptive responses to different ecological contexts—for example, different degrees of temporal variability. Motivated by this question, we develop an analytically tractable mathematical framework to explore the evolution of task allocation in dynamic environments. We find that collective flexibility is not necessarily always adaptive, and fails to evolve in environments that change too slowly (relative to how long tasks can be left unattended) or too quickly (relative to how rapidly task allocation can be adjusted). We further employ the framework to investigate how environmental variability impacts the internal organization of task allocation, which allows us to propose adaptive explanations for some puzzling empirical observations, such as seemingly unnecessary task switching under constant environmental conditions, apparent task specialization without efficiency benefits, and high levels of individual inactivity. Altogether, this work provides a general framework for probing the evolved diversity of task allocation strategies in nature and reinforces the idea that considering a system’s ecology is crucial to explaining its collective organization.

Integral feedback control is at the core of task allocation and resilience of insect societies

A key problem for complex systems is achieving resilience through their (often nonlinear) interactions between components. Social insect colonies are natural examples of highly scalable systems that achieve homeostatic self-regulation based on local interactions. We describe a “functional core model” that we identified in three different insect societies (wasps, ants, and honey bees). This core model is based on self-regulation through a shared (limited) substance that works as an information center and as a buffer system simultaneously. This system has several adaptive properties, as it is robust against environmental disturbances and insensitive against parameter changes. Finding such a “common core model” is of high significance in understanding the discrete transitions from individuality to sociality in several animal species through convergent evolution.

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.

Costs of task allocation with local feedback: Effects of colony size and extra workers in social insects and other multi-agent systems

Adaptive collective systems are common in biology and beyond. Typically, such systems require a task allocation algorithm: a mechanism or rule-set by which individuals select particular roles. Here we study the performance of such task allocation mechanisms measured in terms of the time for individuals to allocate to tasks. We ask: (1) Is task allocation fundamentally difficult, and thus costly? (2) Does the performance of task allocation mechanisms depend on the number of individuals? And (3) what other parameters may affect their efficiency? We use techniques from distributed computing theory to develop a model of a social insect colony, where workers have to be allocated to a set of tasks; however, our model is generalizable to other systems. We show, first, that the ability of workers to quickly assess demand for work in tasks they are not currently engaged in crucially affects whether task allocation is quickly achieved or not. This indicates that in social insect tasks such as thermoregulation, where temperature may provide a global and near instantaneous stimulus to measure the need for cooling, for example, it should be easy to match the number of workers to the need for work. In other tasks, such as nest repair, it may be impossible for workers not directly at the work site to know that this task needs more workers. We argue that this affects whether task allocation mechanisms are under strong selection. Second, we show that colony size does not affect task allocation performance under our assumptions. This implies that when effects of colony size are found, they are not inherent in the process of task allocation itself, but due to processes not modeled here, such as higher variation in task demand for smaller colonies, benefits of specialized workers, or constant overhead costs. Third, we show that the ratio of the number of available workers to the workload crucially affects performance. Thus, workers in excess of those needed to complete all tasks improve task allocation performance. This provides a potential explanation for the phenomenon that social insect colonies commonly contain inactive workers: these may be a 'surplus' set of workers that improves colony function by speeding up optimal allocation of workers to tasks. Overall our study shows how limitations at the individual level can affect group level outcomes, and suggests new hypotheses that can be explored empirically.

Resilience of honeybee colonies via common stomach: A model of self-regulation of foraging

We propose a new regulation mechanism based on the idea of the "common stomach" to explain several aspects of the resilience and homeostatic regulation of honeybee colonies. This mechanism exploits shared pools of substances (pollen, nectar, workers, brood) that modulate recruitment, abandonment and allocation patterns at the colony-level and enable bees to perform several survival strategies to cope with difficult circumstances: Lack of proteins leads to reduced feeding of young brood, to early capping of old brood and to regaining of already spent proteins through brood cannibalism. We modeled this system by linear interaction terms and mass-action law. To test the predictive power of the model of this regulatory mechanism we compared our model predictions to experimental data of several studies. These comparisons show that the proposed regulation mechanism can explain a variety of colony level behaviors. Detailed analysis of the model revealed that these mechanisms could explain the resilience, stability and self-regulation observed in honeybee colonies. We found that manipulation of material flow and applying sudden perturbations to colony stocks are quickly compensated by a resulting counter-acting shift in task selection. Selective analysis of feedback loops allowed us to discriminate the importance of different feedback loops in self-regulation of honeybee colonies. We stress that a network of simple proximate mechanisms can explain significant colony-level abilities that can also be seen as ultimate reasoning of the evolutionary trajectory of honeybees.

Handling interference effects on foraging with bucket brigades

Many kinds of bio-inspired tasks have been tested with swarm robotics and task partitioning is one of the challenging subjects. In nature, it is well known that some colonies of social insects such as honeybees, termites, and ants use task partitioning strategies for their survival. In this paper, we demonstrate an effect of the task partitioning strategy called bucket brigade, which uses the direct transfer of materials or food between a pair of workers. We propose a task partitioning strategy based on the moving speeds of agents for the foraging task. We test various environmental conditions and compare the performance between task partitioning groups and non-partitioning groups. The experimental results show that task partitioning may not always be the best solution for foraging performance. However, when there exists a transfer bottleneck at a central location such as the entrance of the nest, task partitioning can be an effective strategy for reducing the traffic jam and improving the overall foraging performance of a group. The bucket brigade sequenced from the slowest agents (near the food source) to the fastest agents (near the nest) can particularly improve performance significantly in the region with traffic congestion near the nest. Generally, many social insect colonies consist of a number of members, and the entrances of colony nests always suffer from heavy traffic congestion. Our experimental results support the hypothesis that several social insects use one of the task partitioning strategies based on bucket brigades in their foraging tasks.

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.

The Mechanisms of Water Exchange: The Regulatory Roles of Multiple Interactions in Social Wasps

Evolutionary benefits of task fidelity and improving information acquisition via multiple transfers of materials between individuals in a task partitioned system have been shown before, but in this paper we provide a mechanistic explanation of these phenomena. Using a simple mathematical model describing the individual interactions of the wasps, we explain the functioning of the common stomach, an information center, which governs construction behavior and task change. Our central hypothesis is a symmetry between foragers who deposit water and foragers who withdraw water into and out of the common stomach. We combine this with a trade-off between acceptance and resistance to water transfer. We ultimately derive a mathematical function that relates the number of interactions that foragers complete with common stomach wasps during a foraging cycle. We use field data and additional model assumptions to calculate values of our model parameters, and we use these to explain why the fullness of the common stomach stabilizes just below 50 percent, why the average number of successful interactions between foragers and the wasps forming the common stomach is between 5 and 7, and why there is a variation in this number of interactions over time. Our explanation is that our proposed water exchange mechanism places natural bounds on the number of successful interactions possible, water exchange is set to optimize mediation of water through the common stomach, and the chance that foragers abort their task prematurely is very low.

How regulation based on a common stomach leads to economic optimization of honeybee foraging

Simple regulatory mechanisms based on the idea of the saturable 'common stomach' can control the regulation of protein foraging and protein allocation in honeybee colonies and colony-level responses to environmental changes. To study the economic benefits of pollen and nectar foraging strategies of honeybees to both plants and honeybees under different environmental conditions, a model was developed and analyzed. Reallocation of the foraging workforce according to the quality and availability of resources (an 'adaptive' strategy used by honeybees) is not only a successful strategy for the bees but also for plants, because intensified pollen foraging after rain periods (when nectar quality is low) compensates a major fraction of the pollination flights lost during the rain. The 'adaptive' strategy performed better than the'fixed' (steady, minimalistic, and non-adaptive foraging without feedback) or the 'proactive' (stockpiling in anticipation of rain) strategies in brood survival and or in nectar/sugar economics. The time pattern of rain periods has profound effect on the supply-and-demand of proteins. A tropical rain pattern leads to a shortage of the influx of pollen and nectar, but it has a less profound impact on brood mortality than a typical continental rainfall pattern. Allocating more bees for pollen foraging has a detrimental effect on the nectar stores, therefore while saving larvae from starvation the 'proactive' strategy could fail to collect enough nectar for surviving winter.

Divide et impera: subgoaling reduces the complexity of probabilistic inference and problem solving

It has long been recognized that humans (and possibly other animals) usually break problems down into smaller and more manageable problems using subgoals. Despite a general consensus that subgoaling helps problem solving, it is still unclear what the mechanisms guiding online subgoal selection are during the solution of novel problems for which predefined solutions are not available. Under which conditions does subgoaling lead to optimal behaviour? When is subgoaling better than solving a problem from start to finish? Which is the best number and sequence of subgoals to solve a given problem? How are these subgoals selected during online inference? Here, we present a computational account of subgoaling in problem solving. Following Occam's razor, we propose that good subgoals are those that permit planning solutions and controlling behaviour using less information resources, thus yielding parsimony in inference and control. We implement this principle using approximate probabilistic inference: subgoals are selected using a sampling method that considers the descriptive complexity of the resulting sub-problems. We validate the proposed method using a standard reinforcement learning benchmark (four-rooms scenario) and show that the proposed method requires less inferential steps and permits selecting more compact control programs compared to an equivalent procedure without subgoaling. Furthermore, we show that the proposed method offers a mechanistic explanation of the neuronal dynamics found in the prefrontal cortex of monkeys that solve planning problems. Our computational framework provides a novel integrative perspective on subgoaling and its adaptive advantages for planning, control and learning, such as for example lowering cognitive effort and working memory load.

Sting, Carry and Stock: How Corpse Availability Can Regulate De-Centralized Task Allocation in a Ponerine Ant Colony

We develop a model to produce plausible patterns of task partitioning in the ponerine ant Ectatomma ruidum based on the availability of living prey and prey corpses. The model is based on the organizational capabilities of a “common stomach” through which the colony utilizes the availability of a natural (food) substance as a major communication channel to regulate the income and expenditure of the very same substance. This communication channel has also a central role in regulating task partitioning of collective hunting behavior in a supply&demand-driven manner. Our model shows that task partitioning of the collective hunting behavior in E. ruidum can be explained by regulation due to a common stomach system. The saturation of the common stomach provides accessible information to individual ants so that they can adjust their hunting behavior accordingly by engaging in or by abandoning from stinging or transporting tasks. The common stomach is able to establish and to keep stabilized an effective mix of workforce to exploit the prey population and to transport food into the nest. This system is also able to react to external perturbations in a de-centralized homeostatic way, such as to changes in the prey density or to accumulation of food in the nest. In case of stable conditions the system develops towards an equilibrium concerning colony size and prey density. Our model shows that organization of work through a common stomach system can allow Ectatomma ruidum to collectively forage for food in a robust, reactive and reliable way. The model is compared to previously published models that followed a different modeling approach. Based on our model analysis we also suggest a series of experiments for which our model gives plausible predictions. These predictions are used to formulate a set of testable hypotheses that should be investigated empirically in future experimentation.