Negative feedback may suppress variation to improve collective foraging performance.

Social insect colonies use negative as well as positive feedback signals to regulate foraging behaviour. In ants and bees individual foragers have been observed to use negative pheromones or mechano-auditory signals to indicate that forage sources are not ideal, for example being unrewarded, crowded, or dangerous. Here we propose an additional function for negative feedback signals during foraging, variance reduction. We show that while on average populations will converge to desired distributions over forage patches both with and without negative feedback signals, in small populations negative feedback reduces variation around the target distribution compared to the use of positive feedback alone. Our results are independent of the nature of the target distribution, providing it can be achieved by foragers collecting only local information. Since robustness is a key aim for biological systems, and deviation from target foraging distributions may be costly, we argue that this could be a further important and hitherto overlooked reason that negative feedback signals are used by foraging social insects.

Magnitude-sensitive reaction times reveal non-linear time costs in multi-alternative decision-making.

Optimality analysis of value-based decisions in binary and multi-alternative choice settings predicts that reaction times should be sensitive only to differences in stimulus magnitudes, but not to overall absolute stimulus magnitude. Yet experimental work in the binary case has shown magnitude sensitive reaction times, and theory shows that this can be explained by switching from linear to multiplicative time costs, but also by nonlinear subjective utility. Thus disentangling explanations for observed magnitude sensitive reaction times is difficult. Here for the first time we extend the theoretical analysis of geometric time-discounting to ternary choices, and present novel experimental evidence for magnitude-sensitivity in such decisions, in both humans and slime moulds. We consider the optimal policies for all possible combinations of linear and geometric time costs, and linear and nonlinear utility; interestingly, geometric discounting emerges as the predominant explanation for magnitude sensitivity.

Inhibition and Excitation Shape Activity Selection: Effect of Oscillations in a Decision-Making Circuit.

Decision making is a complex task, and its underlying mechanisms that regulate behavior, such as the implementation of the coupling between physiological states and neural networks, are hard to decipher. To gain more insight into neural computations underlying ongoing binary decision-making tasks, we consider a neural circuit that guides the feeding behavior of a hypothetical animal making dietary choices. We adopt an inhibition motif from neural network theory and propose a dynamical system characterized by nonlinear feedback, which links mechanism (the implementation of the neural circuit and its coupling to the animal's nutritional state) and function (improving behavioral performance). A central inhibitory unit influences evidence-integrating excitatory units, which in our terms correspond to motivations competing for selection. We determine the parameter regime where the animal exhibits improved decision-making behavior and explain different behavioral outcomes by making the link between accessible states of the nonlinear neural circuit model and decision-making performance. We find that for given deficits in nutritional items, the variation of inhibition strength and ratio of excitation and inhibition strengths in the decision circuit allows the animal to enter an oscillatory phase that describes its internal motivational state. Our findings indicate that this oscillatory phase may improve the overall performance of the animal in an ongoing foraging task and underpin the importance of an integrated functional and mechanistic study of animal activity selection.

Speed-accuracy trade-offs in best-of-n collective decision making through heterogeneous mean-field modeling.

To succeed in their objectives, groups of individuals must be able to make quick and accurate collective decisions on the best option among a set of alternatives with different qualities. Group-living animals aim to do that all the time. Plants and fungi are thought to do so too. Swarms of autonomous robots can also be programed to make best-of-n decisions for solving tasks collaboratively. Ultimately, humans critically need it and so many times they should be better at it! Thanks to their mathematical tractability, simple models like the voter model and the local majority rule model have proven useful to describe the dynamics of such collective decision-making processes. To reach a consensus, individuals change their opinion by interacting with neighbors in their social network. At least among animals and robots, options with a better quality are exchanged more often and therefore spread faster than lower-quality options, leading to the collective selection of the best option. With our work, we study the impact of individuals making errors in pooling others' opinions caused, for example, by the need to reduce the cognitive load. Our analysis is grounded on the introduction of a model that generalizes the two existing models (local majority rule and voter model), showing a speed-accuracy trade-off regulated by the cognitive effort of individuals. We also investigate the impact of the interaction network topology on the collective dynamics. To do so, we extend our model and, by using the heterogeneous mean-field approach, we show the presence of another speed-accuracy trade-off regulated by network connectivity. An interesting result is that reduced network connectivity corresponds to an increase in collective decision accuracy.

Asynchrony rescues statistically optimal group decisions from information cascades through emergent leaders.

It is usually assumed that information cascades are most likely to occur when an early but incorrect opinion spreads through the group. Here, we analyse models of confidence-sharing in groups and reveal the opposite result: simple but plausible models of naive-Bayesian decision-making exhibit information cascades when group decisions are synchronous; however, when group decisions are asynchronous, the early decisions reached by Bayesian decision-makers tend to be correct and dominate the group consensus dynamics. Thus early decisions actually rescue the group from making errors, rather than contribute to it. We explore the likely realism of our assumed decision-making rule with reference to the evolution of mechanisms for aggregating social information, and known psychological and neuroscientific mechanisms.

A blockchain-based information market to incentivise cooperation in swarms of self-interested robots.

Robot swarms are generally considered to be composed of cooperative agents that, despite their limited individual capabilities, can perform difficult tasks by working together. However, in open swarms, where different robots can be added to the swarm by different parties with potentially competing interests, cooperation is but one of many strategies. We envision an information market where robots can buy and sell information through transactions stored on a distributed blockchain, and where cooperation is encouraged by the economy itself. As a proof of concept, we study a classical foraging task, where exchanging information with other robots is paramount to accomplish the task efficiently. We illustrate that even a single robot that lies to others-a so-called Byzantine robot-can heavily disrupt the swarm. Hence, we devise two protection mechanisms. Through an individual-level protection mechanism, robots are more sceptical about others' information and can detect and discard Byzantine information, at the cost of lower efficiency. Through a systemic protection mechanism based on economic rules regulating robot interactions, robots that sell honest information acquire over time more wealth than Byzantines selling false information. Our simulations show that a well-designed robot economy penalises misinformation spreading and protects the swarm from Byzantine behaviour. We believe economics-inspired swarm robotics is a promising research direction that exploits the timely opportunity for decentralised economies offered by blockchain technology.

Coherent movement of error-prone individuals through mechanical coupling.

We investigate how reliable movement can emerge in aggregates of highly error-prone individuals. The individuals-robotic modules-move stochastically using vibration motors. By coupling them via elastic links, soft-bodied aggregates can be created. We present distributed algorithms that enable the aggregates to move and deform reliably. The concept and algorithms are validated through formal analysis of the elastic couplings and experiments with aggregates comprising up to 49 physical modules-among the biggest soft-bodied aggregates to date made of autonomous modules. The experiments show that aggregates with elastic couplings can shrink and stretch their bodies, move with a precision that increases with the number of modules, and outperform aggregates with no, or rigid, couplings. Our findings demonstrate that mechanical couplings can play a vital role in reaching coherent motion among individuals with exceedingly limited and error-prone abilities, and may pave the way for low-power, stretchable robots for high-resolution monitoring and manipulation.

Magnitude-sensitivity: rethinking decision-making.

Magnitude-sensitivity refers to the result that performance in decision-making, across domains and organisms, is affected by the total value of the possible alternatives. This simple result offers a window into fundamental issues in decision-making and has led to a reconsideration of ecological decision-making, prominent computational models of decision-making, and optimal decision-making. Moreover, magnitude-sensitivity has inspired the design of new robotic systems that exploit natural solutions and apply optimal decision-making policies. In this article, we review the key theoretical and empirical results about magnitude-sensitivity and highlight the importance that this phenomenon has for the understanding of decision-making. Furthermore, we discuss open questions and ideas for future research.

Memory and communication efficient algorithm for decentralized counting of nodes in networks.

Node counting on a graph is subject to some fundamental theoretical limitations, yet a solution to such problems is necessary in many applications of graph theory to real-world systems, such as collective robotics and distributed sensor networks. Thus several stochastic and naïve deterministic algorithms for distributed graph size estimation or calculation have been provided. Here we present a deterministic and distributed algorithm that allows every node of a connected graph to determine the graph size in finite time, if an upper bound on the graph size is provided. The algorithm consists in the iterative aggregation of information in local hubs which then broadcast it throughout the whole graph. The proposed node-counting algorithm is on average more efficient in terms of node memory and communication cost than its previous deterministic counterpart for node counting, and appears comparable or more efficient in terms of average-case time complexity. As well as node counting, the algorithm is more broadly applicable to problems such as summation over graphs, quorum sensing, and spontaneous hierarchy creation.

When less is more: Robot swarms adapt better to changes with constrained communication.

To effectively perform collective monitoring of dynamic environments, a robot swarm needs to adapt to changes by processing the latest information and discarding outdated beliefs. We show that in a swarm composed of robots relying on local sensing, adaptation is better achieved if the robots have a shorter rather than longer communication range. This result is in contrast with the widespread belief that more communication links always improve the information exchange on a network. We tasked robots with reaching agreement on the best option currently available in their operating environment. We propose a variety of behaviors composed of reactive rules to process environmental and social information. Our study focuses on simple behaviors based on the voter model-a well-known minimal protocol to regulate social interactions-that can be implemented in minimalistic machines. Although different from each other, all behaviors confirm the general result: The ability of the swarm to adapt improves when robots have fewer communication links. The average number of links per robot reduces when the individual communication range or the robot density decreases. The analysis of the swarm dynamics via mean-field models suggests that our results generalize to other systems based on the voter model. Model predictions are confirmed by results of multiagent simulations and experiments with 50 Kilobot robots. Limiting the communication to a local neighborhood is a cheap decentralized solution to allow robot swarms to adapt to previously unknown information that is locally observed by a minority of the robots.

Multiscale Modelling Tool: Mathematical modelling of collective behaviour without the maths.

Collective behaviour is of fundamental importance in the life sciences, where it appears at levels of biological complexity from single cells to superorganisms, in demography and the social sciences, where it describes the behaviour of populations, and in the physical and engineering sciences, where it describes physical phenomena and can be used to design distributed systems. Reasoning about collective behaviour is inherently difficult, as the non-linear interactions between individuals give rise to complex emergent dynamics. Mathematical techniques have been developed to analyse systematically collective behaviour in such systems, yet these frequently require extensive formal training and technical ability to apply. Even for those with the requisite training and ability, analysis using these techniques can be laborious, time-consuming and error-prone. Together these difficulties raise a barrier-to-entry for practitioners wishing to analyse models of collective behaviour. However, rigorous modelling of collective behaviour is required to make progress in understanding and applying it. Here we present an accessible tool which aims to automate the process of modelling and analysing collective behaviour, as far as possible. We focus our attention on the general class of systems described by reaction kinetics, involving interactions between components that change state as a result, as these are easily understood and extracted from data by natural, physical and social scientists, and correspond to algorithms for component-level controllers in engineering applications. By providing simple automated access to advanced mathematical techniques from statistical physics, nonlinear dynamical systems analysis, and computational simulation, we hope to advance standards in modelling collective behaviour. At the same time, by providing expert users with access to the results of automated analyses, sophisticated investigations that could take significant effort are substantially facilitated. Our tool can be accessed online without installing software, uses a simple programmatic interface, and provides interactive graphical plots for users to develop understanding of their models.

Psychophysical Laws and the Superorganism.

Through theoretical analysis, we show how a superorganism may react to stimulus variations according to psychophysical laws observed in humans and other animals. We investigate an empirically-motivated honeybee house-hunting model, which describes a value-sensitive decision process over potential nest-sites, at the level of the colony. In this study, we show how colony decision time increases with the number of available nests, in agreement with the Hick-Hyman law of psychophysics, and decreases with mean nest quality, in agreement with Piéron's law. We also show that colony error rate depends on mean nest quality, and difference in quality, in agreement with Weber's law. Psychophysical laws, particularly Weber's law, have been found in diverse species, including unicellular organisms. Our theoretical results predict that superorganisms may also exhibit such behaviour, suggesting that these laws arise from fundamental mechanisms of information processing and decision-making. Finally, we propose a combined psychophysical law which unifies Hick-Hyman's law and Piéron's law, traditionally studied independently; this unified law makes predictions that can be empirically tested.

Model of the best-of-N nest-site selection process in honeybees.

The ability of a honeybee swarm to select the best nest site plays a fundamental role in determining the future colony's fitness. To date, the nest-site selection process has mostly been modeled and theoretically analyzed for the case of binary decisions. However, when the number of alternative nests is larger than two, the decision-process dynamics qualitatively change. In this work, we extend previous analyses of a value-sensitive decision-making mechanism to a decision process among N nests. First, we present the decision-making dynamics in the symmetric case of N equal-quality nests. Then, we generalize our findings to a best-of-N decision scenario with one superior nest and N-1 inferior nests, previously studied empirically in bees and ants. Whereas previous binary models highlighted the crucial role of inhibitory stop-signaling, the key parameter in our new analysis is the relative time invested by swarm members in individual discovery and in signaling behaviors. Our new analysis reveals conflicting pressures on this ratio in symmetric and best-of-N decisions, which could be solved through a time-dependent signaling strategy. Additionally, our analysis suggests how ecological factors determining the density of suitable nest sites may have led to selective pressures for an optimal stable signaling ratio.

A Design Pattern for Decentralised Decision Making.

The engineering of large-scale decentralised systems requires sound methodologies to guarantee the attainment of the desired macroscopic system-level behaviour given the microscopic individual-level implementation. While a general-purpose methodology is currently out of reach, specific solutions can be given to broad classes of problems by means of well-conceived design patterns. We propose a design pattern for collective decision making grounded on experimental/theoretical studies of the nest-site selection behaviour observed in honeybee swarms (Apis mellifera). The way in which honeybee swarms arrive at consensus is fairly well-understood at the macroscopic level. We provide formal guidelines for the microscopic implementation of collective decisions to quantitatively match the macroscopic predictions. We discuss implementation strategies based on both homogeneous and heterogeneous multiagent systems, and we provide means to deal with spatial and topological factors that have a bearing on the micro-macro link. Finally, we exploit the design pattern in two case studies that showcase the viability of the approach. Besides engineering, such a design pattern can prove useful for a deeper understanding of decision making in natural systems thanks to the inclusion of individual heterogeneities and spatial factors, which are often disregarded in theoretical modelling.