Symmetry restoring bifurcation in collective decision-making

Using neuronal models to capture burst-and-glide motion and leadership in fish

While mathematical models, in particular self-propelled particle models, capture many properties of large fish schools, they do not always capture the interactions of smaller shoals. Nor do these models tend to account for the use of intermittent locomotion, often referred to as burst-and-glide, by many species. In this paper, we propose a model of social burst-and-glide motion by combining a well-studied model of neuronal dynamics, the FitzHugh-Nagumo model, with a model of fish motion. We first show that our model can capture the motion of a single fish swimming down a channel. Extending to a two-fish model, where visual stimulus of a neighbour affects the internal burst or glide state of the fish, we observe a rich set of dynamics found in many species. These include: leader-follower behaviour; periodic changes in leadership; apparently random (i.e. chaotic) leadership change; and tit-for-tat turn taking. Moreover, unlike previous studies where a randomness is required for leadership switching to occur, we show that this can instead be the result of deterministic interactions. We give several empirically testable predictions for how bursting fish interact and discuss our results in light of recently established correlations between fish locomotion and brain activity.

Behavioural changes in slime moulds over time

Changes in behaviour over the lifetime of single-cell organisms have primarily been investigated in response to environmental stressors. However, growing evidence suggests that unicellular organisms undergo behavioural changes throughout their lifetime independently of the external environment. Here we studied how behavioural performances across different tasks vary with age in the acellular slime mould Physarum polycephalum. We tested slime moulds aged from 1 week to 100 weeks. First, we showed that migration speed decreases with age in favourable and adverse environments. Second, we showed that decision making and learning abilities do not deteriorate with age. Third, we revealed that old slime moulds can recover temporarily their behavioural performances if they go throughout a dormant stage or if they fuse with a young congener. Last, we observed the response of slime mould facing a choice between cues released by clone mates of different age. We found that both old and young slime moulds are attracted preferentially toward cues left by young slime moulds. Although many studies have studied behaviour in unicellular organisms, few have taken the step of looking for changes in behaviour over the lifetime of individuals. This study extends our knowledge of the behavioural plasticity of single-celled organisms and establishes slime moulds as a promising model to investigate the effect of ageing on behaviour at the cellular level. This article is part of a discussion meeting issue 'Collective behaviour through time'.

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.

Analysis of decisions based on option value (e.g. which pile of coins would you like?) suggests that the optimal rules correspond to simple mechanisms also known to be optimal for perceptual decisions (e.g. which light is brighter?) But, crucially, these analyses assume that the cost of time is linear—when the more usual assumption is made that time discounts multiplicatively (e.g. ‘a bird in the hand is worth two in the bush (and so two in the hand are worth four in the bush)’) then optimal decision-making looks quite different—in particular, the theory predicts that decision-making should be sensitive to the absolute magnitude of the opportunities, such as coin pile sizes, under consideration, in a way that the optimal perceptual mechanisms are not. As well as the theory, we present novel experimental evidence from human decision-making experiments, and foraging slime mould, of precisely such magnitude-sensitivity. This is a rare example of theory in behaviour making a falsifiable prediction that is confirmed in two, highly divergent, species, one with a brain and one without.

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.

Social insect colonies regulate the number of insects foraging at different food sources through a combination of positive and negative feedback signals. Through positive feedback signals—such as ants’ pheromone trails and bees’ waggle dances—insects recruit each other to increase the number of foragers committed to a food source that has been evaluated as profitable. Negative feedbacks are instead inhibitory signals that are delivered to reduce commitment to a food source where an unfavourable change has been detected, for example the arrival of a predator or a decrease in nutritional reward. Our mathematical analysis explains an additional function for negative feedback; inhibitory signals can also be useful in static conditions to reduce the variance in the number of insects allocated to each food source, thus better distributing insects among the available sources. Our results can help explain field observations that are not fully understood yet, such as the periodic delivery of a small number of inhibitory signals among honeybees visiting the same forage patch even in static conditions.

The Neglected Pieces of Designing Collective Decision-Making Processes

Autonomous decision-making is a fundamental requirement for the intelligent behavior of individual agents and systems. For artificial systems, one of the key design prerequisites is providing the system with the ability to make proper decisions. Current literature on collective artificial systems designs decision-making mechanisms inspired mostly by the successful natural systems. Nevertheless, most of the approaches focus on voting mechanisms and miss other fundamental aspects. In this paper, we aim to draw attention to the missed pieces for the design of efficient collective decision-making, mainly information processes in its two types of stimuli and options set.

Phenotypic variability predicts decision accuracy in unicellular organisms

When deciding between different options, animals including humans face the dilemma that fast decisions tend to be erroneous, whereas accurate decisions tend to be relatively slow. Recently, it has been suggested that differences in the efficacy with which animals make a decision relate closely to individual behavioural differences. In this paper, we tested this hypothesis in a unique unicellular organism, the slime mould Physarum polycephalum. We first confirmed that slime moulds differed consistently in their exploratory behaviour from 'fast' to 'slow' explorers. Second, we showed that slow explorers made more accurate decisions than fast explorers. Third, we demonstrated that slime moulds integrated food cues in time and achieved higher accuracy when sampling time was longer. Lastly, we showed that in a competition context, fast explorers excelled when a single food source was offered, while slow explorers excelled when two food sources varying in quality were offered. Our results revealed that individual differences in accuracy were partly driven by differences in exploratory behaviour. These findings support the hypothesis that decision-making abilities are associated with behavioural types, even in unicellular organisms.

Symmetry breaking and inter-clonal behavioural variability in a slime mould

Cells are dynamic systems capable of switching from isotropic growth to polarized growth even in the absence of any pre-existing external asymmetry. Here, we study this process of symmetry breaking in the acellular slime mould Physarum polycephalum. In these experiments, slime moulds could grow on two identical opposed sources of calcium. We highlighted a positive correlation between growth dynamic, level of symmetry breaking and calcium concentration. We identified three populations of slime moulds within our clonal lineage with similar symmetry breaking behaviours but different motility characteristics. These behavioural differences between slime moulds emerged in the absence of any environmental differences. Such behavioural plasticity could generate cellular diversity, which can be critical for survival.

Consensus or Deadlock? Consequences of Simple Behavioral Rules for Coordination in Group Decisions

Coordinated collective behaviors often emerge from simple rules governing the interactions of individuals in groups. We model mechanisms of coordination among ants during cooperative transport, a challenging task that requires a consensus on travel direction. Our goal is to determine whether groups following simple behavioral rules can reach a consensus using minimal information. Using deterministic and stochastic models, we investigate behavioral factors that affect coordination. We define and investigate three types of behavioral rules governing individual behavior that differ in the information available: individuals either 1) have no information, 2) can measure transport success, or 3) measure success while also knowing whether they are aligned with the majority. We find that groups break deadlocks only if individuals more readily give up when they are going against the majority, corresponding to rule type 3 –such groups are “informed.” These behavioral rules succeed through positive and negative feedbacks that are implemented in our model via a single mechanism: individuals only need to measure the relative group sizes to make effective decisions. We also find that groups reach consensus more quickly if they have either a shared bias, high sensitivity to group behavior, or finely tuned persistence. Each of these is a potential adaptation for efficient cooperative transport. This flexibility makes the behavioral rules in the informed case relatively robust to deficiencies in the individuals’ capabilities. While inspired by ants, our results are generalizable to other collective decisions with deadlocks, and demonstrate that groups of behaviorally simple individuals with no memory and extremely limited information can break symmetry and reach a consensus in a decision between two equal options.

Phenotypic variability in unicellular organisms: from calcium signalling to social behaviour

Historically, research has focused on the mean and often neglected the variance. However, variability in nature is observable at all scales: among cells within an individual, among individuals within a population and among populations within a species. A fundamental quest in biology now is to find the mechanisms that underlie variability. Here, we investigated behavioural variability in a unique unicellular organism, Physarum polycephalum. We combined experiments and models to show that variability in cell signalling contributes to major differences in behaviour underpinning some aspects of social interactions. First, following thousands of cells under various contexts, we identified distinct behavioural phenotypes: 'slow-regular-social', 'fast-regular-social' and 'fast-irregular-asocial'. Second, coupling chemical analysis and behavioural assays we found that calcium signalling is responsible for these behavioural phenotypes. Finally, we show that differences in signalling and behaviour led to alternative social strategies. Our results have considerable implications for our understanding of the emergence of variability in living organisms.