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.

Approximations of algorithmic and structural complexity validate cognitive-behavioral experimental results

Being able to objectively characterize the intrinsic complexity of behavioral patterns resulting from human or animal decisions is fundamental for deconvolving cognition and designing autonomous artificial intelligence systems. Yet complexity is difficult in practice, particularly when strings are short. By numerically approximating algorithmic (Kolmogorov) complexity (K), we establish an objective tool to characterize behavioral complexity. Next, we approximate structural (Bennett's Logical Depth) complexity (LD) to assess the amount of computation required for generating a behavioral string. We apply our toolbox to three landmark studies of animal behavior of increasing sophistication and degree of environmental influence, including studies of foraging communication by ants, flight patterns of fruit flies, and tactical deception and competition (e.g., predator-prey) strategies. We find that ants harness the environmental condition in their internal decision process, modulating their behavioral complexity accordingly. Our analysis of flight (fruit flies) invalidated the common hypothesis that animals navigating in an environment devoid of stimuli adopt a random strategy. Fruit flies exposed to a featureless environment deviated the most from Levy flight, suggesting an algorithmic bias in their attempt to devise a useful (navigation) strategy. Similarly, a logical depth analysis of rats revealed that the structural complexity of the rat always ends up matching the structural complexity of the competitor, with the rats' behavior simulating algorithmic randomness. Finally, we discuss how experiments on how humans perceive randomness suggest the existence of an algorithmic bias in our reasoning and decision processes, in line with our analysis of the animal experiments. This contrasts with the view of the mind as performing faulty computations when presented with randomized items. In summary, our formal toolbox objectively characterizes external constraints on putative models of the "internal" decision process in humans and animals.

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.

Insect-inspired AI for autonomous robots

Autonomous robots are expected to perform a wide range of sophisticated tasks in complex, unknown environments. However, available onboard computing capabilities and algorithms represent a considerable obstacle to reaching higher levels of autonomy, especially as robots get smaller and the end of Moore's law approaches. Here, we argue that inspiration from insect intelligence is a promising alternative to classic methods in robotics for the artificial intelligence (AI) needed for the autonomy of small, mobile robots. The advantage of insect intelligence stems from its resource efficiency (or parsimony) especially in terms of power and mass. First, we discuss the main aspects of insect intelligence underlying this parsimony: embodiment, sensory-motor coordination, and swarming. Then, we take stock of where insect-inspired AI stands as an alternative to other approaches to important robotic tasks such as navigation and identify open challenges on the road to its more widespread adoption. Last, we reflect on the types of processors that are suitable for implementing insect-inspired AI, from more traditional ones such as microcontrollers and field-programmable gate arrays to unconventional neuromorphic processors. We argue that even for neuromorphic processors, one should not simply apply existing AI algorithms but exploit insights from natural insect intelligence to get maximally efficient AI for robot autonomy.

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.

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.

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.

Non-numerical strategies used by bees to solve numerical cognition tasks

We examined how bees solve a visual discrimination task with stimuli commonly used in numerical cognition studies. Bees performed well on the task, but additional tests showed that they had learned continuous (non-numerical) cues. A network model using biologically plausible visual feature filtering and a simple associative rule was capable of learning the task using only continuous cues inherent in the training stimuli, with no numerical processing. This model was also able to reproduce behaviours that have been considered in other studies indicative of numerical cognition. Our results support the idea that a sense of magnitude may be more primitive and basic than a sense of number. Our findings highlight how problematic inadvertent continuous cues can be for studies of numerical cognition. This remains a deep issue within the field that requires increased vigilance and cleverness from the experimenter. We suggest ways of better assessing numerical cognition in non-speaking animals, including assessing the use of all alternative cues in one test, using cross-modal cues, analysing behavioural responses to detect underlying strategies, and finding the neural substrate.

Honeybees solve a multi-comparison ranking task by probability matching

Honeybees forage on diverse flowers which vary in the amount and type of rewards they offer, and bees are challenged with maximizing the resources they gather for their colony. That bees are effective foragers is clear, but how bees solve this type of complex multi-choice task is unknown. Here, we set bees a five-comparison choice task in which five colours differed in their probability of offering reward and punishment. The colours were ranked such that high ranked colours were more likely to offer reward, and the ranking was unambiguous. Bees' choices in unrewarded tests matched their individual experiences of reward and punishment of each colour, indicating bees solved this test not by comparing or ranking colours but by basing their colour choices on their history of reinforcement for each colour. Computational modelling suggests a structure like the honeybee mushroom body with reinforcement-related plasticity at both input and output can be sufficient for this cognitive strategy. We discuss how probability matching enables effective choices to be made without a need to compare any stimuli directly, and the use and limitations of this simple cognitive strategy for foraging animals.

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.

The influence of the few: a stable 'oligarchy' controls information flow in house-hunting ants

Animals that live together in groups often face difficult choices, such as which food resource to exploit, or which direction to flee in response to a predator. When there are costs associated with deadlock or group fragmentation, it is essential that the group achieves a consensus decision. Here, we study consensus formation in emigrating ant colonies faced with a binary choice between two identical nest-sites. By individually tagging each ant with a unique radio-frequency identification microchip, and then recording all ant-to-ant 'tandem runs'-stereotyped physical interactions that communicate information about potential nest-sites-we assembled the networks that trace the spread of consensus throughout the colony. Through repeated emigrations, we show that both the order in which these networks are assembled and the position of each individual within them are consistent from emigration to emigration. We demonstrate that the formation of the consensus is delegated to an influential but exclusive minority of highly active individuals-an 'oligarchy'-which is further divided into two subgroups, each specialized upon a different tandem running role. Finally, we show that communication primarily occurs between subgroups not within them, and further, that such between-group communication is more efficient than within-group communication.

Abstract concept learning in a simple neural network inspired by the insect brain

The capacity to learn abstract concepts such as 'sameness' and 'difference' is considered a higher-order cognitive function, typically thought to be dependent on top-down neocortical processing. It is therefore surprising that honey bees apparantly have this capacity. Here we report a model of the structures of the honey bee brain that can learn sameness and difference, as well as a range of complex and simple associative learning tasks. Our model is constrained by the known connections and properties of the mushroom body, including the protocerebral tract, and provides a good fit to the learning rates and performances of real bees in all tasks, including learning sameness and difference. The model proposes a novel mechanism for learning the abstract concepts of 'sameness' and 'difference' that is compatible with the insect brain, and is not dependent on top-down or executive control processing.

Interactions between immunotoxicants and parasite stress: Implications for host health

Many organisms face a wide variety of biotic and abiotic stressors which reduce individual survival, interacting to further reduce fitness. Here we studied the effects of two such interacting stressors: immunotoxicant exposure and parasite infection. We model the dynamics of a within-host infection and the associated immune response of an individual. We consider both the indirect sub-lethal effects on immunosuppression and the direct effects on health and mortality of individuals exposed to toxicants. We demonstrate that sub-lethal exposure to toxicants can promote infection through the suppression of the immune system. This happens through the depletion of the immune response which causes rapid proliferation in parasite load. We predict that the within-host parasite density is maximised by an intermediate toxicant exposure, rather than continuing to increase with toxicant exposure. In addition, high toxicant exposure can alter cellular regulation and cause the breakdown of normal healthy tissue, from which we infer higher mortality risk of the host. We classify this breakdown into three phases of increasing toxicant stress, and demonstrate the range of conditions under which toxicant exposure causes failure at the within-host level. These phases are determined by the relationship between the immunity status, overall cellular health and the level of toxicant exposure. We discuss the implications of our model in the context of individual bee health. Our model provides an assessment of how pesticide stress and infection interact to cause the breakdown of the within-host dynamics of individual bees.

Decision-making without a brain: how an amoeboid organism solves the two-armed bandit

Several recent studies hint at shared patterns in decision-making between taxonomically distant organisms, yet few studies demonstrate and dissect mechanisms of decision-making in simpler organisms. We examine decision-making in the unicellular slime mould Physarum polycephalum using a classical decision problem adapted from human and animal decision-making studies: the two-armed bandit problem. This problem has previously only been used to study organisms with brains, yet here we demonstrate that a brainless unicellular organism compares the relative qualities of multiple options, integrates over repeated samplings to perform well in random environments, and combines information on reward frequency and magnitude in order to make correct and adaptive decisions. We extend our inquiry by using Bayesian model selection to determine the most likely algorithm used by the cell when making decisions. We deduce that this algorithm centres around a tendency to exploit environments in proportion to their reward experienced through past sampling. The algorithm is intermediate in computational complexity between simple, reactionary heuristics and calculation-intensive optimal performance algorithms, yet it has very good relative performance. Our study provides insight into ancestral mechanisms of decision-making and suggests that fundamental principles of decision-making, information processing and even cognition are shared among diverse biological systems.

The evolution of mutualism with modifiers

Mutualisms are widespread, yet their evolution has received less theoretical attention than within-species social behaviors. Here, we extend previous models of unconditional pairwise interspecies social behavior, to consider selection for donation but also for donation-suppressing modifiers. We present conditions under which modifiers that suppress costly donation receive either positive or negative selection; assortment only at the donation locus always leads to selection for donation suppression, as in within-species greenbeard traits. However, genomewide assortment with modifier loci can lead to intermediate levels of donation, and these can differ in the two species even when payoffs from donation are additive and symmetric. When costly donation between species can evolve without being suppressed, we argue that it is most appropriately explained by indirect fitness benefits within the donating species, using partner species as vectors for altruism. Our work has implications for identifying both the stability and the ultimate beneficiaries of social behavior between species.

Individual Confidence-Weighting and Group Decision-Making

Group-living species frequently pool individual information so as to reach consensus decisions such as when and where to move, or whether a predator is present. Such opinion-pooling has been demonstrated empirically, and theoretical models have been proposed to explain why group decisions are more reliable than individual decisions. Behavioural ecology theory frequently assumes that all individuals have equal decision-making abilities, but decision theory relaxes this assumption and has been tested in human groups. We summarise relevant theory and argue for its applicability to collective animal decisions. We consider selective pressure on confidence-weighting in groups of related and unrelated individuals. We also consider which species and behaviours may provide evidence of confidence-weighting, paying particular attention to the sophisticated vocal communication of cooperative breeders.

Can natural selection encode Bayesian priors?

The evolutionary success of many organisms depends on their ability to make decisions based on estimates of the state of their environment (e.g., predation risk) from uncertain information. These decision problems have optimal solutions and individuals in nature are expected to evolve the behavioural mechanisms to make decisions as if using the optimal solutions. Bayesian inference is the optimal method to produce estimates from uncertain data, thus natural selection is expected to favour individuals with the behavioural mechanisms to make decisions as if they were computing Bayesian estimates in typically-experienced environments, although this does not necessarily imply that favoured decision-makers do perform Bayesian computations exactly. Each individual should evolve to behave as if updating a prior estimate of the unknown environment variable to a posterior estimate as it collects evidence. The prior estimate represents the decision-maker's default belief regarding the environment variable, i.e., the individual's default 'worldview' of the environment. This default belief has been hypothesised to be shaped by natural selection and represent the environment experienced by the individual's ancestors. We present an evolutionary model to explore how accurately Bayesian prior estimates can be encoded genetically and shaped by natural selection when decision-makers learn from uncertain information. The model simulates the evolution of a population of individuals that are required to estimate the probability of an event. Every individual has a prior estimate of this probability and collects noisy cues from the environment in order to update its prior belief to a Bayesian posterior estimate with the evidence gained. The prior is inherited and passed on to offspring. Fitness increases with the accuracy of the posterior estimates produced. Simulations show that prior estimates become accurate over evolutionary time. In addition to these 'Bayesian' individuals, we also introduce 'frequentist' individuals that do not use a prior and instead use frequentist inference when estimating the probability. Competition between the two shows that the former tend to have an evolutionary advantage over the latter, as predicted by the literature, and that this advantage is lowest when the information available to individuals poses the least uncertainty.

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.

Evidence for the speed-value trade-off: human and monkey decision making is magnitude sensitive

Complex natural systems from brains to bee swarms have evolved to make adaptive multifactorial decisions. Recent theoretical and empirical work suggests that many evolved systems may take advantage of common motifs across multiple domains. We are particularly interested in value sensitivity (i.e., sensitivity to the magnitude or intensity of the stimuli or reward under consideration) as a mechanism to resolve deadlocks adaptively. This mechanism favours long-term reward maximization over accuracy in a simple manner, because it avoids costly delays associated with ambivalence between similar options; speed-value trade-offs have been proposed to be evolutionarily advantageous for many kinds of decision. A key prediction of the value-sensitivity hypothesis is that choices between equally-valued options will proceed faster when the options have a high value than when they have a low value. However, value-sensitivity is not part of idealised choice models such as diffusion to bound. Here we examine two different choice behaviours in two different species, perceptual decisions in humans and economic choices in rhesus monkeys, to test this hypothesis. We observe the same value sensitivity in both human perceptual decisions and monkey value-based decisions. These results endorse the idea that neural decision systems make use of the same basic principle of value-sensitivity in order to resolve costly deadlocks and thus improve long-term reward intake.

A Model for an Angular Velocity-Tuned Motion Detector Accounting for Deviations in the Corridor-Centering Response of the Bee

We present a novel neurally based model for estimating angular velocity (AV) in the bee brain, capable of quantitatively reproducing experimental observations of visual odometry and corridor-centering in free-flying honeybees, including previously unaccounted for manipulations of behaviour. The model is fitted using electrophysiological data, and tested using behavioural data. Based on our model we suggest that the AV response can be considered as an evolutionary extension to the optomotor response. The detector is tested behaviourally in silico with the corridor-centering paradigm, where bees navigate down a corridor with gratings (square wave or sinusoidal) on the walls. When combined with an existing flight control algorithm the detector reproduces the invariance of the average flight path to the spatial frequency and contrast of the gratings, including deviations from perfect centering behaviour as found in the real bee's behaviour. In addition, the summed response of the detector to a unit distance movement along the corridor is constant for a large range of grating spatial frequencies, demonstrating that the detector can be used as a visual odometer.

Decision-making and action selection in insects: inspiration from vertebrate-based theories

Effective decision-making, one of the most crucial functions of the brain, entails the analysis of sensory information and the selection of appropriate behavior in response to stimuli. Here, we consider the current state of knowledge on the mechanisms of decision-making and action selection in the insect brain, with emphasis on the olfactory processing system. Theoretical and computational models of decision-making emphasize the importance of using inhibitory connections to couple evidence-accumulating pathways; this coupling allows for effective discrimination between competing alternatives and thus enables a decision maker to reach a stable unitary decision. Theory also shows that the coupling of pathways can be implemented using a variety of different mechanisms and vastly improves the performance of decision-making systems. The vertebrate basal ganglia appear to resolve stable action selection by being a point of convergence for multiple excitatory and inhibitory inputs such that only one possible response is selected and all other alternatives are suppressed. Similar principles appear to operate within the insect brain. The insect lateral protocerebrum (LP) serves as a point of convergence for multiple excitatory and inhibitory channels of olfactory information to effect stable decision and action selection, at least for olfactory information. The LP is a rather understudied region of the insect brain, yet this premotor region may be key to effective resolution of action section. We argue that it may be beneficial to use models developed to explore the operation of the vertebrate brain as inspiration when considering action selection in the invertebrate domain. Such an approach may facilitate the proposal of new hypotheses and furthermore frame experimental studies for how decision-making and action selection might be achieved in insects.

Cross inhibition improves activity selection when switching incurs time costs

We consider a behavioural model of an animal choosing between two activities, based on positive feedback, and examine the effect of introducing cross inhibition between the motivations for the two activities. While cross-inhibition has previously been included in models of decision making, the question of what benefit it may provide to an animal’s activity selection behaviour has not previously been studied. In neuroscience and in collective behaviour cross-inhibition, and other equivalent means of coupling evidence-accumulating pathways, have been shown to approximate statistically-optimal decision-making and to adaptively break deadlock, thereby improving decision performance. Switching between activities is an ongoing decision process yet here we also find that cross-inhibition robustly improves its efficiency, by reducing the frequency of costly switches between behaviours.

Self-deception can evolve under appropriate costs

Apparent biases in decision making by animals, including humans, seem to present an evolutionary puzzle, since one would expect decisions based on biased (unrealistic) information to be suboptimal. Although cognitive biases are hard to diagnose in real animals (Marshall et al., 2013b), we investigate Trivers’ proposal that individuals should self-deceive first in order to better deceive others (Trivers, 2011). Although this proposal has been scrutinized extensively (Bandura et al., 2011) it has not been formally modelled. We present the first model designed to investigate Trivers’ proposal. We introduce an extension to a recent model of the evolution of self-deception (Johnson and Fowler, 2011). In the extended model individuals make decisions by taking directly into account the benefits and costs of each outcome and by choosing the course of action that can be estimated as the best with the information available. It is shown that in certain circumstances self-deceiving decision-makers are the most evolutionarily successful, even when there is no deception between these. In a further extension of this model individuals additionally exhibit deception biases and Trivers’ premise (that effective deception is less physiologically costly with the aid of self-deception) is incorporated. It is shown that under Trivers’ hypothesis natural selection favors individuals that self-deceive as they deceive others.

Adaptive topographies and equilibrium selection in an evolutionary game

It has long been known in the field of population genetics that adaptive topographies, in which population equilibria maximise mean population fitness for a trait regardless of its genetic bases, do not exist. Whether one chooses to model selection acting on a single locus or multiple loci does matter. In evolutionary game theory, analysis of a simple and general game involving distinct roles for the two players has shown that whether strategies are modelled using a single ‘locus’ or one ‘locus’ for each role, the stable population equilibria are unchanged and correspond to the fitness-maximising evolutionary stable strategies of the game. This is curious given the aforementioned population genetical results on the importance of the genetic bases of traits. Here we present a dynamical systems analysis of the game with roles detailing how, while the stable equilibria in this game are unchanged by the number of ‘loci’ modelled, equilibrium selection may differ under the two modelling approaches.

Queller's separation condition explained and defended

The theories of inclusive fitness and multilevel selection provide alternative perspectives on social evolution. The question of whether these perspectives are of equal generality remains a divisive issue. In an analysis based on the Price equation, Queller argued (by means of a principle he called the separation condition) that the two approaches are subject to the same limitations, arising from their fundamentally quantitative-genetical character. Recently, van Veelen et al. have challenged Queller's results, using this as the basis for a broader critique of the Price equation, the separation condition, and the very notion of inclusive fitness. Here we show that the van Veelen et al. model, when analyzed in the way Queller intended, confirms rather than refutes his original conclusions. We thereby confirm (i) that Queller's separation condition remains a legitimate theoretical principle and (ii) that the standard inclusive fitness and multilevel approaches are indeed subject to the same limitations.

A mechanism for value-sensitive decision-making

We present a dynamical systems analysis of a decision-making mechanism inspired by collective choice in house-hunting honeybee swarms, revealing the crucial role of cross-inhibitory 'stop-signalling' in improving the decision-making capabilities. We show that strength of cross-inhibition is a decision-parameter influencing how decisions depend both on the difference in value and on the mean value of the alternatives; this is in contrast to many previous mechanistic models of decision-making, which are typically sensitive to decision accuracy rather than the value of the option chosen. The strength of cross-inhibition determines when deadlock over similarly valued alternatives is maintained or broken, as a function of the mean value; thus, changes in cross-inhibition strength allow adaptive time-dependent decision-making strategies. Cross-inhibition also tunes the minimum difference between alternatives required for reliable discrimination, in a manner similar to Weber's law of just-noticeable difference. Finally, cross-inhibition tunes the speed-accuracy trade-off realised when differences in the values of the alternatives are sufficiently large to matter. We propose that the model, and the significant role of the values of the alternatives, may describe other decision-making systems, including intracellular regulatory circuits, and simple neural circuits, and may provide guidance in the design of decision-making algorithms for artificial systems, particularly those functioning without centralised control.

Ubiquity symposium: Evolutionary computation and the processes of life

While evolution has inspired algorithmic methods of heuristic optimization, little has been done in the way of using concepts of computation to advance our understanding of salient aspects of biological phenomena. The authors argue under reasonable assumptions, interesting conclusions can be drawn that are of relevance to behavioral evolution. The authors will focus on two important features of life---robustness and fitness---which, they will argue, are related to algorithmic probability and to the thermodynamics of computation, disciplines that may be capable of modeling key features of living organisms, and which can be used in formulating new algorithms of evolutionary computation.

Consistent implementation of decisions in the brain

Despite the complexity and variability of decision processes, motor responses are generally stereotypical and independent of decision difficulty. How is this consistency achieved? Through an engineering analogy we consider how and why a system should be designed to realise not only flexible decision-making, but also consistent decision implementation. We specifically consider neurobiologically-plausible accumulator models of decision-making, in which decisions are made when a decision threshold is reached. To trade-off between the speed and accuracy of the decision in these models, one can either adjust the thresholds themselves or, equivalently, fix the thresholds and adjust baseline activation. Here we review how this equivalence can be implemented in such models. We then argue that manipulating baseline activation is preferable as it realises consistent decision implementation by ensuring consistency of motor inputs, summarise empirical evidence in support of this hypothesis, and suggest that it could be a general principle of decision making and implementation. Our goal is therefore to review how neurobiologically-plausible models of decision-making can manipulate speed-accuracy trade-offs using different mechanisms, to consider which of these mechanisms has more desirable decision-implementation properties, and then review the relevant neuroscientific data on which mechanism brains actually use.

Do ants need to be old and experienced to teach?

Learning is widespread in invertebrates. However, whether social insects improve their recruitment skills with experience is only beginning to be investigated. Tandem running is a one-to-one form of recruitment used by certain species of ant. It is a remarkable communication system that meets widely accepted criteria for teaching in non-human animals. Here, we determined experimentally to what extent participation in, and efficient execution of, tandem running depends on either the age or the experience of worker ants. To investigate these issues, we constructed colonies of the ant Temnothorax albipennis with different compositions of inexperienced and experienced workers from different age cohorts and then examined which ants participated in tandem runs when they emigrated. Our results show that the ability to participate actively in recruitment by tandem running is present in all worker age groups but the propensity to participate varies with experience rather than age per se. Experienced individuals were more likely to engage in tandem runs, either as leaders or as followers, than young inexperienced individuals, and older experienced ants were more likely to lead tandems than older inexperienced ants. Young inexperienced ants led faster, more rapidly dispersing and less accurately orientated tandem runs than the older experienced ants. Our study suggests that experience (rather than age per se) coupled to stimulus threshold responses might interact to promote a division of labour so that a suitable number of workers actively participate in tandem runs.

Does natural selection favour the Rescorla-Wagner rule?

A fundamental question relating to animal behaviour is how animals learn; in particular, how they come to associate stimuli with rewards. Numerous empirical findings can be explained by assuming that animals use some mechanism similar to the Rescorla-Wagner learning rule, which is a relatively simple and highly general method of updating the associative strength between different stimuli. However, the Rescorla-Wagner rule is often not optimal, which raises the question of why a rule with such properties should have evolved. We consider the evolution of learning rules in a simple environment where there exists an optimal rule of similar complexity to the Rescorla-Wagner rule. We show that because the Rescorla-Wagner rule is less sensitive to changes in its parameters than the optimal rule, there is a wider range of parameter values over which the rule structure is initially viable. Consequently, the Rescorla-Wagner rule can be favoured by natural selection, ahead of other rules which are more accurate.

Stop Signals Provide Cross Inhibition in Collective Decision-Making by Honeybee Swarms

Honeybee swarms and complex brains show many parallels in how they make decisions. In both, separate populations of units (bees or neurons) integrate noisy evidence for alternatives, and, when one population exceeds a threshold, the alternative it represents is chosen. We show that a key feature of a brain—cross inhibition between the evidence-accumulating populations—also exists in a swarm as it chooses its nesting site. Nest-site scouts send inhibitory stop signals to other scouts producing waggle dances, causing them to cease dancing, and each scout targets scouts’ reporting sites other than her own. An analytic model shows that cross inhibition between populations of scout bees increases the reliability of swarm decision-making by solving the problem of deadlock over equal sites.

Is optimism optimal? Functional causes of apparent behavioural biases

We review the use of the terms 'optimism' and 'pessimism' to characterize particular types of behaviour in non-human animals. Animals can certainly behave as though they are optimistic or pessimistic with respect to specific motivations, as documented by an extensive range of examples in the literature. However, in surveying such examples we find that these terms are often poorly defined and are liable to lead to confusion. Furthermore, when considering behaviour within the framework of optimal decision theory using appropriate currencies, it is often misleading to describe animals as optimistic or pessimistic. There are two common misunderstandings. First, some apparent cases of biased behaviour result from misidentifying the currencies and pay-offs the animals should be maximising. Second, actions that do not maximise short-term pay-offs have sometimes been described as optimistic or pessimistic when in fact they are optimal in the long term; we show how such situations can be understood from the perspective of bandit models. Rather than describing suboptimal, unrealistic behaviour, the terms optimism and pessimism are better restricted to informal usage. Our review highlights the importance of choosing the relevant currency when attempting to predict the action of natural selection.

A simple threshold rule is sufficient to explain sophisticated collective decision-making

Decision-making animals can use slow-but-accurate strategies, such as making multiple comparisons, or opt for simpler, faster strategies to find a 'good enough' option. Social animals make collective decisions about many group behaviours including foraging and migration. The key to the collective choice lies with individual behaviour. We present a case study of a collective decision-making process (house-hunting ants, Temnothorax albipennis), in which a previously proposed decision strategy involved both quality-dependent hesitancy and direct comparisons of nests by scouts. An alternative possible decision strategy is that scouting ants use a very simple quality-dependent threshold rule to decide whether to recruit nest-mates to a new site or search for alternatives. We use analytical and simulation modelling to demonstrate that this simple rule is sufficient to explain empirical patterns from three studies of collective decision-making in ants, and can account parsimoniously for apparent comparison by individuals and apparent hesitancy (recruitment latency) effects, when available nests differ strongly in quality. This highlights the need to carefully design experiments to detect individual comparison. We present empirical data strongly suggesting that best-of-n comparison is not used by individual ants, although individual sequential comparisons are not ruled out. However, by using a simple threshold rule, decision-making groups are able to effectively compare options, without relying on any form of direct comparison of alternatives by individuals. This parsimonious mechanism could promote collective rationality in group decision-making.

Inclusive fitness theory and eusociality

Arising from M. A. Nowak, C. E. Tarnita & E. O. Wilson 466, 1057-1062 (2010); Nowak et al. reply. Nowak et al. argue that inclusive fitness theory has been of little value in explaining the natural world, and that it has led to negligible progress in explaining the evolution of eusociality. However, we believe that their arguments are based upon a misunderstanding of evolutionary theory and a misrepresentation of the empirical literature. We will focus our comments on three general issues.

Decision-making under uncertainty: biases and Bayesians

Animals (including humans) often face circumstances in which the best choice of action is not certain. Environmental cues may be ambiguous, and choices may be risky. This paper reviews the theoretical side of decision-making under uncertainty, particularly with regard to unknown risk (ambiguity). We use simple models to show that, irrespective of pay-offs, whether it is optimal to bias probability estimates depends upon how those estimates have been generated. In particular, if estimates have been calculated in a Bayesian framework with a sensible prior, it is best to use unbiased estimates. We review the extent of evidence for and against viewing animals (including humans) as Bayesian decision-makers. We pay particular attention to the Ellsberg Paradox, a classic result from experimental economics, in which human subjects appear to deviate from optimal decision-making by demonstrating an apparent aversion to ambiguity in a choice between two options with equal expected rewards. The paradox initially seems to be an example where decision-making estimates are biased relative to the Bayesian optimum. We discuss the extent to which the Bayesian paradigm might be applied to the evolution of decision-makers and how the Ellsberg Paradox may, with a deeper understanding, be resolved.

The donation game with roles played between relatives

We consider a social game with two choices, played between two relatives, where roles are assigned to individuals so that the interaction is asymmetric. Behaviour in each of the two roles is determined by a separate genetic locus. Such asymmetric interactions between relatives, in which individuals occupy different behavioural contexts, may occur in nature, for example between adult parents and juvenile offspring. The social game considered is known to be equivalent to a donation game with non-additive payoffs, and has previously been analysed for the single locus case, both for discrete and continuous strategy traits. We present an inclusive fitness analysis of the discrete trait game with roles and recover equilibrium conditions including fixation of selfish or altruistic behaviour under both behavioural contexts, or fixation of selfish behaviour under one context and altruistic behaviour under the other context. These equilibrium solutions assume that the payoff matrices under each behavioural context are identical. The equilibria possible do depend crucially, however, on the deviation from payoff additivity that occurs when both interacting individuals act altruistically.

On optimal decision-making in brains and social insect colonies

The problem of how to compromise between speed and accuracy in decision-making faces organisms at many levels of biological complexity. Striking parallels are evident between decision-making in primate brains and collective decision-making in social insect colonies: in both systems, separate populations accumulate evidence for alternative choices; when one population reaches a threshold, a decision is made for the corresponding alternative, and this threshold may be varied to compromise between the speed and the accuracy of decision-making. In primate decision-making, simple models of these processes have been shown, under certain parametrizations, to implement the statistically optimal procedure that minimizes decision time for any given error rate. In this paper, we adapt these same analysis techniques and apply them to new models of collective decision-making in social insect colonies. We show that social insect colonies may also be able to achieve statistically optimal collective decision-making in a very similar way to primate brains, via direct competition between evidence-accumulating populations. This optimality result makes testable predictions for how collective decision-making in social insects should be organized. Our approach also represents the first attempt to identify a common theoretical framework for the study of decision-making in diverse biological systems.

Mammalian choices: combining fast-but-inaccurate and slow-but-accurate decision-making systems

Empirical findings suggest that the mammalian brain has two decision-making systems that act at different speeds. We represent the faster system using standard signal detection theory. We represent the slower (but more accurate) cortical system as the integration of sensory evidence over time until a certain level of confidence is reached. We then consider how two such systems should be combined optimally for a range of information linkage mechanisms. We conclude with some performance predictions that will hold if our representation is realistic.

Why do house-hunting ants recruit in both directions?

To perform tasks, organisms often use multiple procedures. Explaining the breadth of such behavioural repertoires is not always straightforward. During house hunting, colonies of Temnothorax albipennis ants use a range of behaviours to organise their emigrations. In particular, the ants use tandem running to recruit naïve ants to potential nest sites. Initially, they use forward tandem runs (FTRs) in which one leader takes a single follower along the route from the old nest to the new one. Later, they use reverse tandem runs (RTRs) in the opposite direction. Tandem runs are used to teach active ants the route between the nests, so that they can be involved quickly in nest evaluation and subsequent recruitment. When a quorum of decision-makers at the new nest is reached, they switch to carrying nestmates. This is three times faster than tandem running. As a rule, having more FTRs early should thus mean faster emigrations, thereby reducing the colony’s vulnerability. So why do ants use RTRs, which are both slow and late? It would seem quicker and simpler for the ants to use more FTRs (and higher quorums) to have enough knowledgeable ants to do all the carrying. In this study, we present the first testable theoretical explanation for the role of RTRs. We set out to find the theoretically fastest emigration strategy for a set of emigration conditions. We conclude that RTRs can have a positive effect on emigration speed if FTRs are limited. In these cases, low quorums together with lots of reverse tandem running give the fastest emigration.

Noise, cost and speed-accuracy trade-offs: decision-making in a decentralized system

Many natural and artificial decision-making systems face decision problems where there is an inherent compromise between two or more objectives. One such common compromise is between the speed and accuracy of a decision. The ability to exploit the characteristics of a decision problem in order to vary between the extremes of making maximally rapid, or maximally accurate decisions, is a useful property of such systems. Colonies of the ant Temnothorax albipennis (formerly Leptothorax albipennis) are a paradigmatic decentralized decision-making system, and have been shown flexibly to compromise accuracy for speed when making decisions during house-hunting. During emigration, a colony must typically evaluate and choose between several possible alternative new nest sites of differing quality. In this paper, we examine this speed-accuracy trade-off through modelling, and conclude that noise and time-cost of assessing alternative choices are likely to be significant for T. albipennis. Noise and cost of such assessments are likely to mean that T. albipennis' decision-making mechanism is Pareto-optimal in one crucial regard; increasing the willingness of individuals to change their decisions cannot improve collective accuracy overall without impairing speed. We propose that a decentralized control algorithm based on this emigration behaviour may be derived for applications in engineering domains and specify the characteristics of the problems to which it should be suited, based on our new results.

Kin selection may inhibit the evolution of reciprocation

Kin selection and reciprocal cooperation provide two candidate explanations for the evolution of cooperation. Models of the evolution of cooperation have typically focussed on one or the other mechanism, despite claims that kin selection could pave the way for the evolution of reciprocal cooperation. We describe a computer simulation model that explicitly supports both kin selection and reciprocal cooperation. The model simulates a viscous population of discrete individuals with social interaction taking the form of the Prisoner's Dilemma and selection acting on performance in these interactions. We recount how the analytical and empirical study of this model led to the conclusion that kin selection may actually inhibit the evolution of effective strategies for establishing reciprocal cooperation.