Collective behavior based on self-organization has been shown in group-living animals from insects to vertebrates. These findings have stimulated engineers to investigate approaches for the coordination of autonomous multirobot systems based on self-organization. In this experimental study, we show collective decision-making by mixed groups of cockroaches and socially integrated autonomous robots, leading to shared shelter selection. Individuals, natural or artificial, are perceived as equivalent, and the collective decision emerges from nonlinear feedbacks based on local interactions. Even when in the minority, robots can modulate the collective decision-making process and produce a global pattern not observed in their absence. These results demonstrate the possibility of using intelligent autonomous devices to study and control self-organized behavioral patterns in group-living animals.

We use a core molecular model capable of generating circadian rhythms to assess the robustness of circadian oscillations with respect to molecular noise. The model is based on the negative feedback exerted by a regulatory protein on the expression of its gene. Such a negative regulatory mechanism underlies circadian oscillations of the PER protein in Drosophila and of the FRQ protein in Neurospora. The model incorporates gene transcription into mRNA, translation of mRNA into protein, reversible phosphorylation leading to degradation of the regulatory protein, transport of the latter into the nucleus, and repression of gene expression by the nuclear form of the protein. To assess the effect of molecular noise, we perform stochastic simulations after decomposing the deterministic model into elementary reaction steps. The oscillations predicted by the stochastic simulations agree with those obtained with the deterministic version of the model. We show that robust circadian oscillations can occur already with a limited number of mRNA and protein molecules, in the range of tens and hundreds, respectively. Entrainment by light͞dark cycles and cooperativity in repression enhance the robustness of circadian oscillations with respect to molecular noise.circadian clocks ͉ stochastic simulations ͉ model ͉ Drosophila ͉ Neurospora

Group-living animals are often faced with choosing between one or more alternative resource sites. A central question in such collective decision making includes determining which individuals induce the decision and when. This experimental and theoretical study of shelter selection by cockroach groups demonstrates that choices can emerge through nonlinear interaction dynamics between equal individuals without perfect knowledge or leadership. We identify a simple mechanism whereby a decision is taken on the move with limited information and signaling and without comparison of available opportunities. This mechanism leads to optimal mean benefit for group individuals. Our model points to a generic self-organized collective decision-making process independent of animal species.collective behavior ͉ nonlinear dynamics ͉ self-organization

The question of how individuals in a population organize when living in groups arises for systems as different as a swarm of microorganisms or a flock of seagulls. The different patterns for moving collectively involve a wide spectrum of reasons, such as evading predators or optimizing food prospection. Also, the schooling pattern has often been associated with an advantage in terms of energy consumption. In this study, we use a popular aquarium fish, the red nose tetra fish, Hemigrammus bleheri, which is known to swim in highly cohesive groups, to analyze the schooling dynamics. In our experiments, fish swim in a shallow-water tunnel with controlled velocity, and stereoscopic video recordings are used to track the 3D positions of each individual in a school, as well as their tail-beating kinematics. Challenging the widespread idea of fish favoring a diamond pattern to swim more efficiently [Weihs D (1973) Nature 241:290-291], we observe that when fish are forced to swim fast-well above their free-swimming typical velocity, and hence in a situation where efficient swimming would be favored-the most frequent configuration is the "phalanx" or "soldier" formation, with all individuals swimming side by side. We explain this observation by considering the advantages of tail-beating synchronization between neighbors, which we have also characterized. Most importantly, we show that schooling is advantageous as compared with swimming alone from an energy-efficiency perspective.fish swimming | collective dynamics | pattern formation | synchronization | energy efficiency T he dynamics of animal groups is driven by many different factors, such as foraging, social life, or survival instinct against predators (1). The collective movements are built from local interactions between the individuals constituting the group (2, 3). Apart from behavioral aspects, the benefit from schooling has often been associated with group optimization in terms of hydrodynamic resistance (4). A fish school represents a typical case of such cohesive and collaborative complex systems. The fluid dynamical mechanisms influencing the motion of fish in a school have been described in essence in the early study of Weihs (5). He demonstrated, using a 2D model, that if each fish maintains a specific position within the school, forming a diamond pattern, the hydrodynamic interactions will globally improve the swimming performance. The basic idea is that fish in a school optimize swimming by interacting constructively with the vortices shed by the local leading individuals; such constructive interactions require a precise synchronization between fish. This study has been followed by an extensive number of studies modeling or simulating fish school swimming configurations to validate Weihs' hypothesis (6-8). It has been shown that by following this strategy, fish could improve their efficiency by ∼20% (8, 9). However, the idea that a beneficial situation in terms of swimming power can be achieved for the group by maintaining a specific complex pattern remai...

We report a study of the influence of molecular fluctuations on a limit-cycle model of circadian rhythms based on the regulatory network of a gene involved in a biochemical clock. The molecular fluctuations may become important because of the low number of molecules involved in such genetic regulatory networks at the subcellular level. The molecular fluctuations are described by a birth-and-death stochastic process ruled by the chemical master equation of Nicolis and co-workers and simulated by Gillespie’s algorithm. The robustness of the oscillations is characterized, in particular, by the probability distribution of the first-return times and the autocorrelation functions of the noisy oscillations. The half-life of the autocorrelation functions is studied as a function of the size of the system which controls the magnitude of the molecular fluctuations and of the degree of cooperativity of some reaction steps of the biochemical clock. The role of the attractivity of the limit cycle is also discussed.

In this work, we address the case of red nose tetra fish Hemigrammus bleheri swimming in groups in a uniform flow, giving special attention to the basic interactions and cooperative swimming of a single pair of fish. We first bring evidence of synchronization of the two fish, where the swimming modes are dominated by 'out-phase' and 'in-phase' configurations. We show that the transition to this synchronization state is correlated with the swimming speed (i.e. the flow rate), and thus with the magnitude of the hydrodynamic pressure generated by the fish body during each swimming cycle. From a careful spatio-temporal analysis corresponding to those synchronized modes, we characterize the distances between the two individuals in a pair in the basic schooling pattern. We test the conclusions of the analysis of fish pairs with a second set of experiments using groups of three fish. By identifying the typical spatial configurations, we explain how the nearest neighbour interactions constitute the building blocks of collective fish swimming.

Whereas it is relatively easy to account for the formation of concentric (target) waves of cAMP in the course of Dictyostelium discoideum aggregation after starvation, the origin of spiral waves remains obscure. We investigate a physiologically plausible mechanism for the spontaneous formation of spiral waves of cAMP in D. discoideum. The scenario relies on the developmental path associated with the continuous changes in the activity of enzymes such as adenylate cyclase and phosphodiesterase observed during the hours that follow starvation. These changes bring the cells successively from a nonexcitable state to an excitable state in which they relay suprathreshold cAMP pulses, and then to autonomous oscillations of cAMP, before the system returns to an excitable state. By analyzing a model for cAMP signaling based on receptor desensitization, we show that the desynchronization of cells on this developmental path triggers the formation of fully developed spirals of cAMP. Developmental paths that do not correspond to the sequence of dynamic transitions no relay-relay-oscillations-relay are less able or fail to give rise to the formation of spirals.The aggregation of Dictyostelium discoideum amoebae after starvation provides one of the best examples of spatiotemporal pattern formation at the supracellular level. This transition from a unicellular to a multicellular stage of the life cycle occurs by a chemotactic response to cyclic AMP (cAMP) signals emitted by aggregation centers in a periodic manner (1-3). Amoebae are capable of relaying the signals emitted periodically by a center located in their vicinity. This excitable response to periodic signals explains the wavelike nature of aggregation over territories whose dimensions can reach up to 1 cm: within each aggregation territory, the amoebae move toward a center in concentric or spiral waves with a periodicity of the order of 5 to 10 min (4 -6). Waves of cellular movement correlate with waves of cAMP (7); the latter present a striking similarity to waves observed in oscillator y chemical systems such as the BelousovZhabotinsky reaction (8).As shown by computer simulations using a model for cAMP relay and oscillations based on receptor desensitization proposed by Martiel and Goldbeter (9, 10), concentric waves can readily be explained by assuming the existence of a pacemaker generating periodic pulses of cAMP in the midst of a field of excitable cells. It is much more difficult to explain the origin of spontaneously occurring spiral waves of cAMP. A common artifice to obtain spirals, also used for Dictyostelium (11)(12)(13)(14), is to break concentric or planar waves; as the medium is excitable, spirals develop at the extremities of the broken wave. More recently, Pálsson and Cox (15) have used the above-mentioned model (9) to show that the random generation of cAMP pulses after the passage of a wave can give rise to the formation of spirals. Levine et al. (16) also considered the random generation of cAMP pulses in a hybrid model including cAMP produ...

Biomimetic robots are promising tools in animal behavioural studies. If they are socially integrated in a group of animals, they can produce calibrated social stimuli to test the animal responses. However, the design of such social robots is challenging as it involves both a luring capability including appropriate robot behaviours, and the acceptation of the robots by the animals as social companions. Here, we investigate the integration of a biomimetic robot driven by biomimetic behavioural models into a group of zebrafish (Danio rerio). The robot behaviours are based on a stochastic model linking zebrafish visual perception to individual behaviour and calibrated experimentally to correspond to the behaviour of zebrafish. We show that our robot can be integrated into a group of zebrafish, mimic their behaviour and exhibit similar collective dynamics compared to fish-only groups. This study shows that an autonomous biomimetic robot was enhanced by a biomimetic behavioural model so that it can socially integrate into groups of fish.