A data-driven method for reconstructing and modelling social interactions in moving animal groups.

Group-living organisms that collectively migrate range from cells and bacteria to human crowds, and include swarms of insects, schools of fish, and flocks of birds or ungulates. Unveiling the behavioural and cognitive mechanisms by which these groups coordinate their movements is a challenging task. These mechanisms take place at the individual scale and can be described as a combination of interactions between individuals and interactions between these individuals and the physical obstacles in the environment. Thanks to the development of novel tracking techniques that provide large and accurate datasets, the main characteristics of individual and collective behavioural patterns can be quantified with an unprecedented level of precision. However, in a large number of studies, social interactions are usually described by force map methods that only have a limited capacity of explanation and prediction, being rarely suitable for a direct implementation in a concise and explicit mathematical model. Here, we present a general method to extract the interactions between individuals that are involved in the coordination of collective movements in groups of organisms. We then apply this method to characterize social interactions in two species of shoaling fish, the rummy-nose tetra (Hemigrammus rhodostomus) and the zebrafish (Danio rerio), which both present a burst-and-coast motion. From the detailed quantitative description of individual-level interactions, it is thus possible to develop a quantitative model of the emergent dynamics observed at the group level, whose predictions can be checked against experimental results. This method can be applied to a wide range of biological and social systems. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Collective decision-making in white-faced capuchin monkeys.

In group-living animals, collective movements are a widespread phenomenon and occur through consensus decision. When one animal proposes a direction for group movement, the others decide to follow or not and hence take part in the decision-making process. This paper examines the temporal spread of individual responses after the departure of a first individual (the initiator) in a semi-free ranging group of white-faced capuchins (Cebus capucinus). We analysed 294 start attempts, 111 succeeding and 183 failing. Using a modelling approach, we have demonstrated that consensus decision-making for group movements is based on two complementary phenomena in this species: firstly, the joining together of group members thanks to a mimetic process; and secondly, a modulation of this phenomenon through the propensity of the initiator to give up (i.e. cancellation rate). This cancellation rate seems to be directly dependent upon the number of followers: the greater this number is, the lower the cancellation rate is seen to be. The coupling between joining and cancellation rates leads to a quorum: when three individuals join the initiator, the group collectively moves. If the initiator abandons the movement, this influences the joining behaviour of the other group members, which in return influences the initiator's behaviour. This study demonstrates the synergy between the initiator's behaviour and the self-organized mechanisms underlying group movements.

From individual to collective displacements in heterogeneous environments.

Animal displacement plays a central role in many ecological questions. It can be interpreted as a combination of components that only depend on the animal (for example a random walk) and external influences given by the heterogeneity of the environment. Here we treat the case where animals switch between random walks in a homogeneous 2D environment and its 1D boundary, combined with a tendency for wall-following behaviour (thigmotactism) that is treated as a Markovian process. In the first part we use mesoscopic techniques to derive from these assumptions a set of partial differential equations (PDE) with specific boundary conditions and parameters that are directly given by the individual displacement parameters. All assumptions and approximations made during this derivation are rigorously validated for the case of exploratory behaviour of the ant Messor sanctus. These PDE predict that the stationary density ratio between the 2D (centre) and 1D (border) environment only depends on the thigmotactic component, not on the size of the centre or border areas. In the second part we test this prediction with the same exploratory behaviour of M. sanctus, in particular when many ants move around simultaneously and may interact directly or indirectly. The prediction holds when there is a low degree of heterogeneity (simple square arena with straight borders), the collective behaviour is "simply" the sum of the individual behaviours. But this prediction breaks down when heterogeneity increases (obstacles inside the arena) due to the emergence of pheromone trails. Our approach may be applied to study the effects of animal displacement in any environment where the animals are confronted with an alternation of 2D space and 1D borders as for example in fragmented landscapes.

A new test of random walks in heterogeneous environments.

Environmental heterogeneities can change animal movement in two different manners. First, they can modify movement characteristics (move lengths or turning angles), in which case the movement remains of the diffusive kind. Second, they can bias displacement towards a particular direction in which case it becomes non-diffusive. We propose in this paper a simple method that only requires computing the mean length of a sample of trajectories in some bounded area to distinguish between these two kinds of movement. We show through simulations that the method allows to detect the presence of heterogeneities that orient animal movement. We apply it to experimental trajectories of Messor sancta ants engaged in corpse aggregation to show that their displacement is oriented at the contact of the formed corpse piles and that their trajectories become non-diffusive.

Model of droplet dynamics in the Argentine ant Linepithema Humile (Mayr).

The formation of droplets of ants Linepithema humile (Mayr) is observed under certain experimental conditions: a fluctuating aggregate forms at the end of a rod and a droplet containing up to 40 ants eventually falls down. When the flux of incoming ants is sufficient, this process can continue for several hours, leading to the formation and fall of tens of droplets. Previous work indicates that the time series of drop-to-drop intervals may result from a nonlinear low-dimensional dynamics, and the interdrop increments exhibit long-range anticorrelations. A model of aggregation and droplet formation, based on experimental observations, is introduced and shown to reproduce these properties.

Inspiration for optimization from social insect behaviour.

Research in social insect behaviour has provided computer scientists with powerful methods for designing distributed control and optimization algorithms. These techniques are being applied successfully to a variety of scientific and engineering problems. In addition to achieving good performance on a wide spectrum of 'static' problems, such techniques tend to exhibit a high degree of flexibility and robustness in a dynamic environment.

Three-dimensional architectures grown by simple 'stigmergic' agents.

A simple model of multi-agent three-dimensional construction is presented. The properties of this model are investigated. Based on these properties, a fitness function is defined to characterize the structured patterns that can be generated by the model. The fitness function assigns a value to each pattern. The choice of the fitness function is validated by the fact that human observers tend to view patterns with high (resp. low) fitness as structured (resp. unstructured). A genetic algorithm based on this fitness function is used to explore the space of possible patterns. The genetic algorithm is able to make use of sub-modules of existing patterns and recombine them to produce novel patterns, but strong epistatic interactions among genes make the fitness landscape rugged and prevent more complex patterns from being produced.

A brief history of stigmergy.

Stigmergy is a class of mechanisms that mediate animal-animal interactions. Its introduction in 1959 by Pierre-Paul Grassé made it possible to explain what had been until then considered paradoxical observations: In an insect society individuals work as if they were alone while their collective activities appear to be coordinated. In this article we describe the history of stigmergy in the context of social insects and discuss the general properties of two distinct stigmergic mechanisms: quantitative stigmergy and qualitative stigmergy.

Dominance orders in animal societies: the self-organization hypothesis revisited.

In previous papers (Theraulaz et al., 1995; Bonabeau et al., 1996) we suggested, following Hogeweg and Hesper (1983, 1985), that the formation of dominance orders in animal societies could result from a self-organizing process involving a double reinforcement mechanism: winners reinforce their probability of winning and losers reinforce their probability of losing. This assumption, and subsequent models relying on it, were based on empirical data on primitively eusocial wasps (Polistes dominulus). By reanalysing some of the experimental data that was previously thought to be irrelevant, we show that it is impossible to distinguish this assumption from a competing assumption based on preexisting differences among individuals. We propose experiments to help discriminate between the two assumptions and their corresponding models-the self-organization model and the correlational model. We urge other researchers to be cautious when interpreting their dominance data with the 'self-organization mindset'; in particular, 'winner and loser effects', which are often considered to give support to the self-organization assumption, are equally consistent with the correlational assumption.

Group and mass recruitment in ant colonies: the influence of contact rates

The influence of contact rates on the efficiency (the ability to exploit a profitable environment) and flexibility (the ability to track down a changing environment) of foraging in ants is studied theoretically in the case where foraging relies on a mixture of group and mass recruitment. It is shown that a combination of efficiency and flexibility can be reached across a range of group sizes if (1) mass recruitment is combined with a low level of group recruitment, and (2) contact rates are weakly regulated. These results are discussed in relation to empirical work. Copyright 1998 Academic Press

The synchronization of recruitment-based activities in ants.

A simple model of recruitment-based foraging in ants illustrates the idea that synchronized patterns of activity can endow a colony with the ability to forage more efficiently when a minimal number of active individuals is required to establish and maintain food source exploitation. This model, which can be extended to other activities that involve recruitment, may help explain why bursts of synchronization have been observed in several species of ants.

Within-brood competition and the optimal partitioning of parental investment.

In this article, we introduce a simple within-brood competitive growth model that maximizes parental fitness in unpredictable food conditions in species that exhibit parental care, progressive provisioning, and an initial brood overproduction. We argue that competition between siblings may provide a proximate mechanism for parents to adjust the number of surviving offspring or the social organization of the group in social species to food conditions.

Self-organization in social insects.

Self-organization was introduced originally in the context of physics and chemistry to describe how microscopic processes give rise to macroscopic stuctures in out-of-equilibrium systems, Recent research that extends this concept to ethology suggests that it provides a concise description of a wide range of collective phenomena in animals, especially in social insects. This description does not rely on individual complexity to account for complex spatiotemporal features that emerge at the colony level, but rather assumes that intractions among simple individuals can produce highly structured collective behaviours.

Coordination in distributed building.

A formal model of distributed building is presented that was inspired by the observation of wasp colonies. Algorithms have been obtained that allow a swarm of simple agents, moving randomly on a three-dimensional cubic lattice, to build coherent structures.

Joint memory.

Joint memory is defined as the property of a social group in actualizing its own past transformations. It may result from the coupling of individual memories or be inscribed in the external environment. The concept of joint memory becomes heuristic when it subsumes an ensemble of social processes that are sufficiently integrated to be treated as an entity belonging to the real world. In social insects, colonies can perform action-perception loops which give rise to collective outcomes based on past experience; selective pressures could favour individual behavioural algorithms the combination of which provides a historical record organizing activities both in space and time. In contrast, social groups do not appear sufficiently autonomous in most vertebrates for joint memory be more than a way of seeing collective performances. However, in human beings, the development of external representations has made possible the growth of a socially distributed cognition; the accumulation of epigenetic events through cultural processes produces a set of material and symbolic products that feed back upon the conditions of evolution of the species.