David J. T. Sumpter

From Disorder to Order in Marching Locusts

Recent models from theoretical physics have predicted that mass-migrating animal groups may share group-level properties, irrespective of the type of animals in the group. One key prediction is that as the density of animals in the group increases, a rapid transition occurs from disordered movement of individuals within the group to highly aligned collective motion. Understanding such a transition is crucial to the control of mobile swarming insect pests such as the desert locust. We confirmed the prediction of a rapid transition from disordered to ordered movement and identified a critical density for the onset of coordinated marching in locust nymphs. We also demonstrated a dynamic instability in motion at densities typical of locusts in the field, in which groups can switch direction without external perturbation, potentially facilitating the rapid transfer of directional information.

The principles of collective animal behaviour

In recent years, the concept of self-organization has been used to understand collective behaviour of animals. The central tenet of self-organization is that simple repeated interactions between individuals can produce complex adaptive patterns at the level of the group. Inspiration comes from patterns seen in physical systems, such as spiralling chemical waves, which arise without complexity at the level of the individual units of which the system is composed. The suggestion is that biological structures such as termite mounds, ant trail networks and even human crowds can be explained in terms of repeated interactions between the animals and their environment, without invoking individual complexity. Here, I review cases in which the self-organization approach has been successful in explaining collective behaviour of animal groups and societies. Ant pheromone trail networks, aggregation of cockroaches, the applause of opera audiences and the migration of fish schools have all been accurately described in terms of individuals following simple sets of rules. Unlike the simple units composing physical systems, however, animals are themselves complex entities, and other examples of collective behaviour, such as honey bee foraging with its myriad of dance signals and behavioural cues, cannot be fully understood in terms of simple individuals alone. I argue that the key to understanding collective behaviour lies in identifying the principles of the behavioural algorithms followed by individual animals and of how information flows between the animals. These principles, such as positive feedback, response thresholds and individual integrity, are repeatedly observed in very different animal societies. The future of collective behaviour research lies in classifying these principles, establishing the properties they produce at a group level and asking why they have evolved in so many different and distinct natural systems. Ultimately, this research could inform not only our understanding of animal societies, but also the principles by which we organize our own society.

Quorum decision-making facilitates information transfer in fish shoals

Despite the growing interest in collective phenomena such as “swarm intelligence” and “wisdom of the crowds,” little is known about the mechanisms underlying decision-making in vertebrate animal groups. How do animals use the behavior of others to make more accurate decisions, especially when it is not possible to identify which individuals possess pertinent information? One plausible answer is that individuals respond only when they see a threshold number of individuals perform a particular behavior. Here, we investigate the role of such “quorum responses” in the movement decisions of fish (three-spine stickleback, Gasterosteus aculeatus). We show that a quorum response to conspecifics can explain how sticklebacks make collective movement decisions, both in the absence and presence of a potential predation risk. Importantly our experimental work shows that a quorum response can reduce the likelihood of amplification of nonadaptive following behavior. Whereas the traveling direction of solitary fish was strongly influenced by a single replica conspecific, the replica was largely ignored by larger groups of four or eight sticklebacks under risk, and the addition of a second replica was required to exert influence on the movement decisions of such groups. Model simulations further predict that quorum responses by fish improve the accuracy and speed of their decision-making over that of independent decision-makers or those using a weak linear response. This study shows that effective and accurate information transfer in groups may be gained only through nonlinear responses of group members to each other, thus highlighting the importance of quorum decision-making.

Inferring the rules of interaction of shoaling fish

Collective motion, where large numbers of individuals move synchronously together, is achieved when individuals adopt interaction rules that determine how they respond to their neighbors’ movements and positions. These rules determine how group-living animals move, make decisions, and transmit information between individuals. Nonetheless, few studies have explicitly determined these interaction rules in moving groups, and very little is known about the interaction rules of fish. Here, we identify three key rules for the social interactions of mosquitofish (Gambusia holbrooki): (i) Attraction forces are important in maintaining group cohesion, while we find only weak evidence that fish align with their neighbor’s orientation; (ii) repulsion is mediated principally by changes in speed; (iii) although the positions and directions of all shoal members are highly correlated, individuals only respond to their single nearest neighbor. The last two of these rules are different from the classical models of collective animal motion, raising new questions about how fish and other animals self-organize on the move.

Fast and accurate decisions through collective vigilance in fish shoals

Although it has been suggested that large animal groups should make better decisions than smaller groups, there are few empirical demonstrations of this phenomenon and still fewer explanations of the how these improvements may be made. Here we show that both speed and accuracy of decision making increase with group size in fish shoals under predation threat. We examined two plausible mechanisms for this improvement: first, that groups are guided by a small proportion of high-quality decision makers and, second, that group members use self-organized division of vigilance. Repeated testing of individuals showed no evidence of different decision-making abilities between individual fish. Instead, we suggest that shoals achieve greater decision-making efficiencies through division of labor combined with social information transfer. Our results should prompt reconsideration of how we view cooperation in animal groups with fluid membership.

Inherent noise can facilitate coherence in collective swarm motion

Among the most striking aspects of the movement of many animal groups are their sudden coherent changes in direction. Recent observations of locusts and starlings have shown that this directional switching is an intrinsic property of their motion. Similar direction switches are seen in self-propelled particle and other models of group motion. Comprehending the factors that determine such switches is key to understanding the movement of these groups. Here, we adopt a coarse-grained approach to the study of directional switching in a self-propelled particle model assuming an underlying one-dimensional Fokker–Planck equation for the mean velocity of the particles. We continue with this assumption in analyzing experimental data on locusts and use a similar systematic Fokker–Planck equation coefficient estimation approach to extract the relevant information for the assumed Fokker–Planck equation underlying that experimental data. In the experiment itself the motion of groups of 5 to 100 locust nymphs was investigated in a homogeneous laboratory environment, helping us to establish the intrinsic dynamics of locust marching bands. We determine the mean time between direction switches as a function of group density for the experimental data and the self-propelled particle model. This systematic approach allows us to identify key differences between the experimental data and the model, revealing that individual locusts appear to increase the randomness of their movements in response to a loss of alignment by the group. We give a quantitative description of how locusts use noise to maintain swarm alignment. We discuss further how properties of individual animal behavior, inferred by using the Fokker–Planck equation coefficient estimation approach, can be implemented in the self-propelled particle model to replicate qualitatively the group level dynamics seen in the experimental data.

Consensus Decision Making by Fish

Decisions reached through consensus are often more accurate, because they efficiently utilize the diverse information possessed by group members [1-3]. A trust in consensus decision making underlies many of our democratic political and judicial institutions [4], as well as the design of web tools such as Google, Wikipedia, and prediction markets [5, 6]. In theory, consensus for the option favored by the majority of group members will lead to improved decision-making accuracy as group size increases [2, 4]. Although group-living animals are known to utilize social information [7-10], little is known about whether or not decision accuracy increases with group size. In order to reach consensus, group members must be able to integrate the disparate information they possess. Positive feedback, resulting from copying others, can spread information quickly through the group, but it can also result in all individuals making the same, possibly incorrect, choice [8, 11, 12]. On the other hand, if individuals never copy each other, their decision making remains independent and they fail to benefit from information exchange [4]. Here, we show how small groups of sticklebacks (Gasterosteus aculeatus) reach consensus when choosing which of two replica fish to follow. As group size increases, the fish make more accurate decisions, becoming better at discriminating subtle phenotypic differences of the replicas. A simple quorum rule proves sufficient to explain our observations, suggesting that animals can make accurate decisions without the need for complicated comparison of the information they possess. Furthermore, although submission to peers can lead to occasional cascades of incorrect decisions, these can be explained as a byproduct of what is usually accurate consensus decision making.

Phase transition between disordered and ordered foraging in Pharaoh's ants

The complex collective behavior seen in many insect societies strongly suggests that a minimum number of workers are required for these societies to function effectively. Here we investigated the transition between disordered and ordered foraging in the Pharaohs ant. We show that small colonies forage in a disorganized manner, with a transition to organized pheromone-based foraging in larger colonies. We also show that when food sources are difficult to locate through independent searching, this transition is first-order and exhibits hysteresis, comparable to a first-order phase transition found in many physical systems. To our knowledge, this is the first experimental evidence of a behavioral phase transition between a maladaptive (disorganized) and an adaptive (organized) state.

From nonlinearity to optimality: pheromone trail foraging by ants

Pheromone trails laid by foraging ants serve as a positive feedback mechanism for the sharing of information about food sources. This feedback is nonlinear, in that ants do not react in a proportionate manner to the amount of pheromone deposited. Instead, strong trails elicit disproportionately stronger responses than weak trails. Such nonlinearity has important implications for how a colony distributes its workforce, when confronted with a choice of food sources. We investigated how colonies of the Pharaohs ant, Monomorium pharaonis, distribute their workforce when offered a choice of two food sources of differing energetic value. By developing a nonlinear differential equation model of trail foraging, and comparing model with experiments, we examined how the ants allocate their workforce between the two food sources. In this allocation, the most profitable feeder (i.e. the feeder with the highest concentration of sugar syrup) was usually exploited by the majority of ants. The particular form of the nonlinear feedback in trail foraging means that when we offered the ants a choice between two feeders of equal profitability, foraging was biased to the feeder with the highest initial number of visitors. Taken together, our experiments illuminate how pheromones provide a mechanism whereby ants can efficiently allocate their workforce among the available food sources without centralized control.

The role of competition and clustering in population dynamics

A simple argument based on the distribution of individuals amongst discrete resource sites is used to show how the form of single species population models depends on the type of competition between, and the spatial clustering of, the individuals. For scramble competition between individuals, we confirm earlier demonstrations that the Ricker model is a direct consequence of a uniform random distribution of individuals across resources. By introducing spatial clustering of individuals according to a negative binomial distribution, we are able to derive the Hassell model. Furthermore, the tent map model is seen to be a consequence of scramble competition and an ideal-free distribution of individuals. To model contest competition under different degrees of spatial clustering we derive a new three-parameter model, of which the Beverton–Holt and Skellam models are special cases, where one of the parameters relates directly to the clustering distribution. Other population models, such as the quadratic model and the theta-Ricker models, cannot be derived in our framework. Taken together our derivations of population models allows us to make a more rigorous prescription for model choice when fitting to particular datasets.