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Review
, 361 (1465), 5-22

The Principles of Collective Animal Behaviour

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Review

The Principles of Collective Animal Behaviour

D J T Sumpter. Philos Trans R Soc Lond B Biol Sci.

Abstract

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.

Figures

Figure 1
Figure 1
Examples of collective animal behaviour. (a) Fish milling (reproduced with permission from Philip Colla, oceanlight.com). (b) The entrance crater to a nest of the ant Messor barbarus (from Theraulaz et al. 2003). (c) Traffic flow in Paris (reproduced with permission from Anthony Atkielski). (d) A bifurcation in a Pharaoh's ant trail (reproduced with permission from Duncan Jackson). (e) A Mexican wave at an American football game (taken from Farkas 2002). (f) A band of marching locusts (reproduced with permission from Iain Couzin).
Figure 2
Figure 2
Couzin et al. (2002) model of fish dynamics. (a) Illustration of the rules governing an individual in the fish model. The individual is centred at the origin: zor, zone of repulsion; zoo, zone of orientation; zoa, zone of attraction. The possible ‘blind volume’ behind an individual is also shown, α, field of perception. Collective behaviours exhibited by the model: (b) swarm, (c) torus and (d) dynamic parallel group.
Figure 3
Figure 3
The emergence of synchronized clapping (from Neda et al. 2000a,b). (a) The average noise intensity of a crowd through time. The first 10 s shows unsynchronized fast clapping, followed by a change to regular slower clapping until around 27 s, followed by synchronized clapping again. (b) A normalized histogram of clapping frequencies for 73 high school students (isolated from each other) for Mode I (solid) and Mode II (dashed) clapping.
Figure 4
Figure 4
How different systems increase output as a function of number of system components. (a) A linear increase in system output with number of components. (b) Model prediction of how the number of foragers visiting a feeder changes with number of ants in the colony. The black line is the predicted stable equilibrium for number of foragers visiting the feeder. The grey line is the unstable equilibrium. If fewer ants than the unstable equilibrium initially discover the source, then the total increase in foragers will be determined by the lower stable equilibrium. However, if the initial discovery is by a larger group than the unstable equilibrium, then the increase will be to the upper equilibrium. The model for the rate of change of ants going to the feeder, x, is dx/dt=αx+βx(nx)sx/(s+x). The figure shows the equilibrium solutions for parameter values: α=0.004 5, β=0.000 15, s=10 and n, the total number of ants, varied between 0 and 65 (see Beekman et al. 2001 for details). (c) Colony size versus the maximum increase in the number of ants walking to a feeder within 40 min of its introduction to an arena containing a starved ant colony (see Beekman et al. 2001 for details). The solid line connects the means of all trials at a given colony size, while crosses represent single trials.
Figure 5
Figure 5
Distribution of the proportion of individuals choosing one of two identical options in binary choice experiments where (a) Pharoah's ant are offered two identical (1.0 M sugar solution) food sources (reproduced from Sumpter & Beekman 2003) and (b) cockroaches are offered two identical shelters (reproduced from Ame et al. 2004).
Figure 6
Figure 6
Algorithms for social insect behaviour. (a) The ‘simple rule of thumb’ used by Lasius niger ants when exploiting liquid food sources (Detrain & Deneubourg 2002; from results of Mailleux et al. 2000). (b) Behaviour control structure of a honey bee forager. Depicted are the seven behavioural categories of foragers. The left part of the diagram represents internally driven categories, the right part, the externally driven categories. Upon locating a rich source, a searching forager becomes employed, whereas upon locating a poor source (including no source), a searching forager returns to the hive and becomes unemployed (for details see Biesmeijer & de Vries 2001). (c) Model of the behaviour of Temnothorax ants when emigrating. Boxes represent behavioural states and arrows transitions between them, labels indicate measured probabilities (Pratt et al. 2005). Colours indicate the four major levels of an ant's commitment to a candidate nest site: exploration (blue), assessment (red), canvassing (amber) and commitment (green).
Figure 7
Figure 7
Examples of response thresholds. (a) The probability of a recruiting Temnothorax albipennis ant performing a transport rather than a tandem run, as a function of the mean nest population (N) of the destination site on her immediately previous visit there (data from Pratt 2005, in press). The fitted line is N6.3/(20.26.3+N6.3). (b) The mean proportion of passer-by's looking up as a function of the size of a group (C) of people stood in the street looking up at a sixth floor window (taken from Milgram 1992). Fitted line is 0.92×C1.04/(1.221.04+C1.04), giving a threshold of 1.22. (c) The probability of a cockroach leaving a shelter as a function of the number of other cockroaches (C) on the site (taken from Ame et al. 2004). Fitted line is 0.06×1/(6+C2). (d) The probability per second of an ant moving away from a stopped group of ants as a function of the number of stopped ants (A; taken from Depickere et al. 2004). Fitted line is 0.35A2.125.

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