Part I
The nature, historical perspective and conceptual background of interpersonal coordination tendencies
The emergence of collective locomotion
Kevin W. Rio and William H. Warren
Collective locomotion is a ubiquitous feature of the natural world, found in living systems great and small â from migrating skin cells to flocks of starlings. In humans, collective locomotion is one form of interpersonal coordination, a term that encompasses many of the social and cultural activities that define our species. Whereas studies of interpersonal coordination often focus on the synchronization of rhythmic movement, the domain also includes non-rhythmic coordination, which calls for other tools of analysis. In this introductory chapter our goal is to examine collective locomotion in bird flocks, fish schools and human crowds as a case study for understanding this broader range of interpersonal coordination. Despite vast differences across species â including morphology, neurophysiology, perception and cognition â these seemingly diverse phenomena obey common principles of self-organization and may share similar local mechanisms.
Introduction
Collective locomotion as self-organization
Herring swim together in schools ranging well into the millions of individuals (Misund, 1993), forming characteristic shapes (Partridge, Pitcher, Cullen, & Wilson, 1980) and responding effectively when attacked by predators (Nottestad & Axelsen, 1999). How can this be? How can such large-scale order emerge out of the behaviour of relatively simple animals, with limited perceptual and cognitive capabilities?
The most complete and compelling answer comes from the study of self-organization (Couzin & Krause, 2003; Haken, 2006). Camazine et al. (2001) describe self-organization as âa process in which the pattern at the global level of a system emerges solely from numerous interactions among the lower-level components of a system. Moreover, the rules specifying interactions among the systemâs components are executed using only local information, without reference to the global patternâ. Individual fish are perceptually coupled to their nearby neighbours and coordinate swimming with them; through a process of self-organization, these local interactions propagate and give rise to the global patterns of collective motion that characterize the school as a whole. The degree of order in the global pattern is characterized by Haken (2006) as the order parameter. Variables that take the ensemble between ordered and disordered states are called control parameters.
Levels of analysis
Local interactions give rise to global patterns â this is the central claim of the self-organization approach to collective behaviour. Analyses can be conducted at the local or global level, but must ultimately characterize the links between them. Sumpter, Mann and Pernea (2012) outline a cogent framework for such a research programme. They characterize studies at each level and the links in both directions, from local to global and from global to local. Making sense of these distinctions is crucial to formulating research strategies to understand collective behaviour, so it will be useful to review them in depth.
At the local or âmicroscopicâ level of analysis, researchers focus on the behaviour of individual agents â be they birds, fish, particles or people. The goal is to understand and ultimately predict how an individual moves in response to its immediate environment, including steering to goals, avoiding obstacles and interacting with other nearby agents. Studies at this level can range from deciphering the perceptual information that guides key behaviours, such as optic flow in walking and flying (Srinivasan, Zhang, Lehrer & Collett, 1996; Warren, Kay, Zosh, Duchon & Sahuc, 2001) or pressure waves in swimming (Partridge & Pitcher, 1980), to the control of steering and obstacle avoidance (Warren & Fajen, 2008), or the social factors that bind two people together while having a conversation (Shockley, Richardson & Dale, 2009). To draw an analogy with physical systems, analysis at the local level is comparable to the study of classical mechanics, where the aim is to work out the kinematic equations of motion for bodies acted upon by a system of forces. Thus, individual agents in a collective occupy the same role as, say, particles in a gas.
The global or âmacroscopicâ level, on the other hand, is concerned with the ensemble properties of the collective as a whole. Analysis at the global level is comparable to the study of classical thermodynamics, which deals with large-scale quantities such as temperature, pressure, entropy and energy that are defined over an entire system. The goal is to understand and ultimately predict how such collective variables change over time and react to changes in the environment. The local properties of individual agents are not considered. Global analyses often consist of analysing the overall collective motion pattern, which can range from disordered chaos in swarms of insects (Kelley & Ouellette, 2013) to organized translational and rotational flows in schools of fish (Couzin, 2009).
The key to self-organization lies in understanding how these local and global scales are related. The most common approach is local-to-global analysis, which seeks to understand how simple interactions between agents at the local level give rise to ordered collective phenomena at the global level. Continuing the physical analogy, local-to-global analyses resemble statistical mechanics, which relates macroscopic thermodynamic properties (e.g. heat) to microscopic properties of interacting particles (e.g. velocity). This local-to-global approach often deploys multi-agent simulations of collective behaviour, in which the goal is to reproduce characteristic global patterns by modelling the behaviour of simple agents and their local interactions. By manipulating the ârulesâ or laws governing these interactions, such simulations can provide insight into the self-organization of collective locomotion, and help explain how complex behaviour emerges from seemingly simple agents. Ultimately, we seek general principles linking the local and global levels, analogous to physical equations that predict the velocity distribution of an ensemble from the equation of motion for individual particles.
A less common, but equally important, approach is global-to-local analysis. Here, the goal is to observe patterns at the global level and use them to infer properties of agents and their interactions at the local level. Regularities in the global patterns or their dynamics place constraints on the rules and models that characterize the local interactions. For example, a collective variable that indexes the degree of coordination between birds in a flock can provide clues about the local coupling, such as how many neighbours each bird responds to (Ballerini et al., 2008), how information about a predator propagates throughout the flock (Cavagna et al., 2010), or whether the coupling yields self-organized criticality in a flock (Bialek et al., 2013). However, due to the âdegeneracyâ of large systems there are limitations to this approach: different local rules can give rise to identical global patterns (Vicsek & Zafeiris, 2012; Weitz et al, 2012). Specifying the rules thus requires experimental manipulation of individuals at the local level (Gautrais et al., 2012; Sumpter, Mann & Pernea, 2012).
Models of collective locomotion
The challenge of unraveling the complexity of collective locomotion has attracted an interdisciplinary community of scientists in fields as wide-ranging as biology, physics, mathematics, cognitive science, computer science, robotics, sociology, geography, architecture and evacuation planning. Since the 1970s, computational modelling has served as a common platform for these efforts. Whether studying aggregations of particles, schools of fish, crowds of people or swarms of robots, there is a familiar arc: researchers propose a set of local rules governing individual locomotion, simulate interactions between individuals, and observe the resulting patterns of collective motion. However, the connections between the local rules or global patterns on the one hand and the observations of actual human or animal behaviour on the other are often tenuous. In this section, several landmark models will be described.
One of the most influential models of collective locomotion was introduced in computer animation by Craig Reynolds (1987), drawing from earlier models of fish schooling (Aoki, 1982; Breder, 1954). Reynoldsâ Boids simulation is an example of agent-based modelling, in which a set of explicit rules defines how each âboidâ (agent) behaves and interacts with other agents. His rules included: (1) repulsion â boids avoid collisions by moving away from nearby neighbours; (2) alignment â boids attempt to match the velocity (speed and heading direction) of nearby neighbours; and (3) attraction â boids move toward the centroid of nearby neighbours. Along with some additional assumptions, these three simple rules produce realistic-looking animations of what Reynolds called âhappy aimless flockingâ. The boids form cohesive flocks, maintain a safe distance from each other, and avoid obstacles by splitting up and rejoining.
What accounts for the modelâs behaviour? First, two of the rules are position-based (repulsion and attraction) and yield a preferred interpersonal distance between agents. This accounts for compact flocks that avoid collisions and reform after splitting around an obstacle. The third rule is velocity-based (alignment), which yields common motion among neighbouring agents. Crucially, collective phenomena emerge from purely local interactions: each boid responds only to neighbours within a fixed radius. Agent-based models thus exhibit self-organization: they demonstrate that global patterns characteristic of collective animal locomotion can, in principle, be reproduced by many locally-interacting agents.
Many subsequent models share these basic components, yielding what Schellink and White (2011) call the attraction-repulsion framework. Couzin, Krause, Ruxton and Franks (2002) showed that a model with three similar rules â repulsion from neighbours in a near zone, attraction to neighbours in a far zone and alignment with neighbours in an intermediate zone (see Huth & Wissel, 1992) â could generate qualitatively different global patterns (Figure 1.1). Specifically, varying the radii of the attraction and repulsion zones produces four distinct forms of aggregation: swarm (high cohesion, low alignment), torus (rotational motion about an empty centre), dynamic parallel (loosely aligned translational motion), and highly parallel (highly aligned translational motion).
This finding illustrates that different large-scale behaviours can result from relatively small changes in the parameters of local rules governing individual agents. Such parameter changes might account for discontinuous transitions observed in animal behaviour, such as a sudden rearrangement in response to the detection of a predator. The model also exhibits hysteresis effects; that is, the threshold of the parameter value for changing from one mode to another depends on the current mode. This is a characteristic property of nonlinear systems (Haken, 2006; Kelso, 1995).
From a physical perspective, Vicsek (1995; Czirok, Stanley, & Vicsek, 1997) proposed a stripped-down model of collective motion, the self-propelled particle (SPP) model, which only includes a velocity-based alignment rule. All particles are assumed to move at the same speed, and on every time step each particle adopts the mean direction of all neighbours within a fixed radius. Noise is introduced into the coupling by adding a random angle to this mean direction at each time step. Remarkably, this minimal heading-matching model is sufficient to generate a noise-induced phase transition from disordered to translational motion as the noise parameter is decreased. Canonical-dissipative models (Ebeling & Schimansky-Geier, 2008; Erdmann, Ebeling &am...