Leaderless control: understanding "unguided" order

What does it mean to be leaderless? To some, being without a leader is tantamount to chaos. To others, leaderlessness is the only acceptable route to fairness. But in both cases, it is assumed that leadership is a fundamental outcome of complexity, for better or for worse. Yet do we even need a leader to have control over a system? Leaderlessness is fundamentally distinct than the bottom-up, emergent organization enabled by distributed (or decentralized) autonomous systems. But is some degree of leadership or supervision neccessary for order and complexity to evolve and be maintained? The short answer is: no, but only in certain contexts and under specific conditions (see Figure 1 for a range of superficial examples).

When a leader assumes and maintains control, in many cases the leader must effectively coordinate the non-uniform distribution of energetic resources, distributed information, or both. Another attribute of leadership is the unidirectional nature of relationships between the leader and other components of the system. From a statistical learning perspective, we can say that true leaderlessness is a blind process in which "follow the leader" tactics cannot be used. That is, a leaderless system is expected to explore multiple options without significant bias towards one option or another. But do these assumptions map to what we see among complex systems in the real world?

Figure 1. Portraits of leaderlessness, from top: shoaling fish, human advocating leaderless social institutions, human flash mobs, and leaderless mRNA molecules (COURTESY: Figure 6 from [1]). But how do they all work? Is there one common mechanism, or a series of interrelated ones?

The first example of leaderless systems I will discuss is that of leaderless molecules. In the biochemistry of cells, there are leaderless proteins and mRNA, both of which are characterized by clevage of the molecule's 3' end, which in turn modifies the site of action [1]. This enables an alternate pathway to be utilized by the cell for specialized signaling tasks. This is also true of the protein interleukin 1-beta, as its lack of the proper signal peptide enables an alternate transport pathway [2]. Upon closer examination, these signaling pathways can be characterized as parallel distributed processing networks with specialized components such as anchors, scaffolds, and adaptors that allow for context-dependent optimization [3].

One way the function of leaderless networked systems can be better understood is through the concept of heterarchy. Heterarchy was first contemplated by Walter McCullough [4], who defined it as a transitive hierarchy organized by self-referential connections (for example from nervous system, see Figure 2). A transitive hierarchy is a set of relationships in which there is no clear dominant state. For example, A is greater than B and B is greater than C, but A is NOT greater than C. This is similar to the reflex arc [4, 5], or re-entrant connections found between isocortex and other parts of the Mammalian brain.

Figure 2.  An early structural diagram of a reflex arc. COURTESY: Figure 1 in [4].

Social systems exhibit many examples of heterarchical structure. In the study of social complexity [6, 7], heterarchy is defined as a hierarchy (or perhaps more precisely, a directed network) in which the rank between levels can be ordered in many different ways. For example, Crumley [6] proposes that heterarchical societies exist in cases where hierarchical social organization is decoupled from top-down control that strict implementations of hierarchy tend to produce. Examples of highly-complex societies exist throughout world history, but it does not follow that this organization always resulted from strict top-down control by a single city or ruler. Likewise, Bondarenko [7] argues that social complexity neccessitates hierarchical organization, but not in a way that restricts control to a single, one-way set of relationships.

Heterarchical relationships also result from the evolution of biological systems [8]. Gunji, Sasai, and Wakisaka [9] define heterarchical relationships as logical inconsistencies between levels of an existing hierarchical system (again, this could be described as a directed network). In the case of an organism, changes in a gene or protein sequence can have effects on multiple levels of biological organization (e.g. morphology and behavior), even if the effects on fitness are contradictory. Heterarchical relations in the structure of an organism may also play a role in confering developmental stability and evolutionary robustness [10].

The simulation of social systems can also reveal how leaderless systems can exhibit dynamic, coherent behavior. Hartman and Benes [11] addressed this using boids (a particle simulation of collective bird behavior). In the original boids simulation [12], coherent flocking behaviors similar to what is observed among birds using just three interaction rules: centering, alignment, and seperation. All rules were followed by each boid, and conformity was assumed throughout the flock. In the case of [11], centering and seperation were achieved not by relying on conformity, but by continually reassigning leadership status to different members of the flock (see Figure 3).

Figure 3. Flocking behaviors in birds as a consequence of continual leadership change. COURTESY: Figure 4 from [11].

Overall, it is the incorporation of self-reference (e.g. feedback or recursion) into a hierarchical structure that allows for heterarchical dynamics to be observed [13]. This can be understood using formal computational models based on connected dynamical systems, but a more intuitive way is to use a thought experiment. This idea came to me while looking through a new book on leaderless political movements [14]. Imagine what a leaderless game of chess would look like. Chess is a game of strategy with many potential moves, but strategy is constrained by the rank of each piece. The rank of each piece does not change, so the overall strategy of the game is oriented by there the king is and where the king will be as the game progresses. In terms of control mechanisms for engineered systems, a leaderless system can produce either multiple stable states over time, or a set of contigency pathways that enable a robust architecture. In both cases, the effects of leaderlessness can be local (as with signaling pathways in the cell) or much more global (as in the case of leaderless chess).


What are the principles learned from this foray into leaderlessness? One is that the existance of a hierarchical structure does not neccessitate strong, centralized leadership. Hierarchical structure is a consequence of scale (order of magnitude) rather than causality (order of events). The second is that transient or composite leadership (shared among parts of the system) seems to be stable and robust, but may not extend to all cases. The third lesson is that leaderlessness has consequences for how a complex system explores its state space. Since leaderlessness is in many ways a transient phenomenon, a fixed strategy is not particularly useful. Instead, leaderlessness may play an underappreciated role in fostering innovation and creativity. There are also many unexplored consequences for our understanding of collective behavior and emergent order which are just now beginning to be understood.

References:

[1] Vesper, O. et.al (2011). Selective Translation of Leaderless mRNAs by Specialized Ribosomes Generated by MazF in Escherichia coli. Cell, 147(1), 147-157.

[2] Andrei, C. et.al (1999). The secretory route of the leaderless protein interleukin 1β involves exocytosis of endolysosome-related vesicles. Molecular Biology of the Cell, 10(5), 1463-1475.

[3] Fisher, M.J., Paton, R.C., and Matsuno, K. (1999). Intracellular signalling proteins as ‘smart’ agents in parallel distributed processes. Biosystems, 50(3), 159–171.

[4] McCullough, W.S. (1945). A heterarchy of values determined by the topology of nervous nets. Bulletin of Mathematical Biophysics, 7, 89-93.

[5] Marder, E. and Calabrese, R.L. (1996). Principles of rhythmic motor pattern generation. Physiological Reviews, 76, 687-717.

[6] Crumley, C.L. (1995). Heterarchy and the Analysis of Complex societies. IN Ehrenreih, R.M., Crumley, C.L., and Levy, J.E. (eds) Heterarchy and the Analysis of Complex Societies. American Anthropological Association, Washington, D.C.

[7] Bondarenko, D.M., Grinin, L.E., and Korotayev, A.V. (2002). Alternative pathways of social evolution. Social Evolution and History, 1(1), 54-79.

[8] Shapiro, J.A. (2002). A 21rst century view of evolution. Journal of Biological Physics, 28, 745-764.

[9] Gunji, Y-P., Sasai, K., and Wakisaka, S. (2008). Abstract heterarchy: time/state-scale re-entrant form. BioSystems, 91, 13-33.

[10] Jen, E. (2004). Robust Design: a repertoire of biological, ecological, and engineering case studies. Oxford University Press, New York.

[11] Hartman, C. and Benes, B. (2006). Autonomous boids. Computer Animation and Virtual Worlds, 17(3-4), 199-206.

[12] Reynolds, C. (1987). Flocks, Herds, and Schools: A Distributed Behavioral Model.
See the website http://www.red3d.com/cwr/papers/1987/boids.html for more information.

[13] Gunji, Y-P., Kamiura, M. (2004). Observational heterarchy enhancing active coupling. Physica D, 198, 74-105. AND Sasai, K. and Gunji, Y-P (2008). Heterarchy in biological systems: a logic-based dynamical model of abstract biological network derived from time-scale state. BioSystems, 92, 182-188.

[14] This thought experiment came to me while looking through a new book by Carne Ross called Leaderless Revolution. It is a thoughtful and innovative look at leaderlessness from a political perspective. See the website http://theleaderlessrevolution.com/ for more information on his work in this area. He explores strategies for using leaderless movements to affect social change, and uses the metaphor of chess to summarize the ultimate goals of social movements (although he does not contemplate "leaderless" chess).