Stigmergy as a Universal Coordination Mechanism II: varieties and evolution

Here’s an extract from the sixth and the final article from this special Human-Human Stigmergy issue. It is the second part to Francis Heylighen’s contribution.


In a preceding paper (Heylighen, 2015), stigmergy was defined as a mechanism for the coordination of actions, in which the trace left by an action on some medium stimulates the performance of a subsequent action. This generic definition is applicable to a very broad variety of cases, including the pheromone traces used by ants to find food, the self-organization of chemical reactions, and the implicit collaboration between people via the edits they make in a shared website, such as Wikipedia.

            To bring some order to these phenomena, the present paper will develop a classification scheme for the different varieties of stigmergy. We will do this by defining fundamental dimensions or aspects, i.e. independent parameters along which stigmergic systems can vary. The fact that these aspects are continuous (“more or less”) rather than dichotomous (“present or absent”) may serve to remind us that the domain of stigmergic mechanisms is essentially connected: however different its instances may appear, it is not a collection of distinct classes, but a space of continuous variations on a single theme—the stimulation of actions by their prior results.

            This continuity will further help us to understand the evolution of stigmergic mechanisms, from rudimentary to more sophisticated applications. The paper will in particular focus on the evolution of two applications of stigmergy that are particularly important for humans, cognition and cooperation, arguing that these phenomena, which are traditionally viewed as difficult to explain via conventional evolutionary mechanisms, actually seem to emerge rather naturally via stigmergy.

Individual vs. collective stigmergy

Perhaps the most intuitive aspect along which stigmergic systems can vary is the number of agents involved. In the limit, a single agent can coordinate its different actions via stigmergic interaction with the medium in which it acts.

            An elegant example discussed by (Theraulaz and Bonabeau, 1999) is the solitary wasp Paralastor sp. building its nest in the shape of a mud funnel. The nest emerges in qualitatively different stages S1, S2, …, S5. These subsequently perceived conditions or stimuli each trigger a fitting action or response: S1 -> R1, …, S5 -> R5. Each building action Ri produces as a result a new condition Si+1 that triggers the next action Ri+1. The wasp does not need to have a plan for building such a nest, or to remember what it already did, because the present stage of the activity is directly visible in the trace left by the work already done.

            However, the underlying rule structure becomes apparent when the sequence is disturbed so that stages are mixed up. For example, the wasp’s initial building activity is triggered by the stimulus S1, a spherical hole. When at stage S5 (almost complete funnel) the observer makes such a hole on top of the funnel, the wasp “forgets” that its work is nearly finished, and starts anew from the first stage, building a second funnel on top of the first one. This little experiment shows that the activity is truly stigmergic, and can only run its course when the medium (the mud) reacts as expected to the different actions performed on it, thus registering the information needed to guide the subsequent actions.

            As (Theraulaz and Bonabeau, 1999) suggest, it is likely that collaborative stigmergy evolved from the simpler case of individual stigmergy. Imagine that a second wasp encounters the partially finished nest of the first wasp. It too will be stimulated to act by the perception of the present state of work. It does not matter that this state was achieved by another individual: the wasp anyway has no memory of previous actions—its own or someone else’s. Assume further that the resulting structure is big enough to house the two wasps. In this case, the wasps will have collaboratively built a nest for both, without need for any additional coordination between their genetically programmed building instructions. Assume that the structure is modular, like the nests of social wasps, so that an unlimited number of modules can be added. In that case, the number of wasps that may start working together simply by joining the on-going activity on an existing nest can grow without limit.

            This example illustrates how the number of agents collaborating on a stigmergic project is actually much less fundamental than it may seem. The essence of the activity is always the same. Assuming that the agents have the same skills, adding more agents merely increases manpower and therefore the size of the problem that can be tackled, the speed of advance, or the eventual magnitude of the achievement. Only when the agents are diverse can an increase in their number produce a qualitative improvement in the solution via a division of labor, where differently skilled agents contribute different solutions.

            The only complication added by increasing the number of agents is that agents may get in each other’s way, in the sense that similar individuals perceiving the same stimulus are likely to move to the same place at the same time, thus obstructing each other’s actions. This problem is easily tackled by an additional rule, which is already implicit in individual work but likely to become reinforced during collaborative work: keep a minimum distance from obstacles—including other agents. This rule is a well-known ingredient in the many successful simulations of collectively moving animals, such as flocks, schools or swarms (Okubo, 1986), allowing densely packed groups of agents to follow complex, synchronized trajectories without ever bumping into each other. In combination with the basic stimulation by the stimulus object, this leads to what may look like a carefully thought-out strategy of coordinated movement. An example are group hunting strategies, as used e.g. by lions or wolves (Parunak, 2006). Each wolf is attracted to move towards the prey (basic stimulus). On the other hand, each wolf is stimulated to stay as far away as possible from the other wolves. The result is an efficient encirclement of the prey, which is attacked simultaneously from all sides with no opening left for escape.

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