• The behavior of each caterpillar is simple and the trajectory followed by the procession is identical to that of the lead caterpillar, according to our partner The Conversation.

  • One can, therefore, wonder if the head of the procession is a caterpillar like the others?

  • This analysis was conducted by Philippe Collard, Professor Emeritus in Complex Systems at the University Côte d'Azur.

In single file, in single file: the processions are everywhere, from the queue in front of a ticket office, to the sheep of Panurge, and of course, to the pine processionary caterpillars.

Studying their behavior will serve here as a pretext to dive into the world of complex systems, where "the whole is more than the sum of its parts": from individual behaviors will emerge the non-trivial patterns that govern collective behavior without having to be attributed to part properties;

and, in turn, the overall emergent structures will affect individual behavior.

​For pine processionary caterpillars, "it's all in the head"

We are interested here in the movement of pine caterpillars from the exit of their cocoon to the burial point.

In his

Souvenirs

,

published in 1899, the French entomologist Jean-Henri Fabre wrote:

“The caterpillar at the head of the series probes the mandibles, plows a little, finds out about the terrain.

Where the first has passed, all the others pass in regular file, without empty intervals.

They walk in a single row, in a continuous line, each touching the back of the previous one with their heads.

There is only one will, that of the leader.

There is only one head, so to speak;

the procession is comparable to the chain of segments of an enormous annelid [note: earthworm].

»

Here, there is no complexity yet: the behavior of each caterpillar is simple and the trajectory followed by the procession is identical to that of the leading caterpillar.

A computational simulation where each caterpillar is represented by a virtual agent makes it possible to visualize the consequence of individual behaviors on the shape of a procession.

Jean-Henri Fabre refers to a change in the scale of observation by moving from

caterpillar-individuals

to the

procession-individual

that he assimilates to an enormous earthworm.

This change of point of view is a key step in the study of dynamical systems;

it could, for example, lead us here to no longer simulate a single procession but a

population of processions

in order to know what would happen if two processions interacted during a crossing.

Is the head of the procession a caterpillar like the others?

One way to answer this question is to observe what happens if the lead caterpillar crosses the procession before reaching the burial point.

For this, Jean-Henri Fabre "forced" the leading caterpillar to return to the procession by titillating it with a stick - a common approach among ethologists, which consists of diverting a natural behavior to validate or invalidate a hypothesis.

A computational simulation carried out in a totally flat virtual landscape without any obstacles confirms Jean-Henri Fabre's observations: in the end, the procession follows a closed circuit immutably.

All the caterpillars, including the head, have the same set of behaviors that are triggered depending on the circumstances.

“Forcing” the leading caterpillar to return to the procession

ultimately

induces an influence of each agent on itself;

this results in a retrocontrol of the global shape of the trajectory on the local behavior of each individual.

This illustrates a phenomenon of "immersion" where the causal relationship is reversed, the behavior of the whole affecting the behavior of the parts.

​Why do pine caterpillars follow their leader?

In order to understand why Jean-Henri Fabre's observation "They walk [...] each touching the back of the previous one with their head" is decisive, we are going to assume that there is a lapse of time between the release of two individuals.

A new computational simulation makes it possible to observe that the trajectory of the head and the shape of the procession are then uncorrelated: the procession ends up following the most direct path between the starting and ending points.

The straight line being the shortest path between two points, we can say that, without knowing it, without wanting it, the virtual insects have solved an

optimization problem in

a decentralized way .

We have thus just taken a small step towards complexity: such a problem is trivial when it is expressed by an agent possessing a global understanding of its environment but becomes a challenge if it must be "solved" by a set of interacting entities possessing rudimentary capacities of perception and action.

Beyond optimality, the emergent linear form, independent of any initial form followed by the head agent, has an inherent property of symmetry, a characteristic often observed for forms resulting from a process of morphogenesis (set of laws that determine the shape of organisms).

Moreover, under the assumption that the speed of movement is constant, the mathematician Alfred Bruckstein was able to deduce, via a calculation based on differential equations, the overall behavior, in the long term, of the procession, from the behavior of the individuals. .

We will therefore say that it is a “weak emergence” because the knowledge of the micro-elements allows those of the macro-element.

Towards more complex shapes…

Let us now take some liberties with the reality of pine caterpillars and Alfred Bruckstein's hypothesis by simulating a loop of virtual processionary caterpillars for which the speed of movement, identical for all individuals, is limited and varies over time.

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To specify the way in which the speed varies, it suffices to specify the relation between the speed at the current moment and the speed at the previous moment.

For this we use the "logistic function" (in mathematical language, such a function is written

f (x) = ax (1-x)

, where the control parameter

a

is included in the interval 0 to 4, for

x

between 0 and 1).

To each value of the parameter corresponds a particular model of evolution of the procession.

Computational simulations show that the length of the procession depends on the parameter

a

and evolves over time towards fixed, periodic or chaotic “attractors”.

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In addition, one can observe the emergence of patterns with complex shapes.

The image and the video above illustrate this result by presenting a whole bestiary of looped processions possessing axial or central symmetries which, although stable, are continuously animated by rotational and/or translational movements which induce cyclic structures.

The variety of shapes results from the evolutionary model and the random initial positions of the virtual caterpillars.

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This analysis was written by Philippe Collard, Professor Emeritus in Complex Systems at the University Côte d'Azur.


The original article was published on

The Conversation website

.

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