Complex Dynamics Based on a Quorum: Decision-Making Process by Cockroaches in a Patchy Environment

In the absence of complex communication and a global knowledge of the environment, cockroaches are able to assess the availability of resources and to reach a consensual decision: the group aggregates in a single resting site. We show that the aggregation dynamics and the collective shelter selection of cockroaches are influenced by their social context as, unlike single individuals, groups of cockroaches are more likely to respond to environmental heterogeneities. The decision of individuals to stay under a shelter relies on the modulation of their resting time, according to the perception of two local cues: (1) the shelters luminosity and (2) the number of congeners. This study on the cockroach species Periplaneta americana highlights a shelter-selection mechanism based on an amplification process resulting from the interactions between congeners. This mechanism leads to complex spatiotemporal aggregation dynamics characterized by transient bimodality, bifurcation patterns (shelter selection) and the existence of a quorum size in the settlement behaviour of the cockroaches. Finally, we discuss the generic aspect for other gregarious species of the collective decision-making process demonstrated for cockroaches.     

Mathematical model of self-organizing hierarchies in animal societies

We propose a mathematical approach to the modelling of self-organizing hierarchies in animal societies. This approach relies on a basic positive feedback mechanism that reinforces the ability of a given individual to win or to lose in a hierarchical interaction, depending on how many times it won or lost in previous interactions. Motivated by experiments carried out on primitively eusocial waspsPolistes, the model, is based on coupled differential equations supplemented with a small stochastic term. Numerical integrations allow many different hierarchical profiles to be obtained depending on the model parameters: (1) the particular form of the probability for an individual to win or lose a fight given its history, (2) the probability of interaction between two individuals, (3) the forgetting strength, which determines the rate at which events in the past are forgotten and no longer influence the force of an individual and (4) two individual recognition parameters, which set the contribution of individual recognition in the process of hierarchical genesis. We compare the results, expressed in terms of a hierarchical index or of the Landau number that describes the degree of linearity of the hierarchy, with various experimental results.     

Dynamics of Nest Excavation and Nest Size Regulation of Lasius niger (Hymenoptera: Formicidae)

The adaptation of nest size to its population is one of the most common processes, but little is known about the dynamics nest-building and -enlarging in social context. Furthermore, the mechanisms involved remain totally ignored. We present here the first results of such dynamics in the context of Lasius niger's nest excavation. We find, with an artificial but standardized method, a strong positive correlation between the number of ants and the final nest volume as well as the digging rate. Both grow almost proportionally to population. When the number of individuals is artificially increased (even slightly) in a nest, its dimension is systematically adjusted in the same way as initial excavation. In this process, digging acts as a negative feedback that controls nest enlargement. Experiments revealed that this negative control is due directly to the volume of the nest as well as the physiological or behavioral modification of ants after digging. Finally, amplification of activity was observed during the enlargement phase, suggesting the possible implication of self-organized processes in the volume control mechanism.