Reference
Abstract
Beckers, R., S. Goss, Jean-Louis Deneubourg and J. M. Pasteels. 1989. Colony size, communication and ant foraging strategy . PSYCHE (CAMBRIDGE) 96(3-4) 1989: 239-256, illustr.
Bonabeau, Eric, Guy Theraulaz and Jean-Louis Deneubourg. 1996. Mathematical model of self-organizing hierarchies in animal societies. Bulletin of mathematical biology 58(4): 661-717.
 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 wasps polistes, 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.
Bonabeau, Eric. 1997. Flexibility at the edge of chaos: a clear example from foraging in ants. Acta biotheoretica 45(1): 29-50.
 Starting from a clear, experimentally verified, example of a flexible biological system - an ant colony -, it is hypothesized that adaptability is enhanced at the "edge of chaos", that is, in the vicinity of a point of instability. An ant colony exhibiting an appropriate combination of group and mass recruitment can adaptively switch to a newly introduced food source if it is richer: this is precisely the case of some species, such as tetramorium caespitum, whose behavioral parameters ate argued to be those characterizing the edge of chaos. Several simple models of foraging show the robustness of the argument.
Bonabeau, Eric, Guy Theraulaz and Jean-Louis Deneubourg. 1998. The synchronization of recruitment-based activities in ants. Biosystems-. March, 1998, 45 (3) 195-211.
 A simple model of recruitment-based foraging in ants illustrates the idea that synchronized patterns of activity can endow a colony with the ability to forage more efficiently when a minimal number of active individuals is required to establish and maintain food source exploitation. This model, which can be extended to other activities that involve recruitment, may help explain why bursts of synchronization have been observed in several species of ants.
Bonabeau, Eric, Guy Theraulaz, Jean-Louis Deneubourg and Nigel R. Franks, Oliver Rafelsberger, joly-jean-louis, blanco-stephane. 1998. A model for the emergence of pillars, walls and royal chambers in termite nests. Philosophical-transactions-of-the-royal-society-of-london-b-biological-sciences. Oct. 29, 1998, 353 (1375) 1561-1576.
 A simple model of the emergence of pillars in termite nests by deneubourg is modified to include several additional features that break the homogeneity of the original model: (i) a convection air stream that drives molecules of pheromone along a given direction, (ii) a net flux of individuals in a specific direction, (iii) a well-defined self-maintained pheromone trail, and (iv) a pheromonal template representing the effect of the presence of a queen that continuously emits pheromone. It is shown that, under certain conditions, pillars are transformed into walls or galleries or chambers, and that this transformation may not be driven by any change in the termites' behaviour. Because the same type of response at the individual level can generate different patterns under different conditions, and because previous construction modifies current building conditions, we hypothesize that nest complexity can result from the unfolding of a morphogenetic process that progressively generates a diversity of history-dependent structures.
Bonabeau, Eric, Dagorn-Laurent, Freon-Pierre. 1999. Scaling in animal group-size distributions. Proceedings-of-the-national-academy-of-sciences-of-the-united-states-of-america. April 13, 1999, 96 (8): 4472-4477.
 An elementary model of animal aggregation is presented. The group-size distributions resulting from this model are truncated power laws. The predictions of the model are found to be consistent with data that describe the group-size distributions of tuna fish, sardinellas, and african buffaloes.
Bonabeau,-Eric. 1997. From classical models of morphogenesis to agent-based models of pattern formation. ARTIFICIAL LIFE 3(3), Summer, 1997: 191-211, illustr.
Bonabeau, Eric, F. Henaux, S.Guerin, D. Snyers and Guy Theraulaz. 1988. Routing in Telecommunications Networks with Ant-Like Agents. In: Intelligent Agents for Telecommunications Applications '98 , LNAI 1437, S. Albayrac (Ed.), pp.60-72.Berlin, Springer-Verlag: 1998.
Camazine, Scott. 1991. Self-organizing pattern formation on the combs of honey bee colonies. Behavioral Ecology and Sociobiology, 28:61-76.
Franks, Nigel and Jean-Louis Deneubourg. 1997. Self-organizing nest construction in ants: individual worker behaviour and the nest's dynamics. Animal Behaviour, v.54:779-796.
 We examine nest construction in the ant Leptothorax tuberointerruptus at two levels: (1) the building behaviour of individual workers and (2) the collective properties (temporal and spatial) of the structures they create. We also explore, for the first ti
Franks, Nigel R., N. Gomez, S. Goss and Jean-Louis Deneubourg. 1991. The blind leading the blind in army ant raid patterns: testing a model of self-organization (hymenoptera: formicidae). Journal of insect behavior. 4(5): 583-608.
 We present field experiments and analyses that test both the assumptions and the predictions of a model that showed how the swarm raids of the arym ant eciton burchelli might be self-organizing, i.e., based on hundreds of thousands of interactions among the foraging workers rather than a central administration or hierarchical control. We use circular mill experiments to show that the running velocity of the ants is a sigmoidal function of the strength of their trail pheromones and provide evidence that the swarm raid is structured by the interaction between outbound and inbound forager traffic mediated by the pheromones produced by both of these sets of ants. Inbound traffic is also affected by the distribution of prey, and hence, sites of prey capture alter the geometry of the raid. By manipulating the prey distributions for e. Burchelli swarms, we have made them raid in a form more typical of other army ant species. Such self-organization of raids based on an interaction between the ants and their environment has profound consequences for interpretations of the evolution of army ant species.
Gordon, Deborah M., Richard E. Paul and Karen Thorpe. 1993. What is the function of encounter patterns in ant colonies?. Animal Behaviour, 45:1083-1100.
Gordon, Deborah M. 1999. Interaction patterns and task allocation in ant colonies. Information Processing in Social Insects, Pastells, J.M., Jean Louis Deneubourg and C. Detrain (eds). Birkhuaser Verlag. pp. 51-67.

Kauffman, Stuart. 1991. Antichaos and Adaptation. Scientific American, August.

 Biological evolution may have been shaped by more than just natural selection. Computer models suggest that certain complex systems tend towards self-organization
Theraulaz, Guy and Eric Bonabeau. 1995. Modelling the collective building of complex architectures in social insects with lattice swarms. Journal of theoretical biology 177(4): 381-400.
 In this paper we present a formal model of distributed building inspired by wasp colonies. We characterize a set of distributed stigmergic algorithms that allow a swarm of simple agents to build coherent nest-like structures. The agents that constitute the swarm of builders move randomly on a 3d lattice and can deposit elementary bricks. The agents do not communicate, have no global representation of the architecture they are building, do not possess any plan or blueprint and can only perceive the local configuration of matter surrounding them. Only a few of these configurations are stimulating, that is, trigger a building action. The aim of this paper is not to prove that this model is an accurate model of how wasps behave, but rather to show (i) that such behavioural algorithms can produce coherent biological-like architectures, (ii) that these architectures, if they are to be generated with these behavioural algorithms, require algorithms with specific "coordination" properties, and (iii) finally that algorithms possessing these specific properties produce in turn only very specific, coherent architectures. In effect, we found an empirical one to one correspondence between biological-like architectures and "coordinated algorithms". Coordinated algorithms rely on a partition of the shape to be built into modular subshapes: if a swarm of agents is to build a given coherent architecture, the shape has to be decomposed into a finite number of building steps, with the necessary condition that the local stimulating configurations that are created at a given stage differ from those created at a previous or a forthcoming building stage so as to avoid disorganization of the whole building activity. Moreover, shapes generated with non-coordinated algorithms, for instance when stimulating configurations corresponding to the subshapes overlap and may subsequently affect the overall building process, are unstable, the same given rule table will produce very dissimilar architecture in different simulations. Finally, architectures generated under such conditions were found not to resemble any known biological architecture. We believe that our study constitutes a first step towards a deeper understanding of the origins of natural shapes in terms of the logical constraints that may have affected the evolutionary path.
Theraulaz, Guy, Eric Bonabeau and Jean-Louis Deneubourg. 1998. Response threshold reinforcement and division of labour in insect societies. Proceedings of the Royal Society of London, Series B. 265:327-332.