Model of droplet dynamics in the Argentine ant Linepithema Humile (Mayr).

The formation of droplets of ants Linepithema humile (Mayr) is observed under certain experimental conditions: a fluctuating aggregate forms at the end of a rod and a droplet containing up to 40 ants eventually falls down. When the flux of incoming ants is sufficient, this process can continue for several hours, leading to the formation and fall of tens of droplets. Previous work indicates that the time series of drop-to-drop intervals may result from a nonlinear low-dimensional dynamics, and the interdrop increments exhibit long-range anticorrelations. A model of aggregation and droplet formation, based on experimental observations, is introduced and shown to reproduce these properties.

Swarm intelligence. A whole new way to think about business.

What do ants and bees have to do with business? A great deal, it turns out. Individually, social insects are only minimally intelligent, and their work together is largely self-organized and unsupervised. Yet collectively they're capable of finding highly efficient solutions to difficult problems and can adapt automatically to changing environments. Over the past 20 years, the authors and other researchers have developed rigorous mathematical models to describe this phenomenon, which has been dubbed "swarm intelligence," and they are now applying them to business. Their research has already helped several companies develop more efficient ways to schedule factory equipment, divide tasks among workers, organize people, and even plot strategy. Emulating the way ants find the shortest path to a new food supply, for example, has led researchers at Hewlett-Packard to develop software programs that can find the most efficient way to route phone traffic over a telecommunications network. South-west Airlines has used a similar model to efficiently route cargo. To allocate labor, honeybees appear to follow one simple but powerful rule--they seem to specialize in a particular activity unless they perceive an important need to perform another function. Using that model, researchers at Northwestern University have devised a system for painting trucks that can automatically adapt to changing conditions. In the future, the authors speculate, a company might structure its entire business using the principles of swarm intelligence. The result, they believe, would be the ultimate self-organizing enterprise--one that could adapt quickly and instinctively to fast-changing markets.

Inspiration for optimization from social insect behaviour.

Research in social insect behaviour has provided computer scientists with powerful methods for designing distributed control and optimization algorithms. These techniques are being applied successfully to a variety of scientific and engineering problems. In addition to achieving good performance on a wide spectrum of 'static' problems, such techniques tend to exhibit a high degree of flexibility and robustness in a dynamic environment.

Three-dimensional architectures grown by simple 'stigmergic' agents.

A simple model of multi-agent three-dimensional construction is presented. The properties of this model are investigated. Based on these properties, a fitness function is defined to characterize the structured patterns that can be generated by the model. The fitness function assigns a value to each pattern. The choice of the fitness function is validated by the fact that human observers tend to view patterns with high (resp. low) fitness as structured (resp. unstructured). A genetic algorithm based on this fitness function is used to explore the space of possible patterns. The genetic algorithm is able to make use of sub-modules of existing patterns and recombine them to produce novel patterns, but strong epistatic interactions among genes make the fitness landscape rugged and prevent more complex patterns from being produced.

Pattern formation and optimization in army ant raids.

Army ant colonies display complex foraging raid patterns involving thousands of individuals communicating through chemical trails. In this article we explore, by means of a simple search algorithm, the properties of these trails in order to test the hypothesis that their structure reflects an optimized mechanism for exploring and exploiting food resources. The raid patterns of three army ant species, Eciton hamatum, Eciton burchelli, and Eciton rapax, are analyzed. The respective diets of these species involve large but rare, small but common, and a combination of large but rare and small but common food sources. Using a model proposed by Deneubourg et al. [4], we simulate the formation of raid patterns in response to different food distributions. Our results indicate that the empirically observed raid patterns maximize return on investment, that is, the amount of food brought back to the nest per unit of energy expended, for each of the diets. Moreover, the values of the parameters that characterize the three optimal pattern-generating mechanisms are strikingly similar. Therefore the same behavioral rules at the individual level can produce optimal colony-level patterns. The evolutionary implications of these findings are discussed.

Scaling in animal group-size distributions.

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.

A brief history of stigmergy.

Stigmergy is a class of mechanisms that mediate animal-animal interactions. Its introduction in 1959 by Pierre-Paul Grassé made it possible to explain what had been until then considered paradoxical observations: In an insect society individuals work as if they were alone while their collective activities appear to be coordinated. In this article we describe the history of stigmergy in the context of social insects and discuss the general properties of two distinct stigmergic mechanisms: quantitative stigmergy and qualitative stigmergy.

Dominance orders in animal societies: the self-organization hypothesis revisited.

In previous papers (Theraulaz et al., 1995; Bonabeau et al., 1996) we suggested, following Hogeweg and Hesper (1983, 1985), that the formation of dominance orders in animal societies could result from a self-organizing process involving a double reinforcement mechanism: winners reinforce their probability of winning and losers reinforce their probability of losing. This assumption, and subsequent models relying on it, were based on empirical data on primitively eusocial wasps (Polistes dominulus). By reanalysing some of the experimental data that was previously thought to be irrelevant, we show that it is impossible to distinguish this assumption from a competing assumption based on preexisting differences among individuals. We propose experiments to help discriminate between the two assumptions and their corresponding models-the self-organization model and the correlational model. We urge other researchers to be cautious when interpreting their dominance data with the 'self-organization mindset'; in particular, 'winner and loser effects', which are often considered to give support to the self-organization assumption, are equally consistent with the correlational assumption.

Group and mass recruitment in ant colonies: the influence of contact rates

The influence of contact rates on the efficiency (the ability to exploit a profitable environment) and flexibility (the ability to track down a changing environment) of foraging in ants is studied theoretically in the case where foraging relies on a mixture of group and mass recruitment. It is shown that a combination of efficiency and flexibility can be reached across a range of group sizes if (1) mass recruitment is combined with a low level of group recruitment, and (2) contact rates are weakly regulated. These results are discussed in relation to empirical work. Copyright 1998 Academic Press

The synchronization of recruitment-based activities in ants.

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.

The geographical spread of influenza.

How infectious diseases spread in space within one cycle of an epidemic is an important question that has received considerable theoretical attention. There are, however, few empirical studies to support theoretical approaches, because data are scarce. Weekly reports obtained since 1984 from a network of general practitioners spanning the entire French territory allows the analysis of the spatio-temporal dynamics of influenza over a fine spatial scale. This analysis indicates that diffusion over long distances, possibly due to global transportation systems, is so quick that homogeneous global mixing occurs before the epidemic builds up within infected patches. A simple model in which the total number of cases is given by the empirical time-series and cases are randomly assigned to patches according to the population weight of the patches exhibits the same spatio-temporal properties as real epidemic cycles: homogeneous mixing models constitute appropriate descriptions, except in the vicinity of the epidemic's peak, where geographic heterogeneities play a role.

Within-brood competition and the optimal partitioning of parental investment.

In this article, we introduce a simple within-brood competitive growth model that maximizes parental fitness in unpredictable food conditions in species that exhibit parental care, progressive provisioning, and an initial brood overproduction. We argue that competition between siblings may provide a proximate mechanism for parents to adjust the number of surviving offspring or the social organization of the group in social species to food conditions.

From classical models of morphogenesis to agent-based models of pattern formation.

An extremely large body of theoretical work exists on pattern formation, but very few experimental results have confirmed the relevance of theoretical models. It is argued in this article that the notion of agent-based pattern formation, which is introduced and exemplified, can serve as a basis to study pattern formation in nature, especially because pattern-forming systems based on agents are (relatively) more easily amenable to experimental observations. Moreover, understanding agent-based pattern formation is a necessary step if one wishes to design distributed artificial pattern-forming systems. But, to achieve this goal, a theory of agent-based pattern formation is needed. This article suggests that it can certainly be derived from existing theories of pattern formation.

Self-organization in social insects.

Self-organization was introduced originally in the context of physics and chemistry to describe how microscopic processes give rise to macroscopic stuctures in out-of-equilibrium systems, Recent research that extends this concept to ethology suggests that it provides a concise description of a wide range of collective phenomena in animals, especially in social insects. This description does not rely on individual complexity to account for complex spatiotemporal features that emerge at the colony level, but rather assumes that intractions among simple individuals can produce highly structured collective behaviours.

A simple model for the statistics of events in idiotypic networks.

A simple random graph model of idiotypic networks is introduced: this model allows (1) to evaluate the stability of the network dynamics' fixed points, and (2) to compute the statistics of events triggered in response to the arrival of new molecules (metadynamics) using a dynamic mean-field approximation based on the theory of branching processes. It is shown that (1) the network dynamics is unlikely to have many stable fixed points in a strict sense, but that (2) the reorganizations which the network undergoes owing to the metadynamics are always subcritical if plausible figures are injected into the model. In other words the distance between successive (unstable or weakly stable) fixed points is relatively small, so that the overall behavior is stable.

Coordination in distributed building.

A formal model of distributed building is presented that was inspired by the observation of wasp colonies. Algorithms have been obtained that allow a swarm of simple agents, moving randomly on a three-dimensional cubic lattice, to build coherent structures.