Received15 July 2002Accepted18 September 2002Published online9 December 2002Self-organized lane formation and optimized trafficflow in army antsI. D. Couzin1*and N. R. Fran ks21Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ 08544, USA2Centre for Behavioural Biology, School of Biological Sciences, University of Bristol, Bristol BS8 1UG, U KWe show how the movement rules of individual ants on trails can lead t o a collective choice of directionand the formation of distinct traffic lanes that minimize congestion. We develop and evaluate the resultsof a new model with a quantitative study of the behaviour of the army antEciton burchelli. Colonies ofthis species have up to 200 000 foragers and transport more than 3000 prey items per hour over raidingcolumns that exceed 100 m. It is an ideal species in which to test the predictions of our model becauseit forms pheromone trails that are densely populated w ith very swift ants. The model explores the influ-ences of turning rates and local perception on traffic flow. The behaviour of real army ants is such thatthey occupy the specific region of parameter space in which lanes form and traffic flow is maximized.Keywords: self-organization; mathematical model; computer simulation; social insects1. INTRODUCTIONNetworks that control the flow of resources and infor-mation are ubiquitous in nature. Moreover, the efficiencyof such networks may determine the fundamental scalingproperties of certain organisms (Westet al.1997; Banavaret al.1999; Brown & West 2000). The foraging networksof terrestrial animal societies, and especially those of cer-tain ant species, provide unrivalled opportunities to quan-tify both the beh aviour of individual items of traffic andthe larger-scale patterns of traffic flow. For these reasons,they are ideal subjects with which to test mathematicalmodels that link the behaviour of small components (inthis instance, in dividual ants) to the overall efficiency ofthe dynamic structures they generate.Many ant species create chemical (pheromone) trailnetworks, not only to transport resources and/or infor-mation swiftly and efficiently during foraging, but also forexploration, emigration and coordinating colony defence(Ho¨lldobler & Wilson 1990). Just as the functioning andsuccess of modern cities are dependent on an efficienttransportation system, the effective management of trafficis also essential to insect societies. The flow of traffic alon gtrails is likely to be particularly important in the NewWorld army antEciton burchelli. Colonies of this speciesmay have half a million or more workers, and the ants arestrict carnivores. They stage huge swarm raids, in pursuitof arthropod prey, with up to 200 000 virtually blind for-agers forming trail systems that are up to 20 m wide and100 m or more long (Sc hneirla 1971; Frankset al.1991;Gotwald 1995; Sole´et al.2000). In a single such raid acolony may retrieve more than 30 000 prey ite ms (Franks1985). Moreover, these massive raids are severely timeconstrained. At most, they begin at dawn and end at dusk,when the colony emigrates, under the cover of darkness,to a new nest-site and foraging arena. For this reason,E. burchellicolonies need to operate at a very high tempo(see Frankset al.1999; Boswellet al.2001). These colon-*Author for correspondence ([email protected]).Proc. R. Soc. Lond.B (2003)270, 139–146 139 Ó 2002 The Royal SocietyDOI 10.1098/rspb.2002.2210ies form traffic lanes in their main foraging columns(Franks 1985). We investigate how and why the se trafficlanes form. We first develop a generic mod el for trail fol-lowing by ants, and compare the behaviour of the modelwith empirical data from individual ants following a trailof known concentration. We then parameterize this modelwith new data from an analysis of the movements of indi-vidualE. burchelliworkers. We use this individual-basedmodel to test theories concerning the organization oftraffic on army ant trails, and demonstrate how individualbehaviours lead to crucial properties including direc-tionality, lane formation and the minimization of conges-tion.2. THE MODEL(a) OverviewWe develop a general model of ant behaviour, using anindividual-based simulation approach that takes intoaccount the abilities of ants to detect and avoid collidingwith one an other and to respond to local pheromone con-centration.Nants are simulated, with antihaving positionvector ci(t) and direction vector vi(t). The head of antiisat a point ci(t)11/2bvi(t), wherebis the ant body length.The left and right antennae each extend a distanceffromthe head at an angle of 45° to the ant’s body orientation.In the simulation, ants will turn away from others if theyare approached too closely within either of two local areas.The first is a circle, radiusrd, extending from the ant’scentre, c, representing very close proximity to the bodyand legs of the ant. The second is an arc that extendsahead of the ant a distancerpfrom c and has an internalanglea; this may represent a local visual field in somespecies, whereas in others (such as virtually blind armyants) it is the tactile ran ge of the antennae or the close-range olfactory perception of other ants (figure 1a). Indi-viduals tend to turn away from others within these zoneswith a turning rateua(equation (2.1)), and also to slowdown to avoid collisions with a constant acceleration,2m,unless they have already reached their minimum speed,140 I. D. Couzin and N. R. Franks Traf c  ow in army ants 21301020 304050 602000150010005000_35_30_25_20_15_35_30_25_20_15_35_30_25_20_15ln Qln Qln Qmean distance cm)aa)e)b)c)d) f )rlcFigure 1. (a) Geometry of simulated ants, showing the centre (c) the left and right antennae (landr, respectively) and thebehavioural zones, where a is the internal angle of the zone extending ahead of the ant. (b–d) The results of simulationsshowing the mean distance travelled as a function of the natural log of the amount of trail pheromone (lnQ). The resultsshown are the means of all runs for a given pheromone concentration, where ants approach the trail at angles of 5–90°(at 5°increments, 50 replicates per increment). Simulations were run for 15 000 time-steps per replicate (standard parameters:up=500°s21, s=0.5,Cmax=1.2´10210g cm23). (b) The saturation level of the antennae,Cmax, changes the pheromoneconcentration at which the peak occurs because the response of the antennae is scaled