* Author to whom correspondence should be addressed. E-mail: snicolis@ulb.ac.be. J. theor. Biol. (1999) 198, 575}592 Article No. jtbi.1999.0934, available online at http://www.idealibrary.com on Emerging Patterns and Food Recruitment in Ants: an Analytical Study S. C. NICOLIS* AND J. L. DENEUBOURG Center for Nonlinear Phenomena and Complex Systems, ;niversite H ¸ibre de Bruxelles, Campus Plaine, CP231, 1050 Brussels, Belgium (Received on 1 June 1998, Accepted in revised form on 16 March 1999) A model of food recruitment by social insects accounting for the competition between trails in the presence of an arbitrary number of sources is developed and analysed in detail. Both the case of identical environmental characteristics and the case where one source and the corresponding trail are di!erent from the others are considered. Di!erent collective responses depending on the environmental conditions, and without change of individual behaviour, are shown to exist, associated with the possibility that the colony may be led to exploit one source or a group of sources preferentially. The full bifurcation diagram of steady-state solutions is constructed from which the dominant exploitation patterns are identi"ed. The biological relevance of the results is discussed and suggestions are made for their experimental testing in connection with the recruitment behavior of species using trail recruitment. The same phenom- enological model can be used for di!erent trail-laying species since the predictions are generic and not restricted to a given species, except for the parameter values used.  1999 Academic Press 1. Introduction Amplifying communications occupies an impor- tant place in the organization of animal societies and, most particularly, in social insects. From a theoretical point of view, ampli"cation implies interaction between at least two individuals and is therefore expected to introduce to the dynam- ics a nonlinear element (Nicolis & Prigogine, 1977) that could in principle be manifested at the level of the society as a whole in the form of complex collective spatio-temporal phenomena. Since nonlinearity generally implies multiplicity, these phenomena cannot in principle be pre- dicted without appealing to mathematical modeling linking the characteristics of individual behavior to the collective response (Deneubourg & Goss, 1989; Bonabeau et al., 1997; Theraulaz & Spitz, 1997; Camazine et al., 1999; Detrain and Deneubourg, 1999). One of the most intensely studied cases of communication is food recruitment. Depending on the species, di!erent processes may be in- volved. In bees, it implies direct interactions be- tween individuals (Camazine & Sneyd, 1991; Seeley et al., 1991; Seeley, 1995). In ants, recruit- ment is primarily ensured by chemical means (Sudd, 1957; Wilson 1962, 1971; Ho K lldobler & Wilson, 1991; Robson & Traniello, 1995). In the present paper, we will be concerned by re- cruitment in ant societies associated with forag- ing. Here a scout having discovered a food source returns to the nest, laying a pheromonal trail which stimulates the inactive foragers waiting in the nest (Fig. 1). These recruits can become re- cruiters in their turn. 0022}5193/99/013575#18 $30.00/0  1999 Academic Press