Analyse mathématique du tri du couvain par les fourmis : auto-organisation fonctionnelle dénuée d'intelligence collective

Brood sorting, observed in some ant colonies, is a major example of social insects ability to solve problems at the collective level. Two processes characterize this phenomenon : a process of aggregation of all brood items in a single cluster, coupled with a process of segregation of items in concentric annuli, each containing items of different type. The mechanism of brood sorting, though it has influenced the development of research fields like ants algorithms, remains until now elusive, as no formal explanation was ever given. We present a first mathematical model devoted to brood sorting, based on minimal hypothesis. We prove that aggregation process occurs regardless to the number of ants. Moreover, we establish how concentric structure observed in ant colonies arise. Our results suggest that brood sorting is a case of functional selforganization, rather than collective intelligence.