Social behaviour may enable organisms to occupy ecological niches that would otherwise be unavailable to them. Here we test this major evolutionary principle by demonstrating self-organizing social behaviour in the plant-animal, Symsagittifera roscoffensis. These marine aceol flat worms rely for all of their nutrition on the algae within their bodies: hence their common name. We show that individual worms interact with one another to co-ordinate their movements so that even at low densities they begin to swim in small polarized groups and at increasing densities such flotillas turn into circular mills. We use computer simulations to: (1) determine if real worms interact socially by comparing them with virtual worms that do not interact and (2) show that the social phase transitions of the real worms can occur based only on local interactions between and among them. We hypothesize that such social behaviour helps the worms to form the dense biofilms or mats observed on certain sun-exposed sandy beaches in the upper intertidal of the East Atlantic and to become in effect a super-organismic seaweed in a habitat where macro-algal seaweeds cannot anchor themselves. S. roscoffensis, a model organism in many other areas in biology (including stem cell regeneration), also seems to be an ideal model for understanding how individual behaviours can lead, through collective movement, to social assemblages.