Symmetry Restoring Bifurcation in Collective Decision-Making

How social groups and organisms decide between alternative feeding sites or shelters has been extensively studied both experimentally and theoretically. One key result is the existence of a symmetry-breaking bifurcation at a critical system size, where there is a switch from evenly distributed exploitation of all options to a focussed exploitation of just one. Here we present a decision-making model in which symmetry-breaking is followed by a symmetry restoring bifurcation, whereby very large systems return to an even distribution of exploitation amongst options. The model assumes local positive feedback, coupled with a negative feedback regulating the flow toward the feeding sites. We show that the model is consistent with three different strains of the slime mold Physarum polycephalum, choosing between two feeding sites. We argue that this combination of feedbacks could allow collective foraging organisms to react flexibly in a dynamic environment.Author Summary: Collective decision making is ubiquitous in group-living organisms allowing them to select between several competing resources. It is a self-organized process involving positive feedback mechanisms, whereby the preference for a particular option is reinforced if the option has already been accepted by a part of the group's constituting units. The generally accepted paradigm of collective decision-making is a transition from an exploitation mode where all options are on equal footing, to one in which groups of sufficiently large size are led to focus on a particular option, a phenomenon referred to as symmetry-breaking bifurcation. In the present work we report results based on mathematical modeling in parallel with experiments carried out on the unicellular plasmoidal organism Physarum polycephalum showing that, contrary to the classical paradigm, symmetry is eventually restored for individuals of sufficiently large size (here the plasmodium mass). This possibility, arising from the combination of positive feedbacks and a regulation of the flow by the fraction of system's mass already committed to the options, allows the organism to react flexibly. We argue that, beyond the case of P. polycephalum, this paradigm should apply to many systems possessing the aforementioned feedback and regulatory mechanisms.