The geometry of decision-making
Choosing among spatially-distributed options is a central challenge for animals, from deciding among alternative potential food sources or refuges, to choosing with whom to associate. Using an integrated theoretical and experimental approach (employing immersive virtual reality), we consider the interplay between movement and vectorial integration during decision-making regarding two, or more, options in space. In computational models of this process we reveal the occurrence of spontaneous and abrupt "critical" transitions (associated with specific geometrical relationships) whereby organisms spontaneously switch from averaging vectorial information among, to suddenly excluding one, among the remaining options. This bifurcation process repeats until only one option--the one ultimately selected--remains. Thus we predict that the brain repeatedly breaks multi-choice decisions into a series of binary decisions in space-time. Experiments with fruit flies, desert locusts, and larval zebrafish reveal that they exhibit these same bifurcations, demonstrating that across taxa and ecological context, there exist fundamental geometric principles that are essential to explain how, and why, animals move the way they do.