There exist fundamental geometrical principles that result from the inherent interplay between movement and organisms’ internal representation of space: Animals spontaneously reduce the world into a series of sequential binary decisions

The geometry of decision-making in individuals and collectives. Vivek H. Sridhare et al. Proceedings of the National Academy of Sciences, December 14, 2021 118 (50) e2102157118; https://doi.org/10.1073/pnas.2102157118

Significance: Almost all animals must make decisions on the move. Here, employing an approach that integrates theory and high-throughput experiments (using state-of-the-art virtual reality), we reveal that there exist fundamental geometrical principles that result from the inherent interplay between movement and organisms’ internal representation of space. Specifically, we find that animals spontaneously reduce the world into a series of sequential binary decisions, a response that facilitates effective decision-making and is robust both to the number of options available and to context, such as whether options are static (e.g., refuges) or mobile (e.g., other animals). We present evidence that these same principles, hitherto overlooked, apply across scales of biological organization, from individual to collective decision-making.

Abstract: 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 multichoice 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 contexts, there exist fundamental geometric principles that are essential to explain how, and why, animals move the way they do.

Keywords: ring attractormovement ecologynavigationcollective behaviorembodied choice

      Model Features That Determine Network Behavior

There are key features that are essential to produce the bifurcation patterns observed in our data (i.e., for any decision-making system to break multichoice decisions to a series of binary decisions).

• 1) Feedback processes that provide the system directional persistence and drive such bifurcations are crucial to exhibit the observed spatiotemporal dynamics. In the neural system, this is present in the form of local excitation and long-range/global inhibition (7, 18, 19). However, as shown in our model of collective animal behavior below, we expect that similar dynamics will be observed if the necessary feedbacks are also incorporated into other models of decision-making, such as to PDF sum–based models, for example (20).

• 2) Observing similar decision dynamics requires a recursive (embodied) interplay between neural dynamics and motion in continuous space. Here, the animal’s geometrical relationship with the targets changes as it moves through physical space. Since neural interactions depend on this changing relationship, space provides a continuous variable by which the individual traverses the time-varying landscape of neural firing rates.

These essential features, along with the observed animal trajectories in the two-choice context, are reminiscent of collective decision-making in animal groups [models (41⇓⇓⇓–45), fish schools (46), bird flocks (47), and baboon troops (26)]. Below, we consider an established model of collective decision-making (41) to draw links between these two scales of biological organization—decision-making in the brain and decision-making in animal groups.