Flow Tree: a model for navigator dynamics and environmental complexity.

Navigation is a dynamic process, involving learning new environments and manoeuvring through them. Individuals differ widely in their abilities and strategies. Prior research often uses static measures, such as total distance travelled or location tallies, which overlook the variability and asymmetry in how trajectories unfold. To address this, we introduce the Flow Tree, a novel data structure that encodes how trajectories evolve relative to each other through time and space. Branching points capture when groups split into subgroups, producing a compressed, dynamic trace of group decision-making. We apply Flow Trees to data from 97 participants navigating a virtual reality maze. We define methods to construct and quantify Flow Trees. We show that (i) Flow Tree features are more strongly correlated with path accuracy than static metrics, and (ii) Flow Trees enable data-driven prediction of individual trajectory success. Further, we (iii) introduce a statistical framework to compare groups of Flow Trees, revealing how individual differences, path types and environments affect navigation. For example, successful male and female navigators resulted in significantly different Flow Trees, indicating differences beyond accuracy. By capturing temporal structure and variability, Flow Trees provide a dynamic, interpretable framework to quantify navigation behaviour and analyse group decision-making dynamics.