Abby Bertics - Flow Trees

Flow Trees compress a group of navigation trajectories into a tree where nodes mark where the group splits into subgroups. The Flow Tree's shape and complexity represent how cohesively a group of navigators solve a task.

Abstract

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 (1) Flow Tree features are more strongly correlated with path accuracy than static metrics, and (2) Flow Trees enable data-driven prediction of individual trajectory success. Further, we (3) 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.

Dataset

Virtual-reality maze with 17 plain decision points, 9 object decision points, and 4 landmark paintings. Navigators are placed at a start object and asked to reach a target object within 45 seconds; objects are masked with red spheres during testing to prevent further learning.

The dataset comes from 97 healthy young adults (46 female; ages 18–31) navigating a virtual-reality maze of hedges, built around 26 discrete decision points, 9 of which have objects at dead ends. After a 16-minute exploration phase, each navigator completed 48 timed test trials, each asking them to travel from one object to another. Performance is measured as the proportion of trials each navigator completed successfully (0.02–1.0 across participants). Prior analysis of this dataset (Ward et al.) found that standard exploration metrics like distance travelled or number of turns didn't predict test performance — but metrics related to how *evenly* and *dynamically* someone explored did. That's the gap Flow Trees are built to fill: a way to capture the shape of a group's decisions over time, not just a summary number.

Method

A Flow Tree is built from a set of trajectories that all start at the same place. Moving forward in time, whenever a subset of trajectories makes a different decision than the rest, the group splits and a new branch point is recorded — so the tree's shape traces exactly when and how a group of navigators diverged from one another. The thickest path from root to leaf, called the backbone, represents the most common (and, in this maze, always the shortest) route; trees are summarized with metrics like number of nodes, depth, branching factor, and backbone thickness for statistics and prediction.

Results

Flow Tree features are more strongly correlated with path accuracy than static baselines. Across 72 test paths, complexity-related Flow Tree metrics (number of nodes, branching factor) are strongly negatively correlated with accuracy, while backbone thickness is positively correlated. All are more strongly than traditional, static metrics such as Euclidean distance, path distance, distance travelled, or number of turns.

**p < 0.001. Flow Tree features were significantly more correlated with accuracy than every static baseline (Fisher z-test, see Table S4).

Flow Trees predict individual success, not just path difficulty. Where a navigator departs from the group's "backbone" path predicts their overall success rate (r=0.95, p<0.001). This holds even when only looking at their successful trials (r=0.46, p<0.001), suggesting consistently successful navigators solve routes in a more group-typical way.

Flow Trees can predict success in real time. Using only the first four decisions of a new trajectory, a Flow-Tree-based predictor reaches an average AUC of 0.84 for whether that navigator will reach their target,outperforming trajectory-similarity baselines at every depth (Figure 8, Figure S4).

Flow Trees reveal group differences beyond accuracy. A permutation-testing framework applied to Flow Trees shows that successful male and successful female navigators produce significantly different tree shapes (despite identical success rates), that direction of travel changes group cohesion, and that a maze location's structure (e.g., a dead end vs. a four-way junction) is recoverable purely from how groups of navigators split around it without any spatial information (Figure 7, Table 1).

Generalisability

Flow Trees generalise beyond human data. As a proof of concept, we apply them to mouse maze exploration data, and they reveal two distinct strategies invisible to standard behavioral regimes. One is indistinguishable from a random walk, one is systematically more cohesive.

Funding: Supported by NIH R01NS119468, the UCSB Chancellor's Fellowship, and a gift from the UC Noyce Initiative.