Abstract
Majority-voting or averaging the estimations made by the individuals in a collective are simple rules that can effectively aggregate knowledge under some ideal conditions. However, these rules can catastrophically fail in the frequent situation in which a minority brings knowl-edge to a collective. Aggregation rules should ideally use majorities or averages when most or all members have similar information and focus on a minority when it brings new relevant information to the group. Here we turned to fish schools to test whether aggregation rules that have evolved over hundreds of millions of years can use this flexible aggregation. We tracked each animal in large groups of 60, 80 and 100 zebrafish, Danio rerio, with a newly developed method. We used the trajectories to train deep attention networks and obtained a model that is both predictive and insightful about the structure of fish interactions. A six-dimensional function describes the focal-neighbour interaction and a four-dimensional function how infor-mation is aggregated. The aggregation function shows that each animal sometimes averages approximately 25 neighbours and sometimes focuses on fewer animals down to effectively a single one, and that it can rapidly shift between these extremes depending on the relative po-sitions and velocities of local neighbours. Animal collectives could thus avoid the limitations of simple rules and instead flexibly shift from average many to follow few or one individual.
