Researchers have long noted that individuals occupy consistent spatial positions within animal groups. However, an individual's position depends not only on its own behaviour, but also on the behaviour of others. Theoretical models of collective motion suggest that global patterns of spatial assortment can arise from individual variation in local interaction rules. However, this prediction remains untested. Using high-resolution GPS tracking of members of a wild baboon troop, we identify consistent inter-individual differences in within-group spatial positioning. We then apply an algorithm that identifies what number of conspecific group members best predicts the future location of each individual (we call this the individual's neighbourhood size) while the troop is moving. We find clear variation in the most predictive neighbourhood size, and this variation relates to individuals' propensity to be found near the centre of their group. Using simulations, we show that having different neighbourhood sizes is a simple candidate mechanism capable of linking variation in local individual interaction rules-in this case how many conspecifics an individual interacts with-to global patterns of spatial organization, consistent with the patterns we observe in wild primates and a range of other organisms.

In many animal societies, groups of individuals form stable social units that are shaped by well-delineated dominance hierarchies and a range of affiliative relationships. How do socially complex groups maintain cohesion and achieve collective movement? Using high-resolution GPS tracking of members of a wild baboon troop, we test whether collective movement in stable social groups is governed by interactions among local neighbours (commonly found in groups with largely anonymous memberships), social affiliates, and/or by individuals paying attention to global group structure. We construct candidate movement prediction models and evaluate their ability to predict the future trajectory of focal individuals. We find that baboon movements are best predicted by 4 to 6 neighbours. While these are generally individuals' nearest neighbours, we find that baboons have distinct preferences for particular neighbours, and that these social affiliates best predict individual location at longer time scales (>10 minutes). Our results support existing theoretical and empirical studies highlighting the importance of local rules in driving collective outcomes, such as collective departures, in primates. We extend previous studies by elucidating the rules that maintain cohesion in baboons 'on the move', as well as the different temporal scales of social interactions that are at play.