In social animal groups, an individual's spatial position is a major determinant of both predation risk and foraging rewards. Additionally, the occupation of positions in the front of moving groups is generally assumed to correlate with the initiation of group movements. However, whether some individuals are predisposed to consistently occupy certain positions and, in some instances, to consistently lead groups over time is as yet unresolved in many species. Using the mosquitofish (Gambusia holbrooki), we examined the consistency of individuals' spatial positions within a moving group over successive trials. We found that certain individuals consistently occupied front positions in moving groups and also that it was typically these individuals that initiated group decisions. The number of individuals involved in leading the group varied according to the amount of information held by group members, with a greater number of changes in leadership in a novel compared to a relatively familiar environment. Finally, our results show that the occupation of lead positions in moving groups was not explained by characteristics such as dominance, size or sex, suggesting that certain individuals are predisposed to leadership roles. This suggests that being a leader or a follower may to some extent be an intrinsic property of the individual.