Mechanistic models suggest that individuals' memories could shape home range patterns and dynamics, and how neighbours share space. In social species, such dynamics of home range overlap may be affected by the pre-dispersal memories of immigrants. We tested this "immigrant knowledge hypothesis" in a wild population of chacma baboons (Papio ursinus). We predicted that overlap dynamics with a given neighbouring troop's home range should reflect males' adaptive interests in overlap when the alpha male had immigrated from this neighbouring troop but less so when the alpha male originated from elsewhere. We used data collected between 2005 and 2013 on two neighbouring troops in Namibia, comprising GPS records of daily ranges, male natal origins, daily females' reproductive status, and a satellite index of vegetation growth. We found support for our prediction in line with male reproductive strategies but not in line with foraging conditions. In periods with a higher relative number of fertile females over adult males in the focal troop, male baboons would benefit from reducing overlap with their neighbours to mitigate the costs of between-troop mating competition. This was indeed observed but only when the alpha male of the focal troop was an immigrant from that neighbouring troop, and not with alpha males of other origins, presumably due to their different knowledge of the neighbouring troop. Our findings highlight the role of reproductive competition in the range dynamics of social groups, and suggest that spatial segregation between groups could increase through the combination of dispersal and memory.