Resource competition among central-place foragers often leads to space partitioning, even if individuals do not show signs of direct agonistic interactions. Using simple individual-based simulations, we show that individual-level spatial awareness and memory of resource availability are sufficient to cause spatial segregation in the foraging ranges of colonial animals. The shapes of the foraging distributions are governed by commuting costs, the emerging distribution of depleted resources, and the fidelity of foragers to their colonies. A spatial imbalance between resource requirement and resource availability in one region can propagate through the landscape and lead to non-trivial space-use patterns elsewhere. Interestingly, while better spatial memory increases segregation between neighbouring colonies, it can lower the average intake rate of the population, suggesting a potential trade-off between an individual strive for optimality and population growth rates.