Significance
Marking animals avoid locations recently visited by others. We conceptualized this time nonlocal avoidance behavior as stigmergy, a form of mediated interaction that gives rise to coordinated behavior from seemingly independent individuals. In so doing, the concept of stigmergy is used beyond the realm of eusocial insects. To link the population spatiotemporal patterns that emerge from the individual nonlocal rules of interaction, we construct a collective movement model whereby randomly moving animals have the tendency to avoid marks left by a conspecific, depending on the age of the mark. As a result, we are able to quantify animal decision-making processes in terms of current and past locations of other individuals, linking behavior to history-dependent actions.