Abstract Giuggioli

Animal spacing has important implications for population abundance, species demography and the environment. Mechanisms underlying spatial segregation have their roots in the characteristics of the animals, and their interaction collective as well as individual. Recent studies on scent-marking territorial animals shed light on how the segregation patterns we observe can be explained and quantified through the introduction of the so-called territorial random walkers. This framework represents animals as agents that move at random, mark the locations they visit using scent, that is temporal flags that decay over a finite time, and retreat upon encountering a foreign scent.
Depending solely on the ratio between the time for which the mark is active and the time it takes for the walker to cover its own territory, the system displays different phenomena. Short lived marks produce rapidly morphing, fast travelling territories. A broad range of shapes and territory sizes are observed, and these territories may display ergodic trajectories. Marks that remain active for long times yield slowly moving territories that possess signatures of glassy systems.
From the biological perspective, the emergence of these territorial patterns is an example of a stigmergic process beyond the realm of eusocial insects, whereby agents coordinate each other in an indirect fashion. By leaving a trace in the environment they stimulate the performance of the next action, by the same or a different agent. In that way, subsequent actions tend to reinforce and build on each other, leading to the spontaneous emergence of coherent activities and patterns.