How residency duration affects the outcome of a territorial contest: Complementary game-theoretic models

• First discovers often become owners, but sometimes it is unclear who got there first.
• When rival claims to property arise, contest duration increases with residency time.
• Game-theoretic models based on increasing belief or motivation explain these effects.

While the first individuals to discover and maintain territories are generally respected as owners, under some conditions there may be ambiguity as to who got there first. Here we attempt to understand the evolutionary consequences of this ambiguity by developing a pair of game-theoretic models in which we explicitly consider rival residency-based claims to ownership. Following earlier qualitative explanations for residency effects, we assume that either the value of the territory (Model A) or an interloper׳s self-belief that it is the owner (Model B) increases with duration of residency. Model A clearly demonstrates that if the value of a territory increases to a resident over time, so should its motivation to fight in terms of the effort it invests in fighting. Indeed, only a small increase in territory value with residency duration can be sufficient for longer established residents to win disputes, even without any arbitrary convention or other form of priority effect. Likewise, Model B shows that the observed increase in fighting persistence with residency duration can be readily explained as a consequence of increasing confidence on behalf of the interloper that it is the rightful owner. Collectively, the models help to explain some general findings long observed by empiricists, and shed light on the nature of conflicts that can arise when individuals do not have complete information about rival claims to ownership.