Escalation and Time Costs in Displays of Endurance

Physical endurance is a significant factor in many animal signalling interactions, both in the context of fighting behaviour and of sexual selection. We construct a general model of displays that are physically demanding to maintain, and determine the appropriate behaviour that optimizes an individualʹs expected pay-off. An important feature of the model is the inclusion of explicit time costs associated with the duration of the display. The model can exhibit not just displays of endurance, but also basic “one-off” displays of magnitude, and war-of-attrition-like displays of persistence. We determine necessary conditions for displays of endurance to exist. In addition, our results provide a novel explanation for the occurrence of escalating displays in situations in which time costs rise increasingly rapidly.