| Abstract: | Theoretical and empirical studies have shown that enemy–victim interactions in spatially homogenous environments can exhibit diverging oscillations which result in the extinction of one or both species. For enemy–victim models with overlapping generations, we investigate the dynamical implications of spatial heterogeneity created by enemy-free sinks or victimless sinks. An enemy-free sink is a behavioral, physiological or ecological state that reduces or eliminates the victim's vulnerability to the enemy but cannot sustain the victim population. For victims that move in an ideal-free manner, we prove that the inclusion of an enemy-free sink shifts the population dynamics from diverging oscillations to stable oscillations. During these stable oscillations, the victim disperses in an oscillatory manner between the enemy-free sink and the enemy-occupied patch. Enemy-free sinks with lower mortality rates exhibit oscillations with smaller amplitudes and longer periods. A victimless sink, on the other hand, is a behavioral, physiological or ecological state in which the enemy has limited (or no) access to its victims. For enemies that move in an ideal-free manner, we prove that victimless sinks also stabilize diverging oscillations. Simulations suggest that suboptimal behavior due to information gathering or learning limitations amplify oscillations for systems with enemy-free sinks and dampen oscillations for systems with victimless sinks. These results illustrate that the coupling of a sink created by unstable enemy–victim interactions and a sink created by unsuitable environmental conditions can result in population persistence at the landscape level. |
