Dancing between the devil and deep blue sea: the stabilizing effect of enemy-free and victimless sinks

摘要

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.