The Characteristics of Inducible Defenses Influence Predator-Prey Dynamics

AbstractThe population-level consequences of predator-prey interactions include unstable equilibria and predator-prey cycles with an approximate quarter-period phase lag. Prior studies have found that inducible defenses and rapidly evolving defenses alter the stability and phase lags of predator-prey systems differently: inducible defenses are stabilizing and decrease phase lags more frequently than evolving defenses. Using predator-prey models, we show that inducible and evolving defenses have the same range of possible effects, but the effects of inducible defenses depend on induction stimuli, reversibility, and timing. Inducible defenses responding to predator density, predator and prey densities, or predation cues are often stabilizing, but they can be destabilizing when defense is overexpressed. Only inducible defenses responding to predator and prey densities or the fitness gradient can increase phase lags. Compared with intragenerational reversible defenses, irreversible and transgenerational inducible defenses are less stabilizing and increase lags more when defense costs are sufficiently high; the opposite holds for low defense costs. We predict that inducible defenses are destabilizing and increase phase lags less often than evolving defenses because induction is a negative feedback (a self-limiting effect), whereas disruptive selection on an evolving defense is a positive feedback (a self-amplifying effect).