The characteristics of inducible defenses influence predator-prey dynamics

Empirical and theoretical studies suggest inducible and evolving defenses have different effects on predator-prey dynamics. However, theory for inducible defenses does not account for differences in response stimuli, reversibility, and within-generation versus transgenerational responses. We use predator-prey models to explore how these characteristics influence the effects of inducible defenses on stability and predator-prey oscillations. We find that while inducible defenses are typically stabilizing, defenses responding to any stimuli (predator density, conspecific and predator densities, predation rates, or the fitness gradient) can be destabilizing. Also, while induced defenses typically shorten predator-prey phase lags, defenses that respond to prey densities or the fitness gradient can increase the lags. Our theory helps explain why inducible defenses are less likely to be destabilizing and increase phase lags than evolving defenses: inducible defenses typically have negative feedbacks of the trait on its own dynamics whereas evolving defenses under disruptive selection can have positive feedbacks.