Inducible defenses: continuous reaction norms or threshold traits?

Phenotypically plastic traits can be expressed as continuous reaction norms or as threshold traits, but little is known about the selective conditions that favor one over the other. We study this question using a model of prey defenses in which prey can induce any level of defense conditional on cues that are informative of local predator density. The model incorporates a trade-off between defense expression and fecundity and feedback between the defense level of prey and predator attack rates. Both continuous reaction norms and threshold traits can emerge as evolutionarily stable solutions of defense induction, and we show that the shape of the trade-off curve plays a key role in determining the outcome. Threshold traits are favored when selection is disruptive. Ecological conditions that favor defense dimorphisms in the absence of cues will favor threshold traits in the presence of slightly informative cues. We caution that continuous reaction norms and threshold traits may result in similar patterns of defense expression at the population level, and we discuss potential pitfalls of inferring reaction norm type from observational data.