Table 1. Descriptions of three long-standing hypotheses for plant-herbivore and herbivore-predator interactions and their relation to the tri-trophic interactions hypothesis.

Original hypothesis			Predictions under tri-trophic interactions hypothesis
Name	Factors considered	Predictions
Physiological efficiency	Diet breadth, plant quality	Specialists are better adapted than generalists at using shared plants as food (a>b, c>d, e>f, and g>h) and variation in host-plant quality should have stronger effects on generalists than specialists (a–c<b–d and e–g<f–h)	The benefits of specialization for performance are greater in the presence of natural enemies (e–g≪f–h) than absence of natural enemies (a–c<b–d)
Enemy-free space	Diet breadth, natural enemies	Specialist are better than generalists at using shared plants for predator avoidance (a–e<b–f and c–g<d–h)	The benefits of specialization for predator avoidance are greater on low-quality plants (c–g≪d–h) than high-quality plants (a–e<b–f)
Slow-growth/high-mortality	Plant quality, natural enemies	Low plant quality increases the effects of natural enemies (a–e<c–g and b–f<d–h)	Low plant quality increases the effects of natural enemies more for generalists (b–f≪d–h) than specialists (a–e<c–g)

Parenthetical references to a–h refer to the graphical representation of these predictions shown in Fig. 1.