Invulnerable prey and the paradox of enrichment

In many predator-prey systems, prey individuals make transitions between vulnerable and invulnerable states or locations. The invulnerable (or less vulnerable) class can be individuals occupying a spatial refuge or those engaged in activities that greatly reduce the risk of predation. Simple models are used to show that transitions between such classes have the following consequences: (1) equilibrium prey density increases as the conditions of prey growth are improved and (2) enrichment often cannot destabilize systems with stable equilibrium densities and may stabilize systems that are undergoing limit cycle oscillations. Transitions to and from invulnerable states therefore represent a possible explanation for the lack of examples of destabilization via fertilization (''the paradox of enrichment'') in nature. Other theoretical reasons for the apparent absence of the paradox of enrichment are reviewed, and methods of distinguishing the different mechanisms are discussed.