Reciprocal phenotypic plasticity can lead to stable predator-prey interaction.

1. Inducible defences of prey and inducible offences of predators are prevalent strategies in trophic interactions with temporal variation. Due to the inducible properties of the functional traits themselves, which drive the dynamic predator-prey relationship on an ecological time-scale, predator and prey may reciprocally interact through their inducible traits (i.e. reciprocal phenotypic plasticity). 2. Although overwhelming evidence of the stabilizing effect of inducible traits in either species on community dynamics forcefully suggests a critical ecological role for reciprocal plasticity in predator-prey population dynamics, our understanding of its ecological consequences is very limited. 3. Within a mathematical modelling framework, we investigated how reciprocal plasticity influences the stability of predator-prey systems. 4. By assuming two types of phenotypic shift, a density-dependent shift and an adaptive phenotypic shift, we examined two interaction scenarios with reciprocal plasticity: (i) an arms-race-like relationship, in which the defensive prey phenotype is more protective against both predator phenotypes (i.e. normal and offensive) than the normal prey phenotype, and the offensive predator is a more efficient consumer, preying upon both prey phenotypes (i.e. normal and defensive), than the normal predator and (ii) a matching response-like relationship, in which the offensive predator consumes more defensive prey and fewer normal prey than the normal predator. 5. Results of both phenotypic shift models consistently suggest that given the used set of parameter values, the arms-race-like reciprocal plasticity scenario has the largest stability area, when compared with the other scenarios. In particular, higher stability is achieved when the prey exhibits a high-performance inducible defence. Furthermore, this stabilization is so strong that the destabilizing effects of enrichment may be eliminated, even though the higher flexibility of plasticity does not always stabilize a system. 6. Recent empirical studies support our model predictions. Clear-cut examples of reciprocal phenotypic plasticity show an arms-race-like relationship in which prey species exhibit induced high-performance defences. We may need to re-examine reported predator-prey interactions in which predator or prey exhibits inducible plasticity to determine whether arms-race-like reciprocal plasticity is a general ecological phenomenon.