Optimal defense schedule of annual plants against seasonal herbivores.

Herbivores often have huge impacts on plant performance. In order to reduce damage from herbivory, plants evolve antiherbivore defenses, the mechanisms of which have been studied from a theoretical viewpoint. In the theoretical studies, the models of defense schedules have assumed a uniform intensity of herbivory or a constant rate of encounter of herbivores throughout the season. However, some herbivores apparently appear for only a limited period instead of the whole growing season of the plant. In our study, we analyzed the optimal schedule of defense allocation of the plant under the herbivory that occurs within a limited period with a certain probability. We assumed an annual plant that consists of vegetative and defensive parts and whose growing season is divided into two phases at the time of herbivore emergence. In the phase after the emergence time, the status of a plant can be either with or without herbivore stochastically. The plant is considered to maximize the average vegetative size at the end of the growing season. We found that under the fixed emergence time, inducible defense is favored when the plant growth rate and herbivory intensity are high. Extending this result, we also analyzed the coevolution of plant defense and herbivore emergence time by using invasibility analysis. In the system considered, an equilibrium steady state tends to be absent in herbivore strategy. This suggests polymorphism of herbivore emergence time.