Many plant species defend themselves against herbivorous insects indirectly by producing and releasing induced volatiles to attract natural enemies of the herbivores. In this paper, we consider the recruitment of natural enemies attracted by plant-induced volatiles and introduce the An'Liu'Johnson'Lovett model into the Lotka'Volterra model in an attempt to add this missing vital link in tritrophic interaction. Increase in attraction strength of plant-induced volatiles to the natural enemy leads to high fluctuation amplitude of plant biomass and herbivore population. When the attack strength of natural enemies reaches a certain level, fluctuation amplitude of plant biomass and herbivore population will decrease and plant biomass will approach to its environmental carrying capacity. The simulation demonstrates that plant volatile compounds induced by insects have led to the introduction of a third tritrophic level, e.g., natural enemies, into the plant'herbivore system, resulting in the coexistence of plants, insects, and natural enemies during the evolution process.
Liu, Y. H., Liu, D., An, M., Fu, Y. L., Zeng, R. S., Luo, S. M., Wu, H., & Pratley, J. (2009). Modelling tritrophic interactions mediated by induced defence volatiles. Ecological Modelling, 220(23), 3241-3247. https://doi.org/10.1016/j.ecolmodel.2009.07.003