Insect parasitoids have been widely studied, particularly due to their ecological implications through the study of the special relationships observed among this kind of species, as well as to their expression in mathematical models. However, there are still scarce studies on parasitoid relationships and their expression in more realistic mathematical models. The present work is aimed at deepening into competition relationships among parasitoids. Bearing this purpose in mind, the system shaped by two parasitoids was chosen: Trichogramma brassicae (idiobiont egg parasitoid) and Chelonus oculator (koinobiont egg-larval parasitoid). Both species compete against each other for the same host species (Lepidoptera). The results obtained in the laboratory point out that T. brassicae may be considered a better competitor than Ch. oculator. This is the result of the extrinsic competition due to the substances injected by the female during parasitization. However, our results show this classification into better and worse competitors inaccurate. Thus, these interspecific competition influences are detrimental to both parasitoid species. This is the first time that the effect of this competition is mentioned regarding parasitoid functional response. Our results and their ecological implications are reported and discussed.

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Over the last few decades, important advances have been made in understanding of host-parasitoid relations and their applications to biological pest control. Not only has the number of agent species increased, but new manipulation techniques for natural enemies have also been empirically introduced, particularly in greenhouse crops. This makes biocontrol more complex, requiring a new mathematical modeling approach appropriate for the optimization of the release of agents. The present paper aimed at filling this gap by the development of a temperature-and stage-dependent dynamic mathematical model of the host-parasitoid system with an improved functional response. The model is appropriate not only for simulation analysis of the efficiency of biocontrol agents, but also for the application of optimal control methodology for the optimal timing of agent releases, and for the consideration of economic implications. Based on both laboratory and greenhouse trials, the model was validated and fitted to the data of Chelonus oculator (F.) (Hym.: Braconidae) as a biological control agent against the beet armyworm, Spodoptera exigua Hübner (Lep.: Noctuidae). We emphasize that this model can be easily adapted to other interacting species involved in biological or integrated pest control with either parasitoid or predator agents. Key message• The paper aimed at filling the gap between existing host-parasitoid models and the empirically introduced new manipulation techniques of biocontrol. • The result is a temperature-and stage-dependent dynamic model of the host-parasitoid system, appropriate for simulation analysis and optimization of the release of biocontrol agents • For an illustration, the model is validated and fitted to the data of a concrete host-parasitoid system. • Our model building can be easily adapted to biocontrol by predatory agents.

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