Multi-state models for double transitions associated with parasitism in biological control

Competition between parasitoids can reduce the success of pest control in biological programs using two species as bio-control agents or when multiple species exploit the same host crop. Parasitoid foraging behavior and the ability to identify already parasitized hosts affect the efficacy of parasitoid species as bio-agents to regulate pest insects. We evaluated the behavioural changes of parasitoids according to the quality of hosts ({\it i.e.}, previously parasitised or not), and the characterisation of these transitions over time via multi-state models. We evaluated the effects of previous parasitism of the brown stinkbug {\it Euschistus heros} eggs on the parasitism rate of the species {\it Trissolcus basalis} and {\it Telenomus podisi}. We successively modelled the choice of eggs (with three possibilities: non parasitised eggs, eggs previously parasitised by {\it T. podisi}, and eggs previously parasitised by {\it T. basalis}) and the conditional behaviour given the choice (walking, drumming, ovipositing or marking the chosen egg). We consider multi-state models in two successive stages to calculate double transition probabilities, and the statistical methodology is based on the maximum likelihood procedure. Using the Cox model and assuming a stationary process, we verified that the treatment effect was significant for the choice, indicating that the two parasitoid species have different choice patterns. For the second stage, i.e. behaviour given the choice, the results also showed the influence of the species on the conditional behaviour, especially for previously parasitised eggs. Specifically, {\it T.podisi} avoids intraspecific competition and makes decisions faster than {\it T. basalis}. In this work, we emphasise the methodological contribution with multi-state models, especially in the context of double transitions.