A probabilistic model for the functional response of a parasitoid at the behavioural time scale

1. The aim of this paper is to build a probabilistic model of the functional response of a parasitoid at the behavioural time-scale. The organism used is the eulophid Sympiesis sericeicornis Nees (Hymenoptera: Eulophidae), a polyphagous ectoparasitoid attacking the apple leaf-miner Phyllonorycter cydoniella (D. & S.) (Lepidoptera: Gracillariidae). We deal exclusively with the functional response at the level of a mined leaf and restrict our attention to the cases without superparasitism. 2. We use detailed observations of the behaviour and location of the parasitoid on a leaf to define four behavioural states: searching, hunting on a mine with an unparasitized host, ovipositing, and leaving the leaf. We describe the sequence of behavioural states visited by an embedded markov chain, which is fully determined by the one-step transition probability matrix and the initial probability distribution. 3. The key element of our model is the process of leaving the leaf. We postulate that this can occur only from the searching state, and happens either by necessity, because either available hosts or useable eggs are exhausted, or by choice. We find that the probability of leaving by choice is a monotone increasing function of the number of hosts parasitized. 4. We consider a cohort of females with initial eggload distributed according to a negative binomial distribution whose parameters we obtain from independent data. An exact multinomial test of our model on the data set from which the one-step transition probabilities are obtained gives excellent results. The domain of applicability of the model is extended by relaxing two important assumptions. We also apply the exact multinomial test to an independent data set and again obtain very good results. Sensitivity analysis demonstrates that the model is sensitive to changes in the value of only one parameter.