Assessing superparasitism with a model combining the functional response and the egg distribution of parasitoids

A model for superparasitism in insect parasitoids is developed. This model combines the study of superparasitism in terms of distribution of eggs among hosts (for a given number of hosts) and in terms of functional response (number of hosts attacked for a varying number of hosts available). Thus, it gives a synthetic treatment of problems that had been previously handled with separate models (e.g., Bakker et al. (1972) on one hand and Arditi (1983) on the other hand). The combined model involves several parameters, among which important ones are the propensity to superparasitise, delta, and the average handling times spent on healthy and parasitised hosts, T-h and T-p. Special cases are those of an indiscriminate parasitoid (delta = 1 and T-p = T-h) and of a ''predator-like'' parasitoid (delta = 0 and T-p = 0). In this paper, the emphasis is put on the problems related with model identification and parameter estimation from experimental data. According to the data available, three situations are considered: egg distribution alone, functional response alone, and both combined. The main conclusions are the following. (i) Egg distributions are described correctly when the parasitoid/host ratio is not too high. When the situation is very strained, i.e., when a small number of hosts are available per parasitoid, superparasitsm occurs more frequently than predicted by the model. (ii) Functional response data are usually not precise enough to estimate all model parameters, particularly T-p. That is, it will usually not be possible to assess the discrimination capacity of a given species on the basis of a functional response curve only. (iii) If both a functional response and the corresponding egg distributions are available, it is better to fit the egg distribution model first and, depending on the estimated value of delta, to fit thereafter the appropriate functional response model.