Egg distribution of insect parasitoids: a survey of models

A number of (insect) parasitoids have been found to avoid superparasitism, i.e., these parasitoids distribute their eggs more evenly over the available hosts than might be expected from chance only. By doing so each parasitoid individual ensures a greater probability of survival for its offspring as a result of a reduced within-host-competition.Recently a number of mathematical models have been developed, describing the distribution of the parasitoid eggs in the hosts. This paper gives a survey of these models, placing them within one and the same mathematical framework. An essential conceptual distinction, neglected up to now, emerges: parasitoids can either react to the number of previous visits to a particular host, or they can react to the number of eggs already present in that host.For each model the probability-generating function, the mean, the variance, and the probability distribution of the number of eggs are given, as well as a discussion of estimating and testing procedures. A few possibilities for generalizations of these models are discussed too.