Avoidance-modified generalised distributions and their application to studies of superparasitism

Given an underlying distribution for the number of encounters between parasites and a host this may be generalised by the distribution of the number of eggs per encounter. If eggs are already present, a parasite may avoid oviposition at subsequent encounters. A class of avoidance-modified generalised distributions is presented to model such situations. The case of a solitary (single egg-laying) parasite and a Poisson distribution for the number of encounters gives rise to a distribution of particular interest. Various properties of this distribution are derived and alternative estimation procedures investigated. Estimators based on the method of mean and zero frequency are shown to have the dual advantages over other estimators that have been proposed of simplicity of computation and increased efficiency. Over a wide range of parameter values there is virtually no loss of efficiency in comparison with maximum likelihood estimation.