Population dynamics of a parasite and hyperparasite in a closed system: model analysis and parameter estimation

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Abstract
In this paper, we introduce and test models of the dynamics of a parasite and hyperparasite in a closed system from which the parasite's host is excluded. The models are tested against data for the temporal dynamics of a fungal plant parasite of lettuce, Sclerotinia minor, and a fungal hyperparasite, Sporidesmium sclerotivorum. The models are developed by treating the hyperparasite-parasite dynamics as a classical predator-prey system, but then expanding the prey component into a compartmental system of susceptible (uninfected) and infected parasites. The resulting hybrid model enables the separation of the dynamics of susceptible parasites, which are capable of causing disease, and infected parasites, which support reproduction of the hyperparasite. The influence of different functional and numerical responses are compared by analytical results and by parameter estimation.