Analysis of Kramer's coral-reef food web model

The model of a coral reef ecosystem, proposed by D. B. Kramer and published in Ecology and Society in 2008, explored the implications of changes in biological parameters and changes in economic and social interaction variables governing the fishing behaviour of anglers targeting the two fish species included in the model, herbivore and piscivore fish. This model is parametrized based on evidence provided in the literature. The recognition of multiple species in the model as well as the inclusion of adaptive harvesting behaviour may supposedly allow to explore policy or management options. This paper reviews, extends and sharpens the analysis undertaken in original article, and reveals both mathematical and interpretational mistakes in it. We use analytical and numerical methods to show that, contrary to the assertion in discussed article, some of the equilibrium outcomes are independent of the parameter values that were identified as important in this paper. At the same time the model is highly sensitive to the setting of some parameter values as well as to the structures representing interactions in the model. We suggest ways in which the model can be modified so that it would become interpretable.