A qualitative dynamical modelling approach to capital accumulation in unregulated fisheries

Capital accumulation has been a major issue in fisheries economics over the last two decades, whereby the interaction of the fish and capital stocks were of particular interest. Because bio-economic systems are intrinsically complex, previous efforts in this field have relied on a variety of simplifying assumptions. The model presented here relaxes some of these simplifications. Problems of tractability are surmounted by using the methodology of qualitative differential equations (QDE). The theory of QDEs takes into account that scientific knowledge about particular fisheries is usually limited, and facilitates an analysis of the global dynamics of systems with more than two ordinary differential equations. The model is able to trace the evolution of capital and fish stock in good agreement with observed patterns, and shows that over-capitalization is unavoidable in unregulated fisheries.