Introduction of the benthivorous common carp (Cyprinus carpio) has been identified as one of the main causes of loss of biodiversity and water clarity in numerous shallow lakes and ponds worldwide. Recent observations in experimental fish ponds suggest that the effect of carp on the ecosystem is catastrophic in the sense that a substantial impact occurs only when a critical carp density is exceeded. In search for an explanation, we analyzed a simple model of the interaction between benthivorous fish and their invertebrate benthic prey, and of sediment resuspension resulting from fish feeding behavior. Our results suggest that benthic prey populations should be only moderately depressed until predator fish abundance grows to a critical biomass at which benthos collapses due to overexploitation. This drop in prey density is predicted to result in a sharp increase in water turbidity due to an increase in prey search activity of the fish. For less eutrophic and deeper lakes, where benthos productivity and hence benthivorous fish carrying capacity are lower, water turbidity is predicted to be much less affected. The qualitative patterns are quite robust against assumptions on parameter values and correspond closely to the experimental results and data from lakes suggesting that the model may capture the essence of the mechanism causing a discontinuous effect of benthivorous fish on lake ecosystems.