Intense local fishing pressure is likely to induce significant local decreases in both resource biomass and fishing yields. This is what we term ‘local overfishing’. Such a phenomenon and its consequences for stock assessment are investigated with the fisheries simulator SHADYS (Simulateur halieutique de dynamiques spatiales: spatialized simulator of fisheries dynamics). In SHADYS, resource dynamic is based on an advection–diffusion–reaction equation. After a brief presentation, the simulator is used to characterize the ‘local overfishing’ phenomenon as a ‘wound’ of the population. The latter is subsequently able to ‘heal’ and to recover its initial distribution. We show that, associated with cooperation tactics of the fishing fleets, local overfishing may induce non-linear relationships between catches per unit of effort (CPUE) and fishing effort calculated locally. In particular, it is shown that there is a strictly decreasing relationship between catchability and effort when fishing vessels apply intense local fishing pressure but do not cooperate; that the relationship may increase when vessels cooperate but do not apply intense local fishing pressures; and finally, that it may go through a maximum when, simultaneously, ships cooperate and have high local exploitation rates. These three main types of theoretical relationships correspond well with those observed in reality. The existence of such relationships could be an important source of biases in stock assessment.