Fishing Quotas, Induced Allee Effect and Fluctuation-Driven Extinction

We explore the potential of modifications to standard fishery models (for example Gordon-Schafer-Munro) to help understand events such as the collapse of the North Atlantic cod fishery. In particular we find that quota-driven and similar harvesting strategies induce an effective strong Allee effect (collapse if the population falls below a critical level). In the presence of environmental noise, fish population dynamics is similar to a random walk with (non-linear) drift. The expected survival time (first passage time to collapse) is shown to depend sensitively upon the amount of environmental noise and size of the "safe zone" between the deterministic steady state population and the critical population level at which the system collapses; more precisely it is exponential in the cube of the size of the safe zone divided by the variance of the noise process. Similar scaling can be expected for more survival in more general systems with multiple steady states. Our calculations imply an amplification effect under which small increases in harvest yield large decreases in expected survival time, and one should be cautious in changes in harvesting, especially in fisheries with poor or limited data and fisheries affected by climate change.