Fishing Quotas, Induced Allee Effect, and Fluctuation-Driven Extinction

Harold M Hastings, Bard College at Simon’s Rock, Great Barrington, MA and Hofstra University, Hempstead, NY

Michael Radin, Rochester Institute of Technology, Rochester, NY.

Tamas Wiandt, Rochester Institute of Technology, Rochester, NY.

**Abstract: **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.

*Keywords: *Fishery collapse, Gordon-Schafer-Munro model, harvest quota, environmental noise, generalized random walk with drift, expected survival time test