Scaling of expected survival time in a stochastic harvesting model

We explore the dynamics of modified version of a standard fishery model (Gordon-Schafer-Munro [1]), with additive and multiplicative noise, under a quota-based harvest. A harvest quota induces an effective strong Allee effect (a positive unstable steady state population level, below which populations die out), with expected survival time following generalized Ornstein-Uhlenbeck dynamics [2]. In particular, for additive noise, the expected survival time is exponential in $s^{3}$/$\sigma^{\mathrm{2}}$, where $s$ is the difference between stable and unstable steady state populations and $\sigma $ the noise level. Thus survival time depends sensitively upon harvest quota (which determines steady state population), perhaps a warning to avoid future collapses such as that of the Atlantic cod fishery [3]. 1. Gordon HS. \textit{J Fisheries Board Canada} \textbf{10}, 442 (1953); Schaefer MB. \textit{ibid }\textbf{14}, 669 (1957); Clark, CW, Munro GR. \textit{J Environ Econ and Management} \textbf{2}, 92 (1975). 2. Beale PD. \textit{Phys Rev A} \textbf{40}, 3998 (1989). 3. c.f. www.millenniumassessment.org/