Simulation Study of Biological Reference Points for Summer Flounder

Abstract

The biological reference point F_{x %} (i.e., the fishing mortality rate that maintains the spawning stock biomass per recruit at x% of its unfished value [where x is usually set to 40]) is a commonly used proxy for F _MSY (the fishing mortality rate that results in the maximum sustainable yield). However, F_{x %} is not in general equivalent to F _MSY. To investigate the difference between F_{x %} and F _MSY, we developed a simple simulation model capable of representing the relationship between yield and fishing mortality, maximum spawning potential (%MSP), and the curvature of the stock–recruitment (S–R) curve (parameterized as β) for a stock similar to summer flounder Paralichthys dentatus (a high-β species). The model demonstrates that the dynamic trajectories of the stock are heavily dependent on β. The model confirmed the dependence of equilibrium yield on β and produced a specific relationship between the magnitude of β and yield. A decision-theoretic approach was used to suggest that setting x to 40 reduces yield and that smaller values of x produce greater yields for high-β stocks. The analysis focuses attention on the fact that the choice of F_{x %} as a management tool places extreme reliance on the least known and understood component of fish population dynamics: the S–R relationship. Our conclusion (to use a value of x considerably less than 40 to obtain MSY) was supported by (1) our simulation results, (2) averaging in a decision-theoretic approach, (3) the correspondence of the traditionally computed biomass at the maximum sustainable yield with high values of β, and (4) the values of x reported in the literature.

Received March 14, 2011; accepted August 19, 2011

ACKNOWLEDGMENTS

We would like to thank the editor and anonymous reviewers for their helpful suggestions. This research was supported by the National Oceanic and Atmospheric Administration grant number NA10NMF4720017, issued to Partnership for Mid-Atlantic Fisheries Science.