428 



Abstract — Priors are existing infor- 

 mation or beliefs that are needed 

 in Bayesian analysis. Informative 

 priors are important in obtaining 

 the Bayesian posterior distribu- 

 tions for estimated parameters in 

 stock assessment. In the case of the 

 steepness parameter l/i). the need for 

 an informative prior is particularly 

 important because it determines the 

 stock-recruitment relationships in the 

 model. However, specifications of the 

 priors for the h parameter are often 

 subjective. We used a simple popula- 

 tion model to derive h priors based 

 on life history considerations. The 

 model was based on the evolutionary 

 principle that persistence of any spe- 

 cies, given its life history (i.e., natural 

 mortality rate) and its exposure to 

 recruitment variability, requires a 

 minimum recruitment compensation 

 that enables the species to rebound 

 consistently from low critical abun- 

 dances (iV_,). Using the model, we 

 derived the prior probability distri- 

 butions of the h parameter for fish 

 species that have a range of natural 

 mortality, recruitment variabilities, 

 and iV, values. 



A prior for steepness in 



stock-recruitment relationships, 



based on an evolutionary persistence principle 



XiHe^ 



Marc Mangel^ 



Alec MacCall' 



' Santa Cruz Laboratory 

 Southwest Fisheries Science Center 

 National Marine Fisheries Service 

 Santa Cruz, California 95060 

 E-mail address (for X He) xi he g'noaa gov 



^ Center for Stock Assessment Research 

 Department of Applied Mathematics and Statistics 

 University of California 

 Santa Cruz, California 95064 



Manuscript submitted 20 July 2004 

 to the Scientific Editor's Office. 



Manuscript approved for publication 



30 September 2005 by the Scientific Editor. 



Fish. Bull. 104:428-433 (2006). 



Success in parameter estimation 

 for stock assessment models often 

 requires sufficient data and correct 

 specification of prior distributions for 

 the estimated parameters (Punt and 

 Hilborn, 1997; Needle, 2002). This is 

 especially true for successfully esti- 

 mating stock-recruitment relation- 

 ships with stock assessment models 

 because there often are not sufficient 

 data and there is considerable variabil- 

 ity in stock-recruitment relationships. 

 Even in the cases where there are suf- 

 ficient data, these data can be very 

 noisy and may not show a clear pat- 

 tern for fitting stock-recruitment rela- 

 tionships (Hilborn and Walters, 1992; 

 Williams and Shertzer, 2003; Munch 

 et al., 2005). Yet, stock-recruitment 

 relationships are important in making 

 fisheries management decisions, espe- 

 cially for over-fished stocks such as 

 widow rockfish iSebastes entome- 

 las), bocaccio iSebastes paucisplnis), 

 and darkblotched rockfish (Sebastes 

 crameri) along the west coast of the 

 United States (He et al.i; MacCall-; 

 Punt, 2003; Rogers^). Stocks with low 

 values of steepness have low recruit- 

 ment compensation; therefore stocks 

 will take a long time to rebuild from 

 over-fished status to desired manage- 

 ment levels even though total allow- 

 able catches for these stocks are kept 

 small (Mace and Doonan^). 



In this study, we used a simple 

 population model to derive prior dis- 



tributions (referred to hereafter as 

 "priors") for the steepness parame- 

 ter (hereafter denoted h) (Mace and 

 Doonan^). Prior distributions are 

 probability distributions that repre- 

 sent existing information about pa- 

 rameters. The model was based on the 

 principle that persistence of any fish 

 species, given its life history and its 

 exposure to recruitment variability, 



' He, X., S. V. Ralston, A. D. MacCall. D. E. 

 Pearson, and E.J. Dick. 2003. Status 

 of the widow rockfish resource in 2003. 

 Vol. 1: Status of the Pacific coast ground- 

 fish fishery stock assessment and fishery 

 evaluation, 138 p. Pacific Fishery Man- 

 agement Council, 7700 NE Ambassador 

 Place, Portland, OR. 



- MacCall, A. D. 2003. Status of bocac- 

 cio off California in 2003. Vol. 1: Status 

 of the Pacific coast groundfish fishery 

 stock assessment and fishery evalua- 

 tion, 56 p. Pacific Fishery Management 

 Council, 7700 NE Ambassador Place, 

 Portland, OR. 



'^ Rogers, J. B. 2003. Darkblotched rock- 

 fish [Sebastes crameri) 2003 stock status 

 and rebuilding analysis. Vol. 1; Status of 

 the Pacific coast groundfish fishery stock 

 assessment and fishery evaluation, 56 

 p. Pacific Fishery Management Council, 

 7700 NE Ambassador Place, Portland, 

 OR. 



^ Mace, P. M., and I. J. Doonan. 1988. A 

 generalized bioeconomic simulation model 

 for fish dynamics, 47 p. New Zealand 

 Fishery Assessment Research Document 

 88/4. Fisheries Research Center, P.O. 

 Box 297, Wellington, New Zealand. 



