Porch et al.: A catch-free assessment model with application to Epinephelus ita/ora 



99 



based on completely uninformative priors will be useless 

 for generating advice because the range of plausible 

 outcomes is too large. Accordingly, we view the use 

 of subjective priors primarily as a vehicle for provid- 

 ing more realistic limits on uncertainty and prefer to 

 express the model outcomes in terms of probability 

 statements. For example, the point estimate from the 

 base model indicated that the population would never 

 recover to Sgg,, because the fishing mortality rate under 

 the harvest ban was still slightly above F^g.,. However, 

 consideration of the uncertainty led to the conclusion 

 that the chance of recovering to Sggr; within 15 years 

 was nearly 40%. 



Some sources of uncertainty have not been adequately 

 accounted for in the above assessment. For example, the 

 relationship between fecundity and age is unknown. 

 We used weight-at-age as a proxy for the relative fe- 

 cundity-at-age in our analysis, but it is often the case 

 that fecundity increases with age faster than weight. 

 If this is true for goliath grouper, then our projections 

 would be too optimistic. It should also be remembered 

 that the results apply strictly to the goliath grouper 

 population in southern Florida. It is believed that the 

 center of abundance for the population in U.S. waters 

 is off southern Florida, particularly in the Ten Thou- 

 sand Islands area, but goliath grouper are known to 

 have occurred throughout the coastal waters of Gulf of 

 Mexico and along the east coast of Florida, and on up 

 through the Carolinas. Inasmuch as goliath grouper 

 are not highly migratory, it is possible it may take 

 some additional time for the species to fully occupy its 

 historical range, thus delaying the overall recovery of 

 the U.S. population. 



The primary advantage of the catch-free assessment 

 model proposed in the present study is that it does not 

 require knowledge of the total number of removals. In 

 this light it is worth noting that 623 of the 905 stocks 

 included in the 2000 annual report to Congress on the 

 Status of Fisheries were listed as having unknown sta- 

 tus, often because catch data were either unavailable or 

 deemed unreliable. Thus we expect the proposed method 

 will become increasingly useful as fishery scientists are 

 asked more and more to develop FMPs for poorly moni- 

 tored fisheries. The fact that the model estimates the 

 population's relative abundance, rather than its absolute 

 abundance, is of little consequence when, as is often 

 the case, adjustments to the target fishing mortality 

 rate or catch quota are made in relation to the levels 

 in previous years (Caddy, 2004). Moreover, certain bi- 

 ases tend to cancel out when dimensionless quantities 

 like relative abundance are used. If, for example, only 

 a consistent fraction of the population were sampled, 

 then the absolute estimates of abundance would be 

 biased but the relative estimates would not (Prager et 

 al., 2003). 



The greatest drawback of the catch-free method is 

 probably its inability to provide direct estimates of 

 the equilibrium catch levels associated with particular 

 reference points (e.g., MSY). This situation could per- 

 haps be ameliorated by obtaining estimates of absolute 



abundance from a comprehensive short-term survey 

 covering the entire range of the animal, in which case 

 the relative outputs from the model (including relative 

 catch) could be appropriately scaled. Alternatively, a 

 long-term monitoring program at select sites located 

 throughout the known range of the animal could be es- 

 tablished to detect changes in relative abundance under 

 various closely monitored trial levels of catch. 



Acknowledgments 



The present paper benefitted greatly from the scrutiny 

 given to a related document'' by members of the SEDAR 

 stock assessment review panel (R. Allen, L. Barbieri, 

 J. Brodziak, M. Cufone, D. DeMaria, M. Kingsley, D. 

 Murie, M. Murphy, J. Neer, J. Rooker, R. Taylor, E. 

 Toomer, and J. Wheeler). S. Turner, L. Brooks, and two 

 anonymous reviewers also gave helpful comments on 

 the manuscript. S. Cass-Calay and T. Schmidt secured 

 the goliath grouper length-composition data from the 

 Everglades National Park creel survey; J. Brusher and J. 

 Schull provided the age-length data from their sampling 

 program in the Ten Thousand Islands area. 



Literature cited 



Annala, J. 



1993. Fishery assessment processes in New Zealand's ITQ 



system. In Proceedings of the international symposium 



on management strategies for exploited fish populations. 



21-24 October 1992, Anchorage Alaska (G. Kruse, D. M. 



Eggers, R. J. Marasco, C. Pautzke, and T. J. Quinn II, 



eds. ), p. 791-806. Alaska Sea Grant College Program, 



Univ. Alaska, Fairbanks. AL. 

 Bard, Y. 



1974. Nonlinear parameter estimation. Academic Press, 



San Diego, CA, 341 p. 

 Bullock, L. H., M. D. Murphy, M. F. Godcharles, and M. E. Mitchell. 



1992. Age, growth, and reproduction of jewfish Epineph- 

 elus itajara in the eastern Gulf of Mexico. Fish. Bull. 

 90:243-249. 



Caddy, J. F 



1998. A short review of precautionary reference points and 

 some proposals for their use in data poor situations. FAQ 

 Fish. Tech. Pap. 379, 30 p. FAO, Rome. 

 2004. Current usage of fisheries indicators and reference 

 points, and their potential application to management 

 of fisheries for marine invertebrates. Can. J. Fish. 

 Aquat. Sci. 61:1307-1324. 

 Cadrin, S. X., J. A. Boutillier, and J. S. Idoine. 



2004. A hierarchical approach to determining reference 

 points for Pandalid shrimp. Can. J. Fish. Aquat. Sci. 

 61:1373-1391. 

 FAO (Food and Agricultural Organization). 



1995. Precautionary approach to fisheries. FAO Fish. 

 Tech. Pap. 350, 210 p. FAO, Rome. 

 Gelman, A., J. B. Carlin, H. 8. Stern, and D. B. Rubin. 



1995. Bayesian data analysis, 526 p. Chapman and 

 Hall, London. 

 Goodyear, C. P. 



1993. Spawning stock biomass per recruit in fisheries 



