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



95 



al.^). The second data set included mostly adult animals 

 obtained opportunistically from recreational and com- 

 mercial catches in the eastern Gulf of Mexico (Bullock 

 et al., 1992). The SEDAR stock assessment review panel 

 based their advice on models that used the former selec- 

 tion curve (Kingsley'); however the effect of using the 

 latter curve was examined as a sensitivity analysis. The 

 two curves are contrasted in Fig. 4A. 



The fishing mortality rate on the most vulnerable age 

 class was modeled as follows: 



0/,, 1900 <y< 1979 



'5v'i*2^i979' 1980<y<1990 

 ^3^1980-89 1990 <y 



(24) 



where /, = a time series of historical effort; and 

 (/)j, (t>2, 03, 6y are parameters to be estimated. 



In the present study, effort was assumed to track the 

 U.S. Census'' for the number of people living in South 

 Florida coastal counties between 1900 and 1980. From 

 1980 to 1989 this assumption was no longer required 

 owing to the availability of several time series of relative 

 abundance (see below). Instead, interannual variations 

 in fishing mortality were modeled according to Equation 

 5 with median (^.,Fjc,-c|, log-scale variance a7,.=0.15 and 

 correlation coefficient p^, = 0.5, which essentially amounts 

 to a mild constraint on year-to-year changes in F. The 

 nonzero correlation coefficient is intended to reflect the 

 momentum in effective fishing effort from one year to the 

 next that arises from a combination of market demands 

 and the tendency of many fishermen to target only the 

 species they are most adept at catching. Even so, the 

 relatively large variance term admits substantial inter- 

 annual variations if the data warrant them. Moreover, 

 runs with p^,= 0.0 (no year-to-year momentum) did not 

 produce substantially different results. 



The effect of the harvest moratorium was modeled 

 as a percentage ^g of the average fishing mortality rate 

 in the 1980-89 period. Relatively uninformative priors 

 were used for (p^ and (p^ (Fig. 3, B and C). A somewhat 



* Porch, C. E., A-M. Eklund and G. P. Scott. 2003. An assess- 

 ment of rebuilding times for goliath grouper. Sustainable 

 Fisheries Division Contribution SFD-2003-0018. Southeast 

 Fisheries Science Center, 75 Virginia Beach Drive, Miami, 

 Florida 33149. 26 p. 



5 Kingsley, M. C. S., ed. 2004. The Goliath Grouper in 

 southern Florida: assessment review and advisory report. 

 Report prepared for the South Atlantic Fishery Management 

 Council, the Gulf of Mexico Fishery Management Council, 

 and the National Marine Fisheries Service, 17 p. South 

 Atlantic fishery Management Council, 1 Southpark Circle, 

 Charleston SC"29406. 



^ Population of Florida Counties by Decennial Census: 1900 

 to 1990, 4 p. 1995. Compiled and edited by Richard L. 

 Forstall. Population Division, U.S. Bureau of the Census. 

 Washington, DC 20233 



more informative prior with bounds between 0.01 and 

 0.5 was used for ip., based on the opinions of members 

 of the SEDAR panel (Fig. 3D). 



Survey information Porch and Eklund (2004) have 

 developed relative indices of abundance from two visual 

 surveys: the personal observations of a professional 

 spearfisher (DeMaria") and a volunteer fish-monitor- 

 ing program administered by the Reef Education and 

 Environmental Foundation (REEF 2000). In addition. 

 Cass-Calay and Schmidt*^ have standardized catch rate 

 data collected in the Ten Thousand Islands area by the 

 Everglades National Park (ENP). The two visual surveys 

 are assumed to reflect the abundance of mature fish 

 ages 6 and older (based on diver reports of size). The 

 ENP catch rate index, on the other hand, is assumed to 

 reflect the relative abundance of juveniles with relative 

 vulnerabilities given by the dome-shaped gamma func- 

 tion (normalized to a maximum of 1): 



■'ENP. a 



° ^,l-°/Oin.y. 

 ^100% 



(25) 



where Ojoo', - ^he most vulnerable age; and 

 CV = the coefficient of variation. 



Estimates for ajQ,,,; (3.47) and CV (0.34) were obtained 

 by fitting the mortality-weighted gamma curve to the 

 frequency of ages -7 in the Ten Thousand Islands data 

 mentioned earlier (for more detail see Porch et al.^). The 

 resulting curve is shown in Figure 4B. 



Anecdotal Impressions of stock status Johannes et al. 

 (2000) pointed out that local fishermen often disagree 

 with the conclusions drawn by scientists in data-poor 

 situations and suggest that many times additional data 

 will prove the fishermen correct. As mentioned ear- 

 lier, expert judgements about the relative abundance 

 of a stock can be treated as data or represented by a 

 "prior." We collected information on the value of s at 

 the time moratoriums began (1990) by interviewing 

 fishermen and divers who had been active in southern 

 Florida since the early 1960s or before. Specifically, 

 interviewees were asked to state their perception of 

 the percent reduction in goliath grouper populations 

 from the time they began diving to the time the mora- 

 torium on catch was imposed (1990). The average per- 

 cent reduction reported for large goliath (approximately 

 age 6 and older) was 86% (standard deviation of about 

 13%, Table 1). This information was modeled as data in 

 accordance with Equation 20. 



 DeMaria, D. 2004. Personal, obsery. P.O. Box 420975, 

 Summerland Key, FL 33042. 



** Cass-Calay, S. L., and T. W. Schmidt. In review. Stan- 

 dardized catch rates of juvenile goliath grouper, Epinephelus 

 itajara, from the Everglades National Park Creel Survey, 

 1973-1999. 



