364 



Fishery Bulletin 100(2) 



<2 2000 



Figure 5 



(Ai Annual estimated instantaneous (ishing mortality rates (mean 

 F on ages 4-8), and (B> recruitment to age 1 from calibrated VPA 

 applied to red porgy off the southeastern United States based 

 on primary catch matrix varying instantaneous natural mortality 

 rate (M). 



about 1980 has included only values greater than unity 

 (Fig. IIB). 



Discussion 



This work includes numerous advances from previous 

 assessments (Vaughan et al., 1992; Huntsman et al.^). The 

 major improvements are availability of additional fish- 

 ery-dependent and fishery-independent aging data and of 

 fishery-independent indices for calibrating VPAs. Other 

 changes include expanded geographic range, new esti- 

 mates of sex ratios and maturity schedules, new growth 

 parameters, application of a more modern algorithm for 

 calibrated VPA, and application of a nonequilibrium sur- 

 plus-production model. Our conclusions agree with both 

 earlier assessments in finding a population in decline. 



Because unbiased sampling of wild fish stocks is ex- 

 tremely difficult and fishery data sets are small (in num- 

 ber of years of data), fish population models are not pre- 

 cise approximations of reality. Accurately characterizing 

 uncertainty in assessment results is difficult or impossi- 

 ble: although statistical estimates of uncertainty can be 

 obtained, it is not known how to balance them against fac- 

 tors that tend to increase certainty, such as agreement 

 among data sources or methods and among assessments 

 conducted over time. Anv formal estimate of uncertainty 



hi the present assessment results would be large. None- 

 theless, in light of our use of complementary models, sev- 

 eral independent data sources, and two largely indepen- 

 dent sets of age-length keys, and based on agreement with 

 past assessments, we believe that the present results are 

 unequivocal in their major finding of a severely depleted 

 population. 



By using two treatments of observed zeroes in CPE se- 

 ries, we illustrated that some results can be sensitive to 

 the method used to treat zeroes. Although addition of a 

 constant before logarithmic transformation is a widely 

 used practice and has been a common statistical recom- 

 mendation (e.g. Snedecor and Cochran, 1980; Berry, 1987), 

 it is becoming evident that the practice can be problematic 

 in estimation of abundance indices. Logarithmic transfor- 

 mation is made under the assumption of lognormally dis- 

 tributed data, and presence of zeroes in itself violates that 

 assumption. Moreover, results can depend strongly on the 

 additive constant chosen (Porch and Scott, 1994; Ortiz et 

 al., 2000). The root of the problem is that transformed ze- 

 roes are usually extreme values in the data set and thus 

 highly influential. Several other statistical models have 

 been proposed, of which the most promising in this appli- 

 cation may be the delta-lognormal model (Lo et al., 1992; 

 Ortiz et al., 2000). However, this is still an active area 

 of methodological research, and the matter remains unre- 

 solved. We thus used two treatments of zeroes and have 



