Potts and Manooch Estimated ages of Pagrus pagtvs 



83 



where L^ = back-calculated total length to aniuilusA; 



a = intercept from the linear total lengtii-otohth 



radius regression; 

 b = slope from the linear total length-otolith 



radius regression: 

 L(. = total length at time of capture; 

 /?, = otolith radius to annulus A; and 

 /?(. = total otolith radius at time of capture. 



The von Bertalanffy ecjuation. L, = L |1 - e.\p(-A'(^-/(,)|, 

 was fitted to back-calculated lengths-at-ages for the most 

 recently formed annuli (Ricker, 1975; Everhart et al., 1981; 

 Vaughan and Burton, 1994). Growth parameters were es- 

 timated by using SAS PROC NLIN with the Marquardt 

 Option (SAS Institute, 1982) for all aged fish and for fish 

 obtained from fishery-dependent sampling. 



Differences in mean back-calculated length at age for 

 the most recently formed annulus for the three sample 

 sources, i.e. recreational, commercial, and fishery-indepen- 

 dent, were tested by using the general linear model analy- 

 sis of variance. 



To estimate the whole weight of gutted red porgy landed 

 in the commercial fishery and to estimate stock biomass 

 from assessment models, a regression of hii fisli tveif^ht) 

 on \n(fish length ) was performed and transformed to W = 

 aiL)^, where W = weight in g, and L = total length in mm. 



Age-length keys were constructed from observed age at 

 length by sample source in which the ages were unadjust- 

 ed for time of year. Fish that were aged were assigned to 

 25-mm length intei-vals. 



Results 



Red porgy sampled for our study ranged from 176 to 733 

 mm TL and from 1 17 to 5895 g in whole weight. Ages were 

 determined for 631 of 634 (99'7f) sectioned sagittal oto- 

 liths. Of those aged, 603 idd'v'c) otoliths were considered 

 legible to record measurements from the core to each suc- 

 cessive opaque zone and the otolith margin. On twenty 

 additional samples, we were able to measure only the oto- 

 lith radius. Sectioned otoliths exhibited a recurrent pat- 

 tern of alternating wide translucent zones and thin opaque 

 zones. Estimated ages ranged from 1 to 18 years. 



Analyses of marginal increment data indicated that the 

 opaque zones were annular in nature and were formed in 

 the spring (Fig. 1). Mean relative marginal increments for 

 ages 2 through 8 were lowest in March through May and 

 were the only months that had marginal increments equal 

 to zero. They then steadily increased from June through 

 October and remained high through February. 



Back-calculated total lengths at age of red porgy were 

 estimated from the parameters from the regi-ession equa- 

 tion of total length (L) on otolith radius (R^.). The plot 

 of length on radius was linear, and the linear regression 

 equation that best fitted the data was L = -132.84 -i- 

 10.87(fl ) (;--=0.91, «=623). Using the Francis (1990) body 

 proportional hypothesis, we found that weighted mean 

 back-calculated lengths ranged from 103 mm for age-1 fish 

 to 721 mm for age-18 fish (Table 1). 



The back-calculated lengths at the last annulus forma- 

 tion were used to estimate the von Bertalanffy equation. 

 The equation parameters (±1 SE) were L„ = 644.72 ±17.93, 

 A' = 0. 15 ±0.01, and /„ = -0.76 ±0. 10. The theoretical lengths 

 at age ranged from 149 mm at age 1 to 605 mm at age 18. 

 Theoretical lengths closely fitted the observed and back- 

 calculated lengths through age 14 (Table 1). When we used 

 fishery-dependent samples only to generate the von Berta- 

 lanffy growth equation, the resulting parameters (±1 SE) 

 were L,= 773.73 ±39.49, A' = 0.09 ±0.01 and t„ = -1.96 

 ±0.21. The fishery-dependent theoretical lengths at age 

 ranged from 181 mm at age 1 to 646 mm at age 18. 



We used ages 2 through 6 and data years 1996 through 

 1998 to compare length at age of the three data sources be- 

 cause the three sets overlapped for those ages and years. 

 The ANOVA on the mean back-calculated length at age of 

 the most recently formed annulus between sample sources 

 indicated a significant difference in age at size between 

 the MARMAP, headboat, and commercial red porgy sam- 

 ples (r-=0.88; F-value=522.21; P=0.0001 for all combina- 

 tions) and were represented by the model 



TL = a„ + Ycc + y,,h + ^ /3, A, , 



where c = 1 if fishery = commercial, or c = if fishery i^ 

 commercial; 

 h = 1 if fishery = headboat, or /i = if fishery ^ 



headboat; 

 A, = 1 if age = 2, or A, =0 if age ^ 2, etc.; and 

 J = age categories. 



Average TL = a^ for fishery = fishery-independent and 

 age = 6; average TL = a,, -i- y^.c for fishery = commercial 

 and age = 6; etc. The model indicated no year effect, and no 

 interaction between fishery and age. MARMAP (fishery- 

 independent) samples were smaller at age than those from 

 the commercial and headboat fisheries. Although mean 

 back-calculated lengths at age between headboat and com- 

 mercial data sources were statistically different, the dif- 

 ferences were slight (<15 mm) (Fig. 2). 



