Fischer et al.: Age, growth, mortality, and radiometric age validation of Lut/anus griseus 



309 



with this same method (Baker and Wilson, 2001), we 

 anticipated that gray snapper radiocarbon values would 

 be roughly similar to red snapper values for a given 

 YOB. 



To obtain the oldest portion of the otolith for radio- 

 carbon analysis, right otoliths of older gray snapper 

 with an estimated YOB after the period of atmospheric 

 testing (1973-95) were embedded in araldite epoxy 

 resin and thin sectioned (~1 mm in thickness) through 

 the core with an Isomet low-speed saw. The otolith core 

 region was isolated from the otolith section by using 

 the technique described in Baker and Wilson (2001). 

 Cores were rinsed in double-distilled de-ionized water, 

 allowed to air dry, weighed to the nearest 0.1 mg, and 

 submitted to the accelerator mass spectrometry (AMS) 

 facility in acid-washed 20-mL glass scintillation vials. 

 The mean sample weight submitted for analyses was 

 12.8 mg. 



At the AMS facility, otolith cores underwent acid hy- 

 drolysis with 85% phosphoric acid to yield CO., which 

 was then made into graphite (pure C) by reduction at 

 high temperature under vacuum. The graphite was 

 pressed onto a target, loaded on the AMS unit and 

 analyzed for radiocarbon. Samples were also analyzed 

 for 13 C to correct for natural and machine fractionation 

 effects. Radiocarbon values from individual otolith cores 

 were reported as A 14 C (mean ±SD), the adjusted devia- 

 tion from the radiocarbon activity of 19 th century wood 

 (Stuiver and Polach, 1977). 



The periodicity of opaque zone formation was also 

 examined with edge analysis. The marginal edge of 

 each otolith was examined and coded as 



1 opaque zone forming on otolith margin; 



4 translucent zone forming on margin up to 1/3 com- 

 plete; 



5 translucent zone forming on margin 1/3 to 2/3 com- 

 plete; 



6 translucent zone forming on margin 2/3 to fully 

 complete. 



Percentages of otoliths with opaque margins were plotted 

 by month of capture (Beckman et al., 1989; Campana, 

 2001; Wilson and Nieland, 2001) for all months in which 

 specimens were available. 



In order to examine the predictive capacity of otolith 

 weight (W ) to determine age in gray snapper, sex spe- 

 cific W o -age relationships were fitted by using a power 

 function with least squares with the model: Age = aW b . 

 A likelihood ratio test (Cerrato, 1990) was used to test 

 for differences between male and female models. 



Male and female TW-TL relationships were indepen- 

 dently fitted with linear regression to the model W = 

 aTL h from log 10 -transformed data. Male and female re- 

 gression coefficients were compared with an ANCOVA. 

 Variability in age, TL, and TW-frequency distributions 

 of males and females were compared with Komolgorov- 

 Smirnov two-sample tests (Tate and Clelland, 1957; 

 Sokal and Rohlf, 1995). Growth of gray snapper was 

 modeled by using all specimens of known sex. Von Ber- 



talanffy growth models of TL at age were fitted with 

 nonlinear regression by least squares (SAS 6.11, SAS 

 Institute, 1996, Cary, NO in the form: 



TL,=LM 



„l-*<nl 



where / = age in years; 

 TL = TL at age t; 



L x = the theoretical maximum TL; 

 k = the growth coefficient. 



and 



Because of a lack of smaller individuals in our sample 

 population, no y-intercepts for t were specified and 

 models were forced through (Szedlmayer and Shipp, 

 1994; Fischer et al., 2004) to better estimate juvenile 

 growth. One growth model was generated for all speci- 

 mens of known sex. Additional models were fitted inde- 

 pendently for males and females. Likelihood ratio tests 

 (Cerrato, 1990) were used to test for differences between 

 male and female models. 



The instantaneous total mortality rate (Z) was esti- 

 mated from a catch curve (Nelson and Manooch, 1982; 

 Burton, 2001) assuming our collections represented the 

 actual age distribution of the population. These esti- 

 mates were made with the regression method of plotting 

 the log t , age frequency on age. We used the absolute 

 value of the slope of the linear descending right limb of 

 the curve after full recruitment to estimate Z. 



Estimates of instantaneous natural mortality (M) 

 were computed with several methods. The first estimate 

 of M was based on Hoenig's (1983) longevity-mortality 

 relationship, where the mortality rate is based solely 

 on the oldest specimen encountered in the data set. 

 We also used Hoenig's (1983) relationship for natural 

 mortality with modifications for sample size. Natural 

 mortality was also computed with the method of Pauly 

 (1980) assuming a mean annual water temperature 

 of 25°C. Our mean annual water temperature esti- 

 mate was derived from the data buoys operated by the 

 National Oceanic and Atmospheric Administration's 

 National Oceanographic Data Buoy Center from 1995 

 to 2001. Finally, M was calculated with the Ralston 

 (1987) method, where the estimate of M is based solely 

 on a simple regression involving the Brody growth coef- 

 ficient (k). A significance level of 0.05 was used for all 

 statistical analyses. 



Results 



We sampled 833 gray snapper (441 males, 387 females, 

 and 5 individuals of unknown sex) from the recreational 

 fishery of Louisiana for morphometric data and otoliths. 

 The male:female ratio was 1:0.88; a x 2 test indicated no 

 significant difference between the proportions of males 

 and females (/ 2 =3.52 > P=0.06). Male and female speci- 

 mens ranged from 222 to 732 mm TL and from 254 to 

 756 mm TL, respectively (Fig. 1A). Both sexes exhibited 

 multimodal distributions; males were represented in the 

 greatest numbers at 450 mm TL, compared to 400 mm 



