358 



Fishery Bulletin 105(3) 



Fisheries [NRIFSF], Japan; the Centre de Investiga- 

 cion Cientifica y de Educacion Superior de Ensenada 

 [CICESE], Mexico; and the Institute de Fomento Pes- 

 quero [IFOP], Chile). They provided 20 representative 

 and usable fin ray specimens for swordfish caught by 

 their respective regional fisheries. Specimens spanned 

 all available months of capture and body sizes of both 

 sexes. 



Specimens were processed in identical fashion with- 

 in each laboratory (e.g., the dl2 cut was used by the 

 Honolulu Laboratory for select Hawaii-based fishery 

 specimens). Digitized images of all 100 specimens were 

 prepared at the Honolulu Laboratory and file images 

 were distributed among laboratories. Most laboratories 

 conducted multiple readings by two or more readers, 

 thus enabling evaluation of precision and bias within 

 and among laboratories. 



Statistical analyses 



Conventional descriptive statistics (Zar, 1984) were 

 used to evaluate several interrelated data necessary for 

 verification or corroboration of annular periodicity and 

 size-at-age. We evaluated interrelations among fin ray 

 radius (in mm) and estimated age (in days) based on enu- 

 meration of DGIs and EFL (in cm). Regression models 

 were fitted by using nonlinear least squares (Marquardt 

 algorithm) and the best model was chosen on the basis of 

 relative r'^ values (proc nlin, SAS, vers. 8, SAS Inst., Inc., 

 Gary, NC). Likely sexual dimorphisms in relationships 

 (Sun et al., 2002) were evaluated with ANCOVA (proc 

 glm; SAS, vers. 8, SAS Inst., Inc., Cary, NC). 



Standard graphical methods and statistics (Campana, 

 2001) were used to evaluate between- and within-reader 

 bias (age-bias plots) and precision gauged by the coef- 

 ficient of variation (CV: deviation [ = SD] (100/mean) 

 (Campana et al., 1995; Campana, 2001). Observer bias 

 (accuracy) also was evaluated partly in terms of the 

 majority agreement standard generated by the afore- 

 mentioned inter-laboratory calibration exercise. Preci- 

 sion was evaluated by comparing the repeatability of 

 estimates made by readers 1 and 2 for both the speci- 

 men series provided by the inter-laboratory exercise 

 and the much larger group of specimens that were used 

 for the main study described in this article. CVs were 

 compared both within- and between-readers. 



Growth was described by fitting fin ray-based age 

 estimates to back-calculated body length-at-age by us- 

 ing von Bertalanffy growth formulas (VBGFs). Both 

 standard and generalized VBGFs (Richards, 1959) were 

 evaluated: 



Standard VBGF; L, = L^ (1 - e'* " " '»'); 

 Generalized VBGF; L, = L„ (1 - e-^^^- ""< ' -'o>)'i/'i- ""'; 



where L, = mean eye-to-fork length (EFL, in cm) at 

 age t; 

 L^ = asymptotic length; 

 t = a specific age; 

 <Q = hypothetical age at length zero; 



k and K = growth coefficients; and 

 m = fitted fourth parameter. 



Individual length-at-age was back-calculated by using 

 method II of Sun et al. (2002) which is based on the 

 formula of Ehrhardt et al. (1996); 



EFL, = (i?„/i?tot>'' EFL, 



where £FL, = back-calculated eye-to-fork length at age 

 t; 

 R^j and i?^^, are as previously defined; and 

 b = parameter derived from the relation of 

 EFL to i?,^,. 



EFL was related to R^^^ using the power equation, 



EFL = a R,J, 



where a, h = fitted parameters. 



This model was chosen because of the obvious curvilin- 

 earity of the relationship. Sex effects were evaluated by 

 using ANCOVA. 



Likelihood ratio (LR) tests (Cerrato, 1990; Quinn 

 and Deriso, 1999) were used to evaluate the effects 

 of sex and type of VBGF model for describing the 

 length-at-age relationship. For LR test statistics, the 

 additivity of untransformed data was assumed and 

 the statistics were calculated as two times the log- 

 likelihood: 



LR = [-n 1 2\[\n{2n[SSE I n]) + l], 



where SSE = error sum of squares; and 

 n = number of age classes. 



In both cases, LR test statistics were compared against 

 X~ with df = 1 by using the Akaike information criterion. 



Results 



Accuracy and precision 



A pilot evaluation of the two methods used for viewing 

 fin ray preparations (microscope, digital image analyzer) 

 indicated nearly congruent results (mean difference 

 only 0.12 ±0.087 yr or 3% of a mean age of 3.8 years; 

 matched-pairs ^test; ^=1.38; P=0.17). Directly viewed 

 and image analyzed preparations were therefore consid- 

 ered equivalent (no bias from methods) and were pooled 

 in all subsequent analyses. 



Age-bias plots for readers 1 and 2 indicated variable 

 deviations, small in relation to the age estimates, which 

 lacked major pattern over the range of all putative ages. 

 Reader I's mean age estimates regressed on reader 2's 

 age estimates deviated insignificantly from a slope of 1 

 and an intercept of 0, even if additional positive devia- 

 tions for ages > 8 were included (Table lA). Readers 



