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Fishery Bulletin 104(2) 



present along the inside edge of the cor- 

 pus calcareum at each ring, providing an 

 additional aging feature, particularly in 

 sections where the cut excluded the radi- 

 als of the intermedialia (Fig. IB). Annulus 

 measurements were made from the origin 

 of a wide band to the outer margin of the 

 adjacent narrow band. 



Two readers independently aged all cen- 

 tra two times in blind, randomized trials. 

 This procedure allowed the calculation of 

 within-reader precision, and between-reader 

 precision twice. When there was a disagree- 

 ment between readers, a final age determi- 

 nation was made by both readers viewing 

 the centrum together. Percent agreement 

 {PA=lNo. agreed/No. read]xlOO). and per- 

 cent agreement plus or minus one year (PA 

 [±1 yr]) were calculated for length groups 

 of 10 cm to test for precision. The criticism 

 of percent agreement as a measure of preci- 

 sion has been that it varies widely among 

 species and ages within a species (Beamish 

 and Fournier, 1981; Campana, 2001). The 

 criticism regarding variation among species 

 is irrelevant becauses one is only interested 

 in the particular species one is aging (i.e., 

 these particular species are not compared 

 among other species), but the criticism re- 

 garding variation of ages within a species 

 is not only relevant, but is true. There is, however, 

 validity in using percent agreement with individuals 

 grouped by length as a test of precision because it does 

 not rely on ages (which have been estimated), but rather 

 on lengths, which are empirical values (Goldman, 2004; 

 Cailliet and Goldman, 2004). Ages could be used if and 

 only if, all age classes have been validated. 



The most commonly used methods for evaluating pre- 

 cision among age determinations have been the average 

 percent error (APE ) technique of Beamish and Fournier 

 (1981) and the modification of their method by Chang 

 (1982). However, Hoenig et al. (1995) have demonstrated 

 (using the Beamish and Fournier, 1981, data) that there 

 can be differences in precision that these methods ob- 

 scure because with the APE it is assumed that the 

 variability among observations of individual fish can be 

 averaged over all age groups and that this variability 

 can be expressed in relative terms. Also, APE indices 

 do not result in values that are independent of the age 

 estimates, do not test for systematic differences, and 

 do not distinguish all sources of variability (such as 

 differences in precision with age) (Hoenig et al., 1995). 

 Good APE values appear to tell us only which reader 

 was less variable, not which was better or if either 

 was biased, which is more critical in knowing whether 

 reliable ages can be produced and replicated (i.e. is the 

 error within and between readers due to random error 

 or a systematic bias). 



Campana et al. (1995) stated the importance of a 

 separate measure for bias, and Hoenig et al. (1995) and 



Figure 1 



lA) Sagittal section of a 10-yr-old salmon shark iLamna ditropis) 

 vertebral centrum showing typical banding pattern. CR = centrum 

 radius. (B) Portion of a sagittal section from a salmon shark verte- 

 bral centrum without intermedialia, showing the distinct notching 

 pattern (white arrows) that accompanies the banding pattern and 

 that is used to aid in assessing ages. The 1.0-mm bar applies to both 

 A and B. PB = prebirth ring, B = birth ring and numbers indicate 

 rings or age in years. 



Evans and Hoenig (1998) suggested testing for sys- 

 tematic differences between readers using chi-square 

 tests of symmetry to determine whether differences are 

 systematic (biased) or due to random error. These are 

 statistically rigorous and effective methods for detect- 

 ing bias (Campana, 2001) and were conducted in the 

 present study. These techniques place all age values in 

 contingency tables and test the hypothesis that values in 

 a given table are symmetrical about the main diagonal 

 (Hoenig et al, 1995; Evans and Hoenig, 1998). They can 

 also be set up to test among all individual age classes 

 or groups of age classes (Hoenig et al., 1995). The test 

 statistic (the chi-square variable) will tend to be large if 

 a systematic difference exists between the two readers. 



A relative marginal increment (RMI) analysis was 

 used to verify the temporal periodicity of ring forma- 

 tion in the vertebrae. This is a standardized marginal 

 increment analysis whereby the margin, or growth area 

 of a centrum from the last narrow growth ring to the 

 centrum edge, is divided by the width of the last fully 

 formed growth increment (Branstetter and Musick, 

 1994; Conrath et al., 2002). Resulting RMI values were 

 compared to the month of capture. This analysis was 

 performed on immature and mature sharks separately 

 and combined. Age-zero animals were not included (be- 

 cause they have no fully formed increments). 



The von Bertalanffy growth function was fitted to 

 the vertebral age-at -length data for salmon sharks from 

 the ENP with a nonlinear least squares regression al- 

 gorithm (."nls" in S-Plus, Professional Release 1, Math- 



