286 



Fishery Bulletin 104(2) 



60 80 100 120 140 160 180 200 220 



Precaudal length (cm) 



Figure 6 



Percent versus precaudal length curves for eastern North 

 Pacific female (heavy lines) and male (light lines) salmon 

 sharks (Lamna ditropis) with 95'?- confidence bands on 

 percent mature. Diamond and circle show estimates of 

 median precaudal length at maturity (MPCL) for females 

 and males respectively. Confidence bands (dotted lines) 

 are 2.. 5"" and 97.5'*' empirical percentiles obtained by 

 bootstrapping. 



(Fig. 3 1, demonstrates that vertebral growth patterns 

 are a reliable indicator of age in salmon sharks. Preci- 

 sion was high between and within readers with limited 

 differences (Table 1) that were attributable to random 

 error. These results provided us with a high degree of 

 confidence in the age assessments determined from the 

 von Bertalanffy growth model (with vertebral sample 

 data), and hence in the resulting life history parameter 

 estimates. 



Tanaka (1980) and Nagasawa (1998) stated that salm- 

 on sharks produce one ring per year, but a RMI analy- 

 sis was not provided in their studies. Our RMI analysis 

 verified an annual periodicity of banding patterns for 

 salmon sharks, ranging from 73 cm to 213.4 cm PCL 

 and encompassing ages 1 to 20 for females and ages 1 

 to 17 for males. The major period of growth occurs from 

 May through November, slowing some as January ap- 

 proaches (Fig. 3). A brief cessation, or extreme slowing, 

 of growth (ring formation) occurs between January and 

 March, and growth increases again in April-May. Al- 

 though we were able to examine specimens from every 

 month of the year, additional samples from December 

 through April would enhance RMI precision. 



The similar von Bertalanffy growth parameter es- 

 timates generated from female vertebral sample data, 

 back-calculated data, and the combination of the two 

 indicated that sample size was sufficiently large and 

 encompassed the known size range of the species. Von 

 Bertalanffy parameters for males would have been 

 improved with a larger sample size that would have 

 reduced the difference between values of 'k' from ver- 

 tebral sample and back-calculated data (Table 2). More 

 samples would likely have had little influence on L ^ for 



either sex because salmon sharks close to maximum 

 length were examined in the present study. It is pos- 

 sible that the discrepancy between female and male 

 sample sizes could have influenced the outcome of the 

 likelihood ratio test. However, with the differences in 

 observed maximum length (and estimated L,) between 

 the sexes and the small standard errors associated 

 with the male von Bertalanffy estimates (Table 2). it 

 is unlikely that an increased male sample size would 

 have altered the test result. 



The error associated with back-calculated length ver- 

 sus the actual length at a given age has been a focal 

 point of papers by Campana (1990), Francis (1990) and 

 Ricker (1992) and prompted our evaluation of several 

 proportional back-calculation methods. There was a 

 statistically valid reason for using the quadratic-modi- 

 fied Dahl-Lea (Eq. 3) over the linear-modified Dahl-Lea 

 (Eq. 2) (see "Results" section); however, the only way 

 to cross-compare all four back-calculation methods in 

 a biologically meaningful way was to apply all of them 

 to the vertebral sample data. Both modified Dahl-Lea 

 equations were more accurate in representing the mean 

 sample length-at-age data than the standard Dahl-Lea 

 or the size-at-birth-modified Fraser-Lee equations (Fig. 

 5, A and B). However, the quadratic-modified Dahl-Lea 

 was the best predictor of prior length-at-age (i.e., best 

 resembled our vertebral sample length-at-age data). 

 Although these back-calculation results are, of course, 

 dependent on the assumption that growth has not sig- 

 nificantly changed over time, and are applicable only 

 to salmon sharks, they demonstrate the importance 

 of choosing the appropriate method to minimize error, 

 which results in a greater ability to accurately model 

 growth. Accurate growth parameters will result in more 

 accurate demographic parameters and stock assess- 

 ments, leading to more responsible management. Even 

 greater confidence could be achieved if animals collected 

 in the past were available because they would allow a 

 direct comparison of size-at-age then and now in order 

 to verify that the growth rate for the salmon shark has 

 not changed. 



Our results show that salmon sharks in the ENP 

 attain their maximum size at a faster rate (k) than 

 those from the WNP (Table 2). We were unable to test 

 the statistical significance of these differences because 

 neither Tanaka (1980) nor Nagasawa (1998) provided 

 point estimates and standard error values for their 

 WNP data. There were, however, significant resultant 

 biological differences present. Both female and male 

 salmon sharks reach first age at sexual maturity ap- 

 proximately 2 years earlier in the ENP than in the 

 WNP. Female salmon sharks in the WNP mature be- 

 tween 8 and 10 years of age (Tanaka, 1980; Nagasawa, 

 1998). From the reproductive tracts examined, we found 

 that female salmon sharks in the ENP reach sexual 

 maturity between ages 6 and 9. Although age at first 

 maturity was earlier in the ENP, length at maturity 

 appears to be similar; 160-180 cm PCL in the WNP, 

 and a MPCL = 164.7 cm PCL in the ENP (Fig. 6). Male 

 salmon sharks in the WNP mature at approximately 



