616 



Fishery Bulletin 89|4|, 1991 



c 

 i 



-a 



e 



2000 



200 



Otolith Radius (//in) 



Figure 7 



Plot of terminal standard length and otolith radius for all aged 

 shortbelly rockfish (N 249). Shown is the predicted curve from 

 the segmented model spanning the full range of data (upper 

 panel), with Roman numerals for each of the four distinct 

 growth stanzas. The lower panel enlarges the earliest growth 

 stages (<200(jm OR). Circles are fish taken in Isaacs-Kidd 

 trawls, and triangles are from plankton nets. 



of 7.5-10.0 mm SL (lower panel of Figure 7). Within 

 this range, the relationship of SL to OR did not differ 

 significantly between the nets (t 0.50, df 4, P>0.05). 



Standard length vs. age 



Our back-calculation of standard length-at-age (SLy) 

 is based on the implicit assumption that the mean 

 back-calculated length at any particular age is similar 

 to the mean length of fish actually captured at those 

 earlier ages. Violation of this assumption is the so- 

 called Rosa Lee's phenomenon (Ricker 1979), which 

 can arise when mortality rates are size-selective and 

 from a number of other causes, such as biased sam- 

 pling. However, our data show that mean length-at- 

 age during the first 20 days of life, back-calculated 

 from juveniles at least 60 days old, passes through 

 the observed values of SL and age at the time of cap- 

 ture for young larvae (Fig. 8). This result suggests 



Table 2 



Parameter estimates for the segmented regression model 

 describing the relationship between standard length (mm) 

 and otolith radius (OR. jim); Y-intercept (a), slopes for each 

 segment (b^-b,), and intersection points of the segments 

 (c,-c 3 ) on the X (OR) axis. Note that, except for c,-c 3 , these 

 are algebraic transformations of the actual parameters fitted 

 by the regression procedure (see Appendix B). Estimates of 

 length for a given OR based on the values given below ignore 

 the smoothing described in Appendix B, but will be close ap- 

 proximations of the values that would be obtained using the 

 original parameterization. 



Transformed parameter 



Estimate 



a 



b, 

 b 2 



b 3 



K 



c, 



Co 



2.92 



0.1233 



0.0219 



0.0599 



0.0327 



38.72 



73.10 

 431.31 



(0 



10.0 

 9 

 8 

 7 

 6.0- 

 5 0;, 



- 

 W 4 



o g. 



Back-calculated from juveniles 

 Measured lai 



O T 



§ ° t 



r^-'s 8 

 '' ° § e 8 



§ 8 5 o 







10 



Kge (d) 



15 



20 



Figure 8 



Scattergram of terminal standard length and age for larvae 

 < 20 days (open circles). Solid line depicts the back-calculated 

 mean size-at-age ( ± 1 SD) during the larval stage of juvenile 

 fish (terminal age >60 days). 



that Rosa Lee's phenomenon is unlikely to distort our 



findings to any appreciable degree. 



The predicted fit of the composite function [ SL = 

 g(f(age))] to the back-calculated size data was good 

 (Fig. 9). Note that individual fish followed their own 

 growth trajectories, producing serial correlation in 

 the residuals. The slight lack of fit around age = 70 

 days (see Figure 6) is also seen more easily in this 

 figure. 



