Laidig et al.: Growth dynamics in early life history of Sebastes jordani 



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Validation 



To validate that the increments were formed daily, we 

 only considered samples collected during the May-June 

 survey, because it was the only multiple-day cruise. 

 From the data we identified a well-defined, temporal- 

 ly discrete cohort, and estimated the average change 

 in length of individuals over the duration of the cruise. 

 We compared this rate with the rate of change in length 

 with nominal age from otoliths. 



We identified a temporally discrete cohort as follows. 

 Using the 55 aged fish (mainly juveniles) from the 

 May-June cruise, and assuming that the number of in- 

 crements approximated age in days after extrusion, we 

 linearly regressed age on SL. From the resulting re- 

 gression equation, we estimated the ages of all juveniles 

 caught (all specimens were measured, but only a sub- 

 sample of 55 fish from this cruise was aged). By sub- 

 tracting estimates of age from known dates of capture 

 (measured from the beginning of the year), we esti- 

 mated the dates when the dark check mark formed for 

 all fish sampled. A plot of frequency of occurrence 

 against estimated dates of check mark deposition was 

 used to identify the cohort. We stress that this pro- 

 cedure was used only to identify the cohort for further 

 consideration. The rate of change in length-per-unit- 

 time for fish sampled from the cohort was found by 

 calculating the rate at which the lengths of captured 

 individuals changed over the course of the 30 day 

 cruise. 



Data analysis 



Initial exploratory model development involved fitting 

 a number of equations (by least squares) to the data 

 to characterize two functional relationships: OR = 

 f(age) and SL = g(OR). For the former, we used not 

 only the radius of the otolith at the time of collection 

 (terminal OR), but also back-calculated radii measured 

 at earlier ages. Due to the serial correlation present 

 in these data (multiple observations of OR-at-age from 

 the same fish), we used the grouped jackknife tech- 

 nique (Miller 1974) to estimate standard errors of the 

 parameters. In contrast, we used only terminal values 

 of OR and SL when fitting the latter relationship. Once 

 known, the composition of these two functions {f°g} 

 defined explicitly the dependence of SL on age, i.e., 

 SL = g(f(age)). This procedure provided a better de- 

 scription of the age-length relationship than did the 

 more usual approach of fitting a growth model to back- 

 calculated SL-at-age data, even when complex formula- 

 tions were tried (e.g., the two-stage Gompertz function 

 suggested by Zweifel and Lasker 1976). 



A single-stage Gompertz growth equation (Ricker 

 1979) provided a good description of otolith growth. 



The model has three parameters (OR () , k, and g) and 

 can be expressed as: 



OR = OR,, • exp{k-[l-exp(-g-age)]}. 



Our data showed increasing variance in OR with in- 

 creasing age, so the data and the equation were log- 

 arithmically transformed prior to fitting (Zweifel and 

 Lasker 1976). 



To regress SL on OR, we developed a model con- 

 sisting of four linear segments, each describing a dif- 

 ferent growth stanza (see Appendix B for details). 

 Before selecting this segmented model, we first con- 

 sidered, and then discarded due to lack of fit, a number 

 of continuous models, including the simple two-param- 

 eter linear model, the Gompertz function, and three- 

 parameter power and exponential models with separate 

 Y-intercept terms. 



Once we had established a relationship between SL 

 and OR, we used this relationship to back-calculate SL 

 at ages younger than the terminal age-at-capture. We 

 used the "body-size proportional" method described by 

 Francis (1990) in our back-calculations, in which the 

 length at age i (some age younger than c, the age of 

 collection) for fish j (SLjj) is given by: 



SLii 



g(OR i: ) • (SL cj /g(OR cj )), 



where, as above, g( • ) is the regression equation we 

 developed to predict expected SL from OR, and SL CJ 

 is the measured length of fish j at the time of capture. 

 Note that this method corrects for the deviation be- 

 tween the length predicted by the regression model and 

 actual length at the time of capture. The well-known 

 Fraser-Lee method, which also takes into account ac- 

 tual length of an individual at the time of capture, is 

 inappropriate here because of the non-linear relation- 

 ship between SLjind OR (Campana 1990, Francis 

 1990). The fit of SL = g(f(age)) to the "observed" 

 back-calculated estimates of SLy was then evaluated 

 by examining a plot of the residuals (SL^ - SL). 



Results 



We measured SL of 1511 larval and juvenile short- 

 belly rockfish. Ages were determined for 249 fish that 

 ranged in size from 4.5 to 74.5mm SL. Of these, 194 

 (4.5-15.2 mm SL) were from the three single-day 

 cruises and 55 (14.6-74.5 mm) were from the May- June 

 cruise (Table 1). 



None of the gestating preextrusion larvae that we 

 examined possessed the dark check mark that we used 

 as the starting point for increment counts. Because of 

 this, and the presence of increments in most of the 



