Hobbs et al,: Modification of the biological intercept model to account for ontogenetic effects in Hypomesus transpacificus 



33 



Table 2 



Summary of the three back-calculation models examined in this study: the time-varying growth (TVG) model (Siroiset al. 1998), 

 modified Fry (MF) model (Vigliola et al. 2000). and the biological intercept (BI) model (Campana 1990). L=standard length; 

 if=otolith radius; Lop = standard length-at-biological intercept; L, = standard length-at-age i\ L ,=standard length-at-capture; 

 i?(,p=otolith radius-at-biological intercept; fi, = otolith radius-at-age i\ iJj,p,=otolith radius-at-capture; W=mean otolith increment 

 width during each life stage; W,=otolith increment width at i; G^.=growth effect; and a = allometric shape parameter. 



Back-calculation models 



Equation 



Reference 



Time-varying growth (TVG) 

 Modified Fry (MF) 



Biological intercept (BI) 



Results 



Validation of daily otolith increment formation 



The relationship between the number of increments 

 and days after hatching of delta smelt larvae are 

 shown in (Table 1; Fig. 1). The slope of the regres- 

 sion of increment count on known-age was not sig- 

 nificantly different from one and thus indicated 

 that increment formation occurred daily. However, 

 the intercept was significantly different from zero 

 (P<0.001), indicating that the first increment was 

 not laid at hatching, rather that ring formation 

 began 6 dah. This observation was confirmed by 

 examination of larvae sampled at one and five dah 

 (Table 1). 



Mean somatic and otolith growth 



All somatic otolith-growth relationships were best 

 described by life-stage-specific linear regression 

 models, where larval (0-20 dah, 5-12 mm SL) and 

 juvenile (>20 dah, >12 mm SL) life stages were 

 considered separately. Calculated Akaike informa- 

 tion criterion (Sokal and Rohlf, 1973) for the linear 

 models were lower than polynomial models ranging 

 from the 2"'' to 9'^ orders. Somatic growth showed varia- 

 tions in growth over time: fast growth occurred from 

 hatching to 40 dah, followed by a period of slowed growth 

 from 40 dah up to 80 dah. After 80 dah, fish experienced 

 a period of rapid somatic growth associated with the 

 juvenile stage (Fig. 2, A and C). Otolith growth showed 

 a different trend. Otolith growth was slow from hatching 

 to 40 dah, which then increased exponentially from 40 

 dah to 100 dah, indicating that the relationship between 

 otolith growth and fish growth changes abruptly around 

 40 dah with the completion of caudal flexing (Fig. 2B). 

 Finally, the relationship between otolith size and fish 

 size was best described by a stage-specific linear regres- 

 sion (Fig. 2D), which accounted for the lack of constant 

 linear proportionality of otolith growth to fish growth. It 

 is important to note that some patterns in the residuals 

 were apparent in the early larval stages. However, we do 



not consider these slight deviations to have a significant 

 effect on further residual analyses. 



Growth and ontogenetic effects and size 

 back-calculations 



Correlations of age-independent effects and growth-rate 

 effects are shown in Figure 3, A and B. The strong cor- 

 relation between standard length-on-age residuals and 

 otolith radius-on-age residuals may indicate that otolith 

 size is proportional to fish size. The age-independent 

 variability in the OS-FS relationship was accounted for 

 by examining the unexplained variability in the residual 

 analysis of otolith and fish size-on-age. Only 11% of the 

 unexplained variability could be associated with age- 

 independent effects. The Pearson correlation coefficient 

 for the residual of standard length-on-age and otolith 



