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



37 



OS-FS relationships and inaccurate size back-calcula- 

 tions. Indeed, Otterlei et al. (2002) found significant 

 differences in the OS-FS relationships for Atlantic cod 

 reared at different temperatures and therefore tempera- 

 ture effects can result in biased back-calculations if not 

 considered in back-calculation procedures. 



Despite the strong correlation between otolith and so- 

 matic growth during the preflexion stage, a significant 

 shift in this relationship occurred during caudal fin 

 flexing in the juvenile stage. This morphological transi- 

 tion signals a deviation from constant proportionality 

 in the OS-FS relationship for delta smelt. Therefore, 

 the appropriate choice of a back-calculation model will 

 depend on the form of the relationship between otolith 

 size and fish size. Incorrect assumptions regarding the 

 shape of the OS-FS relationship in various back-cal- 

 culation models may cause errors in back-calculation 

 of size-at-age and the predictability of growth rates 

 (Hare and Cowen, 1995; Otterli et al., 2002). Campana 

 (1990) suggested the use of a stage-specific form of the 

 BI model to account for the ontogenetic shifts in the 

 OS-FS relationship. 



Comparison of the TVG and MF model with 

 the stage-specific BI model 



The ontogenetic stage-specific BI model used in our 

 study provided the most parsimonious size-at-age esti- 

 mates. The TVG consistently underestimated size-at- 

 age, whereas the MF model over-estimated size-at-age 

 for fish greater than 30-40 dah (Fig. 5). Estimated mean 

 size-at-age for the stage-specific BI model was most 

 similar to the observed size-at-age with the minimum 

 and maximum percent deviation of individual size-at- 

 age symmetrically distributed about the mean observed 

 size-at-age. In contrast, the minimum and maximum 

 percent deviation was negative for the TVG model and 

 positive for the MF model (Table 4). 



Unlike the stage-specific BI model, the TVG and MF 

 models did not accurately estimate size-at-age because 

 of ontogenetic shifts in the OS-FS relationships. The 

 TVG model was developed to compensate for growth-rate 

 effects in the OS-FS relationship (Sirois et al., 1998). 

 However, for reared delta smelt, growth rate effects in 

 the OS-FS relationship were minimal. When growth-rate 

 effects are negligible, the results of the TVG and the 

 nonstage-specific BI model should be identical (Sirois et 

 al., 1998). This study demonstrates that when ontoge- 

 netic shifts occur in the OS-FS relationship independent 

 of growth-rate effects, the TVG model may give poor 

 estimates of size-at-age. Moreover, Vigliola et al. (2000) 

 found the MF model accurately estimated size-at-age 

 for three species of Diplodus (seabream), because of the 

 allometric OS-FS relationship. However, for delta smelt, 

 the simple allometric relationship of the MF model con- 

 sistently resulted in an overestimation of size-at-age be- 

 cause of an ontogenetic shift in the OS-FS relationship. 



The transition from the preflexion larval stage to the 

 postflexion juvenile stage created difficulties for accu- 

 rately estimating size-at-age for both the TVG and MF 



models. Owing to the unique ontogenetic shift in the 

 OS-FS relationship that delta smelt undergo, the stage- 

 specific BI model more accurately estimated fish size- 

 at-age. However, because of the variability in observed 

 length-at-age, each model described population growth 

 rates with a high degree of certainty (all r^ values were 

 greater than 0.93). Therefore, we argue that caution 

 should be taken when describing patterns in hatchery- 

 reared growth rates because measured growth rates in 

 our study were significantly reduced in comparison to 

 field growth rates (first author, unpubl. data). Finally, 

 although the intercepts for the stage-specific BI model 

 were derived from the mean population life-stage tran- 

 sition (12 mm SL), the size at life-stage transitions 

 for individuals can be variable, resulting in complex 

 individual biological intercepts that were not taken into 

 consideration. 



Conclusions 



Criteria for choice of growth back-calculation models 



The recent interest in back-calculated size-at-age for 

 individual fish based on otolith increments has resulted 

 in the development of numerous methods to back-calcu- 

 late size-at-age. The choice of various back-calculation 

 methods can be difficult because assumptions underlying 

 each model may not be evaluated completely. To guide 

 the proper choice of back-calculation models, we recom- 

 mend a critical examination of the OS-FS relationship. 

 Furthermore, the assessment of ontogenetic variability 

 and growth effects (i.e.. Hare and Cowan, 1995) should 

 be evaluated prior to choosing a model. Application of 

 back-calculation techniques requires validation of otolith 

 growth and somatic growth relationships for each spe- 

 cies. Therefore, validation may even need to be conducted 

 on a species- or stock-specific basis, and at various levels 

 of environmental variability (see Otterlei et al., 2002). 

 Moreover, accounting for ontogenetic and growth effects 

 on the proportionality of otolith size to fish size will help 

 guide the development and application of appropriate 

 back-calculation models and will lead to accurate esti- 

 mates of size-at-age for fish recruitment studies. Thus, 

 we conclude that the modified BI model will allow for 

 an accurate estimate of growth histories and reliable 

 information for determining factors influencing delta 

 smelt recruitment. 



Acknowledgments 



We thank D. Martasian, J. Raum, L. Lewis, and Z. Kane 

 for the work on this project. We also thank the Associa- 

 tion of Bay Areas Governments (ABAG), Interagency 

 Ecological Program, and the CALFED Bay-Delta Eco- 

 system Restoration Program for Funding; the Graduate 

 Group in Ecology at University of California Davis; and 

 S. Morgan and P. Moyle for helpful comments on the 

 manuscript. 



