Modification of the biological intercept model to account for ontogenetic effects in laboratory-reared delta smelt

Fishery Bulletin, Jan, 2007 by James A. Hobbs, William A. Bennett, Jessica E. Burton, Bradd Baskerville-Bridges

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 estimates. 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 ontogenetic 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 consistently resulted in an overestimation of size-at-age because of an ontogenetic shift in the OS-FS relationship.

The transition from the preflexion larval stage to the postflexion juvenile stage created difficulties for accurately 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.sup.2] 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 transition (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-calculate 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 recommend 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 species. 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 estimates 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.