30 



Abstract — We investigated age, 

 growth, and ontogenetic effects on 

 the proportionality of otolith size to 

 fish size in laboratory-reared delta 

 smelt (Hypomesus transpacificus) 

 from the San Francisco Bay estuary. 

 Delta smelt larvae were reared from 

 hatching in laboratory mesocosms for 

 100 days. Otolith increments from 

 known-age fish were enumerated to 

 validate that growth increments were 

 deposited daily and to validate the 

 age of fish at first ring formation. 

 Delta smelt were found to lay down 

 daily ring increments; however, the 

 first increment did not form until six 

 days after hatching. The relationship 

 between otolith size and fish size was 

 not biased by age or growth-rate 

 effects but did exhibit an interruption 

 in linear growth owing to an ontoge- 

 netic shift at the postflexon stage. To 

 back-calculate the size-at-age of indi- 

 vidual fish, we modified the biological 

 intercept (BI) model to account for 

 ontogenetic changes in the otolith- 

 size-fish-size relationship and com- 

 pared the results to the time-varying 

 growth model, as well as the modified 

 Fry model. We found the modified BI 

 model estimated more accurately the 

 size-at-age from hatching to 100 days 

 after hatching. Before back-calculat- 

 ing size-at-age with existing models, 

 we recommend a critical evaluation 

 of the effects that age, growth, and 

 ontogeny can have on the otolith- 

 size-fish-size relationship. 



Modification of the biological intercept model to 

 account for ontogenetic effects in laboratory-reared 

 delta smelt (Hypomesus transpacificus)* 



James A. Hobbs (contact author) ^-^ 



William A. Bennett''^ 



Jessica E. Burton' 



Bradd Baskerville-Bridges^ 



Email address fori A Hobbs: |ahobbs@ ucdavis.edu 



' Bodega Marine Laboratory 

 2099 Westside Road 

 Bodega Bay, California 94923-0247 



^ John Muir Institute for the Environment 

 University of California, Davis 

 One Shields Ave, 

 Davis, California 95616 



5 Department of Animal Sciences 

 University of California, Davis 

 One Shields Ave 

 Davis. California 95616 



Manuscript submitted 24 November 2004 

 to the Scientific Editor's Office. 



Manuscript approved for publication 

 15 March 2006 by the Scientific Editor. 



Fish. Bull. 105:30-38 (2007). 



Otolith-based back-calculation models 

 of size-at-age rely on the assumption 

 that the relationship between otolith 

 and somatic growth is a constant pro- 

 portion. This has often been exam- 

 ined by simply correlating otolith size 

 with fish size for different aged fish. 

 However, correlations of size among 

 similarly growing body parts over 

 time may not equate to proportional 

 growth among these body parts (Cock, 

 1966). A comprehensive evaluation 

 of the assumption of proportionality 

 requires examining whether somatic 

 variability is independent of age in 

 the otolith-size-fish-size (OS-FS) 

 relationship (Hare and Cowen, 1995). 

 This requires an assessment of the 

 residual variability between otolith 

 size and fish size-on-age to remove 

 the potential influence of age that can 

 bias the OS-FS relationship (Hare 

 and Cowen, 1995). Furthermore, the 

 "growth effect," where slow-growing 

 fish have larger otoliths than fast- 

 growing fish for similar-size fish, and 

 the "ontogenetic effect," where shifts 

 in the OS-FS relationship occur, also 

 need to be addressed before back- 

 calculations. None of these proposed 

 factors necessarily operate in isola- 



tion and can occur simultaneously in 

 multiple life stages (Hare and Cowen, 

 1995; Vigliola et al., 2000; Merita and 

 Matsuishi, 2001). Therefore, before 

 choosing an appropriate model for 

 back-calculating size-at-age, it is 

 necessary to identify the potential 

 mechanisms responsible for variabil- 

 ity in the OS-FS relationship. 



Back-calculation models differ pri- 

 marily in their ability to compensate 

 for potential deviations away from a 

 constant proportion between otolith 

 size and fish size. The biological in- 

 tercept (BI) model (for details on the 

 model see Campana [1990]) compen- 

 sates for growth effects by incorporat- 

 ing estimates of fish size and otolith 

 size at the origin of the OS-FS pro- 

 portionality. The time-varying growth 

 (TVG) model adjusts the contribution 

 of small and large increments with 

 regard to body size (see Sirois et al. 

 [1998] for full details), whereas the 

 modified Fry (MF) model directly in- 

 corporates the allometric shape of the 



Contribution number 2313 from the 

 Bodega Marine Laboratory, Bodega Bay, 

 California 94923-0247. 



