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

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 ontogenetic shift at the postflexon stage. To back-calculate the size-at-age of individual fish, we modified the biological intercept (BI) model to account for ontogenetic changes in the otolith-size-fish-size relationship and compared 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-calculating 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.

**********

Otolith-based back-calculation models of size-at-age rely on the assumption that the relationship between otolith and somatic growth is a constant proportion. This has often been examined 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 isolation and can occur simultaneously in multiple life stages (Hare and Cowen, 1995; Vigliola et al., 2000; Morita 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 variability in the OS-FS relationship.

Back-calculation models differ primarily in their ability to compensate for potential deviations away from a constant proportion between otolith size and fish size. The biological intercept (BI) model (for details on the model see Campana [1990]) compensates for growth effects by incorporating estimates of fish size and otolith size at the origin of the OS-FS proportionality. 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 incorporates the allometric shape of the relationship into the back-calculation model (for details see Vigliola et al. [2000]). Therefore, although these models can compensate for growth effects when age and ontogenetic effects are linked, they cannot provide accurate estimates when ontogenetic influences act independently of effects caused by growth and age. One means of compensating for ontogenetic shifts in the OS-FS relationship is to use the BI model separately for specific life stages. This model can be useful for providing accurate back-calculations across stage-specific transitions, such as metamorphosis (Jenkins, 1987; Campana, 1990; Otterlei et al., 2002).

We first assess whether the number of ring increments in otoliths accurately reflects absolute age in larvae and juvenile cultured (known-age) delta smelt (Hypomesus transpacificus). Second, we evaluate the degree to which age-independent variability occurs in the OS-FS relationship, as well as whether growth rate and ontogenetic effects modify the proportionality of otolith growth to fish growth. Finally, we modify the BI model to account for ontogenetic stage-specific transitions of the OS-FS relationship and compare these results with those from the TVG and MF models to a to assess the performance of our model for size-at-age back-calculations for delta smelt.

The delta smelt is a small osmerid fish endemic to the San Francisco Bay estuary (McAllister, 1963; Moyle, 2002). Historically one of the most common fishes, it was listed as "threatened" under the Federal and State Endangered Species Acts in 1993 (Moyle et al., 1992; USFWS, 1995; Sweetnam, 1999). Recent precipitous declines in the populations have led to a major investigation regarding the cause of such declines. A few of the potential sources include contaminants and exotic species (Bennett and Moyle, 1996; Bennett et al., 2005), both of which may result in reduced growth rates and poor recruitment. Examination of these hypotheses requires accurate estimates of back-calculated size-at-age for a growth-history assessment of the delta smelt (Fujiwara et al., 2005).