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

Otolith-size--fish-size relationship

The results of this study showed that minimal age-independent variability occurred in the OS-FS relationship and that growth rate effects were negligible (Fig. 3, A and B). Removing the effect of age resulted in a strong correlation between otolith growth and fish growth, indicating that at the preflexion stage, otolith growth was proportional to somatic growth. However, the OS-FS relationship showed a significant interruption in linear growth due to an ontogenetic shift at the postflexion stage, thus demonstrating that the assumption of constant proportionality was violated (Fig. 4). Moreover, this change in proportionality corresponded with the transition from preflexion larvae to postflexion-stage juveniles. Several studies, across broad taxonomic orders have demonstrated similar deviations from proportionality in the OS-FS relationship (e.g., flatfish (Rhombosolea tapirina and Ammotretis rostratus) [Jenkins, 1987], rainbow smelt (Osmerus mordax) [Sirois et al., 1998], and Atlantic cod (Gadus morhua) [Otterlei et al., 2002]), which were also associated with life-stage transitions.

Measured growth-rate effects were weak for delta smelt (Fig. 3B) and, thus, are not likely to further explain the age-independent variability in the OS-FS relationship. In contrast, Sirois et al. (1998), found significant growth-rate effects in the OS-FS relationship for rainbow smelt. Furthermore, Hare and Cowen (1995) found both growth-rate effects and ontogenetic shifts in the OS-FS relationship for bluefish larvae (Pomatomus saltatrix). These studies highlight the different mechanisms responsible for the variability in the otolith and somatic growth relationship, and, thus, potential violations in the constant assumed proportionality for linear back-calculation models.

Other factors that can influence the OS-FS relationship include temperature and salinity. In the field, delta smelt can experience a broad range of temperatures during their larval stage. The effects of differing temperatures at this life stage on the OS-FS relationship and the influence on otolith back-calculations from field-caught fish is unknown. It is assumed that otolith growth is allometric to fish growth during seasonally variable temperatures. For our study, delta smelt were reared in temperature and salinity controlled conditions, and therefore temperature and salinity were considered to have negligible effects and did not influence the variability in the OS-FS relationship. However, temperature variability can result in different OS-FS relationships and inaccurate size back-calculations. Indeed, Otterlei et al. (2002) found significant differences in the OS-FS relationships for Atlantic cod reared at different temperatures and therefore temperature effects can result in biased back-calculations if not considered in back-calculation procedures.

Despite the strong correlation between otolith and somatic growth during the preflexion stage, a significant shift in this relationship occurred during caudal fin flexing in the juvenile stage. This morphological transition 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-calculation 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.