where δt and δt − 1 are the average fish tissue δ13C or δ15N values at times t and t − 1, and Bt and Bt − 1 are the average fish wet weights. With this model, we assumed that temporal changes in muscle tissue isotope δ values are only caused by dilution from new tissue growth and the relative contribution of tissue turnover is negligible, which has been widely affirmed for juvenile fishes (Gamboa-Delgado et al., 2008; Sakano et al., 2005; Vander Zanden et al., 1998).