δXPOM ~ glm(f(class) + f(layer) + f(season) + Lon + Lat + C/N + T + S + Chl + Nit]                                             (2) where δXPOM, Lon, Lat, C/N, T, S, Chl, and Nit denote δ13CPOM or δ15NPOM, longitude, latitude, C:N ratio, temperature, salinity, chlorophyll-a concentration, and nitrate concentration, respectively. The chlorophyll-a and nitrate concentrations were transformed into logarithmic values. The arguments of the f functions are categorical variables that are used to simulate non-linear relationships. The numbers of classes were defined by GMM and BIC, while those of layer and season were three each (surface, subsurface, and 100-m depth in layer and winter [January–February], spring [March–June], and summer [July–September] in season). The explanatory variables used in the full GLMs were chosen based on the retraction of multicollinearity. We also used GLM approaches that included a quadratic expression in the model, as Nakamura et al. (2022) did, as well as a generalized additive model approach, as Kodama et al. (2021) did. However, as the deviance explained values of the models did not improve, we opted for the simple GLM approach.