Terrestrial index modelling
Prior to estimating the contribution of terrestrial species to the diet of individual fish (i.e., terrestrial index), we corrected for the influence of environmental (or dietary ) water on the δ2H of fish (Solomon et al. 2009) and followed the approach outlined in Vander Zanden et al. (2016):
\begin{equation} \omega_{\text{compound\ }}=\ {1-\left(1-\omega\right)}^{TL-1}\nonumber \\ \end{equation}
Where \(\omega_{\text{compound\ }}\)is the proportion of water δ2H in δ2H values of fish consumers,\(\omega\) is the proportion of water δ2H entering the consumer. For \(\omega\), we assumed a value of 0.2 as suggested by Wilkinson et al. (2015). We did not estimate the trophic level ( TL) of the fish, but assumed a theoretical level of 2.5, as we analyzed omnivorous species and individuals.
In a second step, we modelled δ2H values for fish consumers either obtaining their unexchangeable hydrogen either entirely from aquatic, or terrestrial resources:
\begin{equation} \delta^{2}H_{C\ 100\%\ aquatic\ }=\left(\omega_{\text{compound\ }}\times\ \delta^{2}H_{\text{water\ }}\right)+\left(1-\ \omega_{\text{compound\ }}\right)\times\ \delta^{2}H_{\text{aquatic\ }}\nonumber \\ \end{equation}\begin{equation} \delta^{2}H_{C\ 100\%\ terrestrial\ }=\left(\omega_{\text{compound\ }}\times\ \delta^{2}H_{\text{water\ }}\right)+\left(1-\ \omega_{\text{compound\ }}\right)\times\ \delta^{2}H_{\text{terrestrial\ }}\nonumber \\ \end{equation}
\(\delta^{2}H_{\text{water\ }}\)is the δ2H of the river water. We did not collect water samples ourselves, but instead used a mean value (-55.06 ‰) from Chen et al. (2023), who collected river water in Spremberg and Zerre in June and December 2021. For\(\delta^{2}H_{\text{aquatic\ }}\), we used the mean value of seston (from locations downstream and upstream of the dam respectively), whereas for \(\delta^{2}H_{\text{terrestrial\ }}\), we used the mean value of the terrestrial insects (from locations downstream and upstream of the dam respectively).
The terrestrial index for individual fish was modelled, using a modified two-end members mixing model similar to the allochthony index from Keva et al. (2022).
\begin{equation} terrestrial\ index\ =\ \frac{{(\delta}^{2}H_{\text{C\ \ }}-\ \delta^{2}H_{C\ 100\%\ aquatic\ })}{{(\delta}^{2}H_{C\ 100\%\ terrestrial\ }-\ \delta^{2}H_{C\ 100\%\ aquatic\ })}\nonumber \\ \end{equation}
\(\delta^{2}H_{\text{C\ \ }}\)is the measured value of the individual fish consumer. The terrestrial index ranges from 0-1, with high values indicating the incorporation of hydrogen from terrestrial insects, while low values indicate the incorporation of hydrogen from aquatic insects.