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.