## 2 Materials and Methods
### Stable Isotope Analysis  
We first analyzed the natural abundance and isotopic composition of energy sources (carbon and nitrogen) in the _Microcyts aeruginosa_ and _Unio douglasiae_ samples. We then examined the assimilation of \({}^{13}\)C- and \({}^{15}\)N-enriched sources derived from the plankton food web during laboratory incubation with _Unio douglasiae_. When both carbon and nitrogen isotope tracers were added to M-water, inorganic forms of both \({}^{13}\)C and \({}^{15}\)N tracers were assimilated into cyanobacteria through photosynthesis and newly biosynthesized phytoplankton cells. Increase in the atom% of filter feeders indicates the assimilation of newly biosynthesized phytoplankton cells into mussels through feeding activity.  
Briefly, the bivalve samples were dissected to separate the digestive gland, stomach, muscle (abductor), gill, and mantle (three samples per tissue). All tissue samples were freeze-dried and ground to a fine powder using a grinder (FRITSCH-Planetary Mono Mill, Pulverisette 6, Germany). Homogenized powder samples of each tissue were decalcified with 1 N HCl for at least 24 h to remove the remaining carbonates. However, subsamples for \(\delta^{15}\)N analysis were not treated with acid because HCl treatment may affect the \(\delta^{15}\)N value [22; 23]. Following acid treatment, the samples were re-dried using a freeze drier, ground to a fine powder, and thoroughly mixed prior to analysis. Stable carbon and nitrogen isotopic ratios were measured using a continuous-flow isotope-ratio mass spectrometer (Isoprime; GV Instrument, UK) coupled to an elemental analyzer (Euro EA 3000-D, Italy).  
Figure 2: Distribution of shell length and weight (ash-free dry-matter: AFDM) of freshwater bivalve _Unio douglasiae_ Griffith et Pidgeon used in this study (\(n=83\)).  
Isotopic ratios are presented as \(\delta\) values (%) relative to the Vienna Pee Dee Belennite (vPDB) standard and atmospheric N\({}_{2}\) for carbon and nitrogen, respectively. The reference materials were IAEA-CH6 (6\({}^{13}\)C = \(-\)10.45 \(\pm\) 0.04%) and IAEA-N1 (8\({}^{15}\)N = 0.4 \(\pm\) 0.2%). The analytical precision was within 0.2% and 0.3% for carbon and nitrogen, respectively. Isotopic ratios were expressed as per mil (%) using the standard delta (\(\delta\)) notation (Equation (3)):  
\[\delta\) X = {(R\({}_{\rm sample}-R\)std)/R\({}_{\rm std}\)} \(\times\) 1000 (%)  
where X = \({}^{13}\)C or \({}^{15}\)N, R = \({}^{13}\)C/\({}^{12}\)C or \({}^{15}\)N/\({}^{14}\)N, and std (standard) = vPDB for carbon or atmospheric N\({}_{2}\) for nitrogen. The \(\delta\)-values were converted to atom%, which is more appropriate for labeled samples [24]. The conversion was performed using Equation (4):  
\[\rm A\ (atom\%)=100/[1/[(\delta\ sample/1000+1)\times a_{ns}]+1] \tag{4}\]  
where the a\({}_{ns}\) values for carbon and nitrogen were 1.118 \(\times\) 10\({}^{-2}\) and 3.677 \(\times\) 10\({}^{-3}\), respectively.  
The assimilation rate (AR) of _Unio douslusiae_ of labeled phytoplankton in M-water was calculated using the method described by [PERSON] et al. (1987) [25] (Equation (5)):  
\[\rm ARs\ (\mu g\ C\ mg^{-1}\!\cdot\!h^{-1})=\{(C_{is}-C_{ns})/(C_{ic}-C_{ns}) \}\times C/t \tag{5}\]  
where C\({}_{is}\) is the atom% of \({}^{13}\)C in the incubated sample, C\({}_{ns}\) is the atom% of \({}^{13}\)C in a natural (non-incubated) sample, C\({}_{ic}\) is the atom% of \({}^{13}\)C in inorganic carbon, t is the incubation time (h), and C is the concentration of particulate organic carbon (POC) (\(\mu g\ C\ mg^{-1}\ h^{-1}\)).