## 2 Materials and Methods
### Ea-Irms  
Isotopic analysis was performed by Delta V Advantage, an isotope ratio mass spectrometer, coupled with Flash 2000, an elemental analyzer (both Thermo Fisher Scientific, Bremen, Germany), operating in dynamic flash combustion mode.  
Small pieces (<4 mm largest dimension) were cut from each sample and introduced into tin capsules. Capsules were gently crimped closed and introduced into the combustion reactor by means of MAS 200 R autosampler (Thermo Fisher Scientific, Bremen, Germany),and the reaction was supported by an oxygen pulse of 3 s. The furnace temperature was 900 \({}^{\circ}\)C. A helium flow of 100 mL/min carried the gases formed during combustion through the chromium oxide catalyst, the reduced copper and the silver cobaltous-cobaltic oxide layer. After water removal on a magnesium perchlorate trap, gases reached the GC separation column through the ConFlo IV interface and then were subjected to the isotopic composition determination on IRMS. The isotopic composition was equal to the ratio between the abundance of the heavy isotopic form compared to the light one (\({}^{13}\)C/\({}^{12}\)C) and was expressed as a deviation in parts per thousand (%), from an internationally identified standard benchmark material (Vienna Pee Dee Belemnite--VPDB). Carbon isotopic ratios were expressed according to the Equation (1):  
\[\delta^{13}\mathrm{C}\left(\%_{\mathrm{o}}\right)=\left[(^{13}\mathrm{C}/^{12 }\mathrm{C}_{\mathrm{sample}})/(^{13}\mathrm{C}/^{12}\mathrm{C}_{\mathrm{VPDB}})-1 \right]\times 1000 \tag{1}\]  
where \({}^{13}\)C/\({}^{12}\)C is the ratio between abundances of the masses of the heavy isotope and of the light one, \({}^{13}\)C/\({}^{12}\)C\({}_{\mathrm{sample}}\) is the ratio measured in the sample and\({}^{13}\)C/\({}^{12}\)C\({}_{\mathrm{VPDB}}\) is the ratio measured for the international standard. A positive value of \(\delta^{13}\)C showed that the heavy isotope had been enriched in the sample compared to the standard, while a negative value showed that, in the sample, the heavy isotope had been depleted.  
This number was then multiplied by 1000 so that \(\delta^{13}\)C was expressed in units of parts per thousand (%).  
Reference materials sucrose IAEA CH6 (\(-\)10.449 \(\pm\) 0.033%, International Atomic Energy Agency, IAEA, Vienna, Austria), caffeine IAEA-600 (\(-\)27.771 \(\pm\) 0.043%, International Atomic Energy Agency, IAEA, Vienna, Austria) oxalic acid (\(-\)14.48 \(\pm\) 0.21%, International Atomic Energy Agency, IAEA, Vienna, Austria) and L-glutamic acid (\(-\)26.389 \(\pm\) 0.042%, National Institute of Standards and Technology, NIST, Gaithersburg, MD, USA) were used to calibrate the instrument.  
The \(\delta^{13}\)C values for the standards were linearly plotted against their expected values (certified) with a regression coefficient (R\({}^{2}\)) ranging from 0.95 to 0.99 in order to ensure the complete combustion of the samples. The linear regression curve was then applied to correct the \(\delta^{13}\)C results for the samples [14].  
The measurement trueness was evaluated through the analysis of certified material CH7 polyethylene IAEA (\(-\)32.04 \(\pm\) 0.04%, International Atomic Energy Agency, IAEA, Vienna, Austria). The analytical precision of carbon isotope measurements, calculated as the mean of standard deviations (see Table 1) was 0.2%.