## 2 Materials and Methods
### Microalgae Growth and Nutrient Recycling from Liquid Digestate and Liquid Slurry  
The first set of experiments was developed in batch mode, without external O2 input, to evaluate the performance of microalgae in removing nutrients from diluted slurry and digestate samples. As previously noted, in order to avoid inhibitions, three dilutions were prepared from the initial effluents DL0 and SL0: 1/10, 1/3, and 1/2 noted as 10%, 30%, and 50%, so COD and NH4-N concentrations were approximately equal to or less than those of municipal wastewater taken as a reference, cf. reference [22]. During this series of experiments, Erlenmeyer flasks of a 200 mL working volume, containing liquid substrate, were inoculated with 10% (_v/v_) Ma-B flocs as inoculum. Erlenmeyer flasks were incubated at 25 \({}^{\circ}\)C, under 16/8 h light/dark cycles, and mixed by an orbital shaker at 250 rpm for 14 days.  
All experiments were performed in triplicate. Liquid effluents were analyzed daily for COD and NH4-N concentrations. The growth of microalgae was estimated in terms of chlorophyll(a) concentration expressed in mg Chl (a)\(\cdot\)g\({}^{-1}\) VSS. Indeed, the amount of Chl (a) is related to the dominance of microalgae presence and allows the calculation of the Autotrophic Index (AI) defined as the ratio of non-photosynthetic organic material amounts to live plant (photosynthetic) material amounts. The AI is generally used to qualify surface waters and effluents where high values indicate large amounts of non-photosynthetic organic material [21]. In our case, the AI is used to describe the trophic state of the microalgae-bacteria community and identify the community abundance: Autotrophic or heterotrophic dominance. To interpret our results, we chose to refer to the decrease in the AI value, indicating the evolution towards an autotrophic dominance. The predominance of autotrophic organisms is given by the lower values of AI.  
The total concentration of Chlorophyll(a) was obtained after extraction from a 10 mL sample with 10 mL of the methanol solution (1M) for 24 h in darkness at 4 \({}^{\circ}\)C. The suspension was centrifuged at 4000 rpm for 15 min. The absorbance was measured with a spectrophotometer (UV-Vis 2550, Shimadzu, Kyoto, Japan) at 652 nm and 665 nm according to the measurement protocol defined by [PERSON] et al. [23]:  
Chlorophyll(a) = 16.29 \(\times\) A\({}_{665}\) - 8.54 \(\times\) A\({}_{652}\).  
The autotrophic index (mg VSS-mg\({}^{-1}\) Chl (a)) was calculated according to [PERSON] et al. [21] to determine the dominance of microorganisms. Specific growth rates (\(\upmu\)) were also calculated using the following equation:  
\[\mu=\frac{\ln\left(\frac{X_{\mathrm{t}}}{X_{0}}\right)}{t-t_{0}}\]  
where \(X_{0}\) is the concentration of algal biomass measured as the chlorophyll (a) content (mg Chl (a)-g\({}^{-1}\)VSS) at the initial time (\(t_{0}\)) and \(X_{t}\) is the concentration of algal biomass at a specific time (f). Finally, microscopic observations of the morphology of Ma-B flocs were performed using a LEITZ Dialux 20 microscope (Stuttgart, Germany) connected to a SONY color camera (3 CCD), Stuttgart, Germany, and then the images of the Ma-B flocs were analyzed using Visilog 6.3 software (French free software) to identify the microalgal communities present in the samples.