## 2 Membership-Fusing Model of Sludge-Treatment Process
### Sludge-Treatment Process and Representative Methanogen  
The prior technical route to treat surplus sludge for a wastewater treatment plant in China is thickening, thermal hydrolysis, AD, dewatering and final disposal [1], as is shown in Figure 2. To be specifically, thickening, either gravity, or floatation, or mechanical thickening, aims to reduce water content of the sludge to be about 95%, which benefits the subsequent steps. Thermal hydrolysis purposes to improve the efficiency of AD process by enhancing the degradability of organic compounds and methane yields [13; 14]. AD is the critical processing stage to degrade sludge. Dewatering, belt dewatering, centrifugal dewatering, and plate-frame dewatering included, is designed to compress the sludge volume, which alleviates the burden on the final disposal. To understand the efficiency of the sludge-treatment process, AD processing stage is widely considered to be the essential point [5; 6]. As is shown in Figure 2, the three stages--two stages before AD which could affect the effect of AD, and ADstage, defined as Stage I, II, and III--must be the concerned processing stages in the sludge-treatment process. Sampling points are set at the exit of each processing stage among the three stages to collect sludge samples for further analysis on methanogen community, as is shown in Figure 2. Sludge samples from sampling point I, after thickening and before thermal hydrolysis, could characterize the feature of sludge in stage I. Sampling point II and III, after thermal hydrolysis and before AD, and after AD and before dewatering, could represent stage II and III, respectively. Paralleling sludge samples with a certain number, usually ranging from 3 to 10, are gathered from each processing stage. The quantity ratio of _Methanosaeta_ to _Methanobacterium_ could represent the shift of methanogen community, defined as the independent variable \(x\), calculated by Equation (1):  
\[x=\frac{R_{1}}{R_{2}} \tag{1}\]  
where \(R_{1}\) and \(R_{2}\) stand for the reads of genes of the genera of _Methanosaeta_ and _Methanobacterium_, respectively. High-throughput sequencing technology is applied to measure the quantities of the two genera of methanogens. Each sludge sample generates a great deal of reads of genes pertaining  
Figure 1: Procedure to build the membership-fusing model. Figure 2: Sludge-treatment process and distribution of sampling points. to various methanogens by the gene sequencing. Summing the reads of genes belonging to genus _Methanosaeta_ and genus _Methanobacterium_ up, respectively, and then do the ratio of the two sums to generate a certain value of \(x\). The representative role of _Methanosaeta_[8] and _Methanobacterium_[37] is clarified as follow: first, previous studies have found that acetonitrile methanogen _Methanosaeta_ and hydrogenotrophic methanogen _Methanobacterium_ are the two main functional methanogens in AD process [37; 38]. Secondly, their relative shift in quantity varies greatly in each sludge-processing stage, owing to the different growing requirements of these two genera of methanogens and the specific environment each stage provides [7; 8; 37]. Lastly, the relative variation of these two genera of methanogens is in a dynamic stable range of change in each stage due to the relatively steady surrounding of each processing stage. Consequently, a specific \(x\) value could reflect a specific state of the methanogen community, characterize a sludge-processing stage among the three stages, and reveal the efficiency and environmental condition of the representative processing stage. The value of \(x\) is distributed in a certain range for the three-stage sludge-treatment process and \(x\) also has a relative stable value range for each processing stage. Specifically, for stage I, the physical treatment provides the same environmental stress for the two genera of methanogens and the \(x\) value is usually below 10.