The modularity matrix Bnxn was constructed by subtracting the null model from Anxn (see Materials and Methods). The null model for the RMT was chosen as a random network, where each node in the network was randomly connected with other nodes. The random network was generated by randomizing the original network connectivity distribution, which matches the RMT connectivity distribution with R2 value of 0.99. The modularity of the original network was significantly higher than that of the random network. The calculation of the null model was obtained by iteratively randomizing the original network to calculate the M values and the average M of 10 random networks. This process was repeated 10 times, and the average M of the 10 random networks was reported as the null model. The M values of the original networks were calculated in every step (Figure 1). When the modularity matrix was Bnxn, the corresponding eigenvalue was positive and the eigenvector was the leading eigenvector in the network, i.e. with the highest eigenvalue. This eigenvector was sorted to determine the module divisions of the original network. The mathematical derivation and the direct calculation of the M value of the network is shown in the Materials and Methods section. The MENAP R script (Figure 3) can be used to construct and analyze the molecular ecological network (MEN) based on metagenomics data. The MENAP pipeline can be downloaded and run locally, and is also online at https://github.com/SCBOT/MENAP .
Application of the MENAP pipeline to characterize the response of microbial community to experimental warming in Lake DePue (Figure 2) showed that modularity value increased with the increase of temperature. This result is in agreement with previous studies that showed that bacterial networks in the surface waters of Lake Huron became increasingly modular with the increase of temperature due to greater resource competition [61, 62]. For example, the microbial network in the surface waters of Lake Huron were composed of 14 modules at 5°C, which decreased to 5 modules at 20°C .
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