Fig. 2

New methods for detecting potential correlations. a The presence–absence matrix is the binary form of original abundance matrix. In this matrix, columns present samples, rows present species, and entries are the presence (1) or absence (0) of a species. Samples are organized as a presence–absence matrix in which i = 1 to R rows and j = 1 to C columns. The entry a_ij in the matrix represents the presence (1) or absence (0) of species j in sample i. b Co-occurrence probability matrix for the sample data. In loose definition method, co-occurrence means two species in the same sample have both non-zero abundance. The co-occurrence probability of two species is defined as co-occurrence times / total sample count. c Network establishment based on different co-occurrence probability thresholds. Traditional network construction workflow only calculates correlations between species between 100% co-occurrence probability (left network), which is too strict for sparse distribution. More correlations are detected between co-occurrence probability set to 60% (right network, correlations detected by loose definition only were colored in red). d An overview of the PCA-PMI process. Species abundance distribution was calculated by the mutual information method and then the zero-order network, which contains all the mutual information, was constructed. PCA-PMI process was applied to adjust the zero-order network until no correlations changed