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Distances between matrices were calculated using a probabilistic method [ 56].
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To determine correlation between the microbial community composition and the metabolic profiles, distance matrices using Manhattan distances [16] for microbial and metabolic profiles were calculated independently, then Pearson correlation coefficients between the two distance matrices were calculated.
Genetic distance was calculated on the basis of the number of shared bands between isolates, and similarity matrices were calculated by using the Dice coefficient (14 ).
It should be noted that the score matrices were calculated between probes and galleries with the same quality values.
Correlation matrices were calculated for both experiments and connections between genes set at the 0.8 and 0.7 thresholds, respectively.
The geographic distance matrices were calculated from the minimum distance of different groups between the 21 populations.
The distance matrices were calculated by Tree-Puzzle (version 5.2) [5.2.
Subsequently, data matrices were calculated.
Three different distance matrices were calculated.
To measure the similarity between trees, the CC of two matrices is calculated.
The inverse matrices are calculated using (3).
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