Linear correlation analysis in finding interactions: Half of predicted interactions are undeterministic and one-third of candidate direct interactions are missed

An ecological network can be constructed by calculating the sampling data of taxon  sample type. A statistically significant Pearson linear correlation means an indirect or direct linear interaction between two taxa, and a statistically significant partial correlation based on Pearson linear correlation, due to elimination of indirect effects of other taxa, means a candidate direct interaction between two taxa. People always use Pearson linear correlation to find interactions. However, some undeterministic interactions may be found and some candidate direct interactions may be missed when using this method. The results show that partial linear correlation (y) is approximately half of the Pearson linear correlation (x) (y=-0.0064+0.4785x, r 2 =0.173, p<0.00001, n=1447), which means that indirect interactions increase mean interaction strength of taxa in the network. In all predicted interactions by partial linear correlation, about 34.35% (x, 0100%) (i.e., one-third) of them are not successfully detected by linear correlation. In all predicted interactions by Pearson linear correlation, 50.58% (y, 0100%) (i.e., half) of them are undeterministic interactions, i.e., not successfully detected by partial linear correlation, and 49.42% (z, 0100%) (i.e., half) of them are candidate direct interactions, i.e., successfully detected by partial linear correlation also. The proportion of missed (x), mis-predicted (y) and precisely predicted candidate direct interactions (z) by Pearson linear correlation analysis decreases (r=-0.49, p=0.07), increases (r=0.48, p=0.08), and decreases (r=-0.48, p=0.08) slightly with the number of taxa (m) respectively. Results show that the precisely predicted (z) candidate direct interactions by Pearson linear correlation analysis are not necessarily those with the highest Pearson linear correlations. We should not try to choose a portion (e.g., 49.42% (z)) of predicted interactions with the greatest Pearson linear correlations as candidate direct interactions. We suggest jointly using Pearson linear correlation and partial linear correlation to analyze various interactions. Candidate direct interactions detected by both linear correlation measures should be the most focused interactions, seconded by those interactions detected by partial linear correlation only and by Pearson linear correlation only.