General correlation and partial correlation analysis in finding interactions: with Spearman rank correlation and proportion correlation as correlation measures

Between-taxon interactions can be detected by calculating the sampling data of taxon sample type. In present study, Spearman rank correlation and proportion correlation are chosen as the general correlation measures, and their partial correlations are calculated and compared. The results show that for Spearman rank correlation measure, in all predicted candidate direct interactions by partial correlation, about 16.77% (x, 0-45.4%) of them are not successfully detected by Spearman rank correlation. In all predicted interactions by Spearman rank correlation, 47.56% (y, 0-100%) of them are undeterministic interactions, i.e., not successfully detected by partial correlation. In all predicted interactions by Spearman rank correlation, 53.45% (z, 0-100%) of them are candidate interactions, i.e., successfully detected by partial correlation. The regression relationship between Spearman rank correlation (r) and its partial correlation (pr) is pr=0.0102+0.1085r (R2=0.0181, p<0.00001, n=1004). For proportion correlation measure, in all predicted candidate interactions by partial correlation, about 6.82% (x, 0-28.64%) of them are not successfully detected by proportion correlation. In all predicted interactions by proportion correlation, 72.24% (y, 28.01-100%) of them are undeterministic interactions. In all predicted interactions by proportion correlation, 27.76% (z, 0-71.99%) of them are candidate interactions. The regression relationship between proportion correlation and its partial correlation is pr=0.07+0.0592r (R2=0.0213, p<0.00001, n=1447). The proportion of missed (x), mis-predicted (y) and precisely predicted candidate direct interactions (z) by general correlation analysis increases, increases, and decreases with the number of taxa respectively. Relationships between general correlation (r) and partial correlation (pr) mean that indirect interactions increase mean interaction strength of taxa. The precisely predicted (z) candidate direct interactions by Spearman rank correlation and proportion correlation analysis are not necessarily those with the highest Spearman rank correlations and proportion correlations. Jointly using correlation and partial correlation measures to analyze various interactions is the most reliable choice. Candidate direct interactions detected by both correlation and partial correlation measures should be the most focused interactions, seconded by those interactions detected by partial correlation only and by correlation only.