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Fig. 2 Map of the world showing geographic locations of all the networks used in the study. Colored dots are shaded according to 1e number of the five common induced subgraphs in each network.

Figure 2 Map of the world showing geographic locations of all the networks used in the study. Colored dots are shaded according to 1e number of the five common induced subgraphs in each network.

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Table 1 Mean number of individuals per sample for each functional group. Interactions (the interactions found in higher levels are also listed) with statistically significance for reliability
Table 1 Mean number of individuals per sample for each functional group. Interactions (the interactions found in higher levels are also listed) with statistically significance for reliability
Table 1 Networks used in analysis. Networks published prior to 2010 were downloaded from the Ecopath website (www.ecopath org). All networks were assigned both a three letter abbreviation (Abbr.) and a number (Num.) that is used in subsequent tables and ficures.
Table 1 Networks used in analysis. Networks published prior to 2010 were downloaded from the Ecopath website (www.ecopath org). All networks were assigned both a three letter abbreviation (Abbr.) and a number (Num.) that is used in subsequent tables and ficures.
Table 2 Metadata describing the motivation for creating the food web model and the different emphasis on species groupings in each study system. See Table 1 for full ecosystem names associated with the first column, ‘ Abbr.’. ‘Percent of FW nodes aggregated’ is the number of species groups that contain multiple species divided by the total number of species groups in the original food web model, as defined by the author, ‘FW nodes’. ‘RAM nodes’ is the number of nodes in the RAM after removing evclhlcityv and detritne
Table 2 Metadata describing the motivation for creating the food web model and the different emphasis on species groupings in each study system. See Table 1 for full ecosystem names associated with the first column, ‘ Abbr.’. ‘Percent of FW nodes aggregated’ is the number of species groups that contain multiple species divided by the total number of species groups in the original food web model, as defined by the author, ‘FW nodes’. ‘RAM nodes’ is the number of nodes in the RAM after removing evclhlcityv and detritne
Fig. 1 The five six-node graphs below are those that appear in 14 RAMS (Fig. 1a) and 13 RAMS (Figs. 1b-1e). None of the graphs in Fig. | appear as induced subgraphs in any of the RRAMS. radius of a graph is the lowest eccentricity.
Fig. 1 The five six-node graphs below are those that appear in 14 RAMS (Fig. 1a) and 13 RAMS (Figs. 1b-1e). None of the graphs in Fig. | appear as induced subgraphs in any of the RRAMS. radius of a graph is the lowest eccentricity.
Fig. 5 a-b Principal components of (a) food web and (b) RAM networks. See Table 1 for key of numeric labels of networks.
Fig. 5 a-b Principal components of (a) food web and (b) RAM networks. See Table 1 for key of numeric labels of networks.
Fig. 6 a-b Dendrogram resulting from cluster analysis of (a) food web and (b) RAM networks. A unique color is assigned to each group of nodes within the dendrogram whose linkage is less than 70% of the maximum linkage. X-axis: the numeric network abbreviations specified in Table 1. Y-axis: distance between two networks being connected.
Fig. 6 a-b Dendrogram resulting from cluster analysis of (a) food web and (b) RAM networks. A unique color is assigned to each group of nodes within the dendrogram whose linkage is less than 70% of the maximum linkage. X-axis: the numeric network abbreviations specified in Table 1. Y-axis: distance between two networks being connected.
Fig. 1 Some of the rice arthropods. Pictures were taken by the author on July 29, 2015, from Kaili, Guizhou, China.
Fig. 1 Some of the rice arthropods. Pictures were taken by the author on July 29, 2015, from Kaili, Guizhou, China.
Table 1 Comparison of results of Spearman rank correlation (SRC) and partial Spearman correlation (Partial SRC) No. SS Yes Partial SRC but SS Not SRC: Total No. of statistically significant Partial SRC (p<0.01) but statistically not significant SRC (ps0.01); No. SS Yes SRC but SS Not Partial SRC: Total No. of statistically significant SRC (ps0.01) but statistically not significant Partial SRC (ps0.01); No. SS Yes SRC & SS Yes Partial SRC: Total No. of both statistically significant SRC (ps0.01) anc statistically significant Partial SRC (ps0.01). For proportion correlation measure, in all predicted candidate direct interactions by partial correlation, about 6.82% (X, 0~28.64%) of them are not successfully detected by proportion correlation (Table 2). In all predicted interactions by proportion correlation, 72.24% (y, 28.01~100%) of them are undeterministic interactions, i.e., not successfully detected by partial correlation. In all predicted interactions by proportion correlation, 27.76% (Z, 0~71.99%) of them are candidate direct interactions, i.e., successfully detected by partial correlation (Table 1). The regression relationship between proportion correlation (1) and its partial correlation (pr) is
Table 1 Comparison of results of Spearman rank correlation (SRC) and partial Spearman correlation (Partial SRC) No. SS Yes Partial SRC but SS Not SRC: Total No. of statistically significant Partial SRC (p<0.01) but statistically not significant SRC (ps0.01); No. SS Yes SRC but SS Not Partial SRC: Total No. of statistically significant SRC (ps0.01) but statistically not significant Partial SRC (ps0.01); No. SS Yes SRC & SS Yes Partial SRC: Total No. of both statistically significant SRC (ps0.01) anc statistically significant Partial SRC (ps0.01). For proportion correlation measure, in all predicted candidate direct interactions by partial correlation, about 6.82% (X, 0~28.64%) of them are not successfully detected by proportion correlation (Table 2). In all predicted interactions by proportion correlation, 72.24% (y, 28.01~100%) of them are undeterministic interactions, i.e., not successfully detected by partial correlation. In all predicted interactions by proportion correlation, 27.76% (Z, 0~71.99%) of them are candidate direct interactions, i.e., successfully detected by partial correlation (Table 1). The regression relationship between proportion correlation (1) and its partial correlation (pr) is
No. SS Yes Partial PC but SS Not PC: Total No. of statistically significant Partial PC (p<0.01) but statistically not significant PC (ps0.01); No. SS Yes PC but SS Not Partial PC: Total No. of statistically significant PC (ps0.01) but statistically not significant Partial PC (ps0.01); No. SS Yes PC & SS Yes Partial PC: Total No. of both statistically significant PC (ps0.01) and statistically significant Partial PC (ps0.01).
No. SS Yes Partial PC but SS Not PC: Total No. of statistically significant Partial PC (p<0.01) but statistically not significant PC (ps0.01); No. SS Yes PC but SS Not Partial PC: Total No. of statistically significant PC (ps0.01) but statistically not significant Partial PC (ps0.01); No. SS Yes PC & SS Yes Partial PC: Total No. of both statistically significant PC (ps0.01) and statistically significant Partial PC (ps0.01).
Table 3 Statistically significant Spearman rank correlations and true interactions determined by partial correlations (in bold). As done in Zhang and Li (2015), we suggest jointly using general correlation and partial correlation to analyze various interactions. Candidate direct interactions detected by both general correlation measures should be the most focused interactions, seconded by those interactions detected by partial correlation only and by general correlation only.
Table 3 Statistically significant Spearman rank correlations and true interactions determined by partial correlations (in bold). As done in Zhang and Li (2015), we suggest jointly using general correlation and partial correlation to analyze various interactions. Candidate direct interactions detected by both general correlation measures should be the most focused interactions, seconded by those interactions detected by partial correlation only and by general correlation only.
Table 1 Network information based on Pearson linear correlation and partial linear correlation (Zhang, 2011).
Table 1 Network information based on Pearson linear correlation and partial linear correlation (Zhang, 2011).
ke > ps0.1; **: 5: p<0.05; 05; ***: p<0.01; n=15. Table 2 Pearson linear correlations between various measures. Let ID numbers 1-9 in Table 2 be sample size (1), total number of taxa (2), possible maximum interactions (i.e., total Pearson linear correlations, N) (3), mean of Pearson linear correlations (PLCs) (4), number of statistically significant direct + indirect linear interactions derived from Pearson linear correlation (p<0.01; L) (5), L/N (%) (6), mean of partial linear correlations (Partial PLCs) (7), number of statistically significant candidate direct linear interactions derived from partial linear correlation (p<0.01; LP) (8), and LP/N (%) (9). The calculated Pearson linear correlations between various measures are indicated in Table 2. The calculated Pearson linear correlations between various measures are indicated in Table 2. As indicated in Fig. 1, linear regression relationships can be found between some measures.
ke > ps0.1; **: 5: p<0.05; 05; ***: p<0.01; n=15. Table 2 Pearson linear correlations between various measures. Let ID numbers 1-9 in Table 2 be sample size (1), total number of taxa (2), possible maximum interactions (i.e., total Pearson linear correlations, N) (3), mean of Pearson linear correlations (PLCs) (4), number of statistically significant direct + indirect linear interactions derived from Pearson linear correlation (p<0.01; L) (5), L/N (%) (6), mean of partial linear correlations (Partial PLCs) (7), number of statistically significant candidate direct linear interactions derived from partial linear correlation (p<0.01; LP) (8), and LP/N (%) (9). The calculated Pearson linear correlations between various measures are indicated in Table 2. The calculated Pearson linear correlations between various measures are indicated in Table 2. As indicated in Fig. 1, linear regression relationships can be found between some measures.
Table 3 Simplified approximate quantities to estimate network properties.
Table 3 Simplified approximate quantities to estimate network properties.
Fig. 1 Upper: linear relationship between the number of candidate direct linear interactions (y) and the number of indirect + direct linear interactions (x) calculated by Pearson linear correlation measure; Middle: linear relationship between the proportion of direct interactions in possible maximum interactions (y%) and mean Pearson linear correlation (x); Lower: linear relationship between partial linear correlation (y) and Pearson linear correlation (x).
Fig. 1 Upper: linear relationship between the number of candidate direct linear interactions (y) and the number of indirect + direct linear interactions (x) calculated by Pearson linear correlation measure; Middle: linear relationship between the proportion of direct interactions in possible maximum interactions (y%) and mean Pearson linear correlation (x); Lower: linear relationship between partial linear correlation (y) and Pearson linear correlation (x).
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