Results
At the meta-ecosystem level, relative patch size and resource flows interacted to influence the total biomass of the meta-ecosystems, as revealed by the analysis of deviance of the mixed effect model (Fig. 2, Chisq = 21.21, Df = 2, p < 0.001). Resource flows increased the total biomass in autotrophic-dominated meta-ecosystems (turquoise solid vs. dashed lines in Fig. 2,LASH–SHLA  sustained on average 0.22 mm2 more biomass than LA|SH , SE = 0.08, z ratio = 2.72, p = 0.006) and decreased the total biomass in heterotrophic-dominated meta-ecosystems (yellow solid vs. dashed lines in Fig. 2, LHSA–SALH sustained on average 0.39 mm2 less biomass thanLH|SA , SE = 0.11, z ratio = -3.71, p < 0.001). Resource flows did not affect the total biomass in equally-dominated meta-ecosystems (grey solid vs. dashed lines in Fig. 2, SE = 0.09, z ratio = -0.29, p = 0.769). Furthermore, relative patch size made total biomass differ among connected meta-ecosystems. Autotrophic-dominated connected meta-ecosystems had more total biomass than equally-dominated meta-ecosystems (turquoise vs grey solid lines in Fig. 2,LASH–SHLA sustained on average 0.48 mm2 more biomass thanMHMA–MAMH , SE = 0.08, z ratio = 5.67, p < 0.001) and equally-dominated meta-ecosystems had more total biomass than heterotrophic-dominated meta-ecosystems (grey vs. yellow solid lines in Fig. 2,MHMA–MAMH sustained on average 0.62 mm2 more biomass thanLHSA–SALH , SE = 0.10, z ratio = -6.06, p < 0.001).
Relative patch size similarly influenced the total biomass among unconnected meta-ecosystems, with total biomass decreasing from autotrophic-dominated meta-ecosystems to equally-dominated meta-ecosystems and heterotrophic-dominated meta-ecosystems (Fig. 2, dashed lines; comparing turquoise vs. grey, LA|SH sustained on average 0.23 mm2 more biomass thanMH|MA , SE = 0.09, z ratio = 2.67, p = 0.008; comparing grey vs. yellow, MH|MA sustained on average 0.26 mm2 more biomass than LH|SA , SE = 0.94, z ratio = -2.74, p = 0.006).
At the local level, in autotrophic patches, relative patch size and connection via resource flows interacted to influence biomass density (Fig. 3, Chisq = 6.44, Df = 2, p = 0.040). The connection increased the biomass density of large and small but not medium autotrophic local patches (solid vs. dashed green lines in Fig. 3; in top panel,LASH sustained on average 0.26 mm2/ml more biomass density than LA , SE = 0.12, z ratio = 2.16, p = 0.031; in bottom panel, SALH sustained on average 0.48 mm2/ml more biomass density than SA , SE = 0.20, z ratio = 2.37, p = 0.018; in middle panel, biomass did not differ between MAMH andMA , SE = 0.13, z ratio = - 0.57, p = 0.568). Furthermore, patch size influenced local autotrophic biomass density, as in unconnected autotrophic patches the biomass density significantly increased from small to medium and to large patches (green dotted lines in Fig. 3; in top vs. bottom panels, LA sustained on average 1.53 mm2/ml more biomass density than SA , SE = 0.18, z ratio = -8.46, p < 0.001; in middle vs. bottom panels,MA sustained on average 1.49 mm2/ml more biomass density than SA , SE = 0.18, z ratio = 8.254, p < 0.001).
Also at the local level, in heterotrophic patches, patch size and connection via resource flows interacted to influence biomass density (Fig. 3, Chisq = 15.002, Df = 2, p = 0.001). The connection decreased the biomass density of small and large but not medium heterotrophic local patches (solid vs. dashed blue lines in Fig. 3; in top panel,SHLA  sustained on average 0.76 mm2/ml less biomass density than SH , SE = 0.18, z ratio = -4.19, p < 0.001; in bottom panel,LHSA sustained on average 0.50 mm2/ml less biomass density than LH , SE = 0.15, z ratio = -3.292, p = 0.001; in middle panel, biomass density inMHMA  and MH  are not significantly different, SE = 0.15, z ratio = 0.61, p = 0.540). Furthermore, patch size influenced biomass density. Indeed, biomass density increased from small to large patches in unconnected heterotrophic patches, although not between small and medium patches (dotted blue lines in Fig. 3; in top vs. bottom panels, LH sustained on average 0.50 mm2/ml more biomass density than SH , SE = 0.15, z ratio = 3.33, p = 0.001; in middle vs. bottom panels, biomass density in MH and SH are not significantly different, SE = 0.16, z ratio = 1.23, p = 0.217).
At the local level, patch size and connection via resource flows also interacted to influence the median body size in both heterotrophic and autotrophic ecosystems (see Appendix S1) and the biodiversity of heterotrophic ecosystems (see Appendix S2). Detailed results of these analyses can be found in the respective appendices.