  Indirect effects are powerful influences in ecosystems that may maintain
species diversity and alter apparent relationships between species in
surprising ways. Here, we applied Network Environ Analysis to 50
empirically-based trophic ecosystem models to test the hypothesis that indirect
flows dominate direct flows in ecosystem networks. Further, we used Monte Carlo
based perturbations to investigate the robustness of these results to potential
error in the underlying data. To explain our findings, we further investigated
the importance of the microbial food web in recycling energy-matter using
components of the Finn Cycling Index and analysis of Environ Centrality. We
found that indirect flows dominate direct flows in 37/50 (74.0%) models. This
increases to 31/35 (88.5%) models when we consider only models that have
cycling structure and a representation of the microbial food web. The
uncertainty analysis reveals that there is less error in the I/D values than
the $\pm$ 5% error introduced into the models, suggesting the results are
robust to uncertainty. Our results show that the microbial food web mediates a
substantial percentage of cycling in some systems (median = 30.2%), but its
role is highly variable in these models, in agreement with the literature. Our
results, combined with previous work, strongly suggest that indirect effects
are dominant components of activity in ecosystems.
