Background/Question/Methods Organisms are linked together in ecosystems by a network of energy, matter, and informational exchanges. This network allows one species to influence others without direct contact. These indirect effects can be dominant components of ecological and evolutionary relationships, and are a prime source of ecological complexity. Here, we build on earlier work to show that environ indirect effects tend to develop rapidly in network models of energy-matter flux in ecosystems. We addressed two related questions. First, how much of the potentially infinite extended network is required for (1) the proportion of total system throughflow (TST) derived from indirect flux to exceed that from direct flux, and (2) to account for 50% and 95% of TST? We estimated this by determining the pathway length at which these conditions occurred. Second, what is the decay rate for energy-matter in these thermodynamically open ecosystems? We investigated these questions first in sixteen seasonal network models of nitrogen flux in the Neuse River Estuary, NC, and then in several previously published models of biogeochemical cycling and energy dynamics to determine the generality of our results.

Results/Conclusions Our results show that indirect effects develop rapidly in network models of energy-matter flux in ecosystems. In all of the models we investigated the indirect component of TST exceeded direct by a pathway of length 3. There was no temporal variation in the Neuse Estuary models, and no difference between biogeochemical and energy based models. This result strongly suggests that even in structurally dynamic models that might change configuration before a given extended network is fully realized, indirect effects can be dominant components of the system activity. There was larger variation in the pathway lengths at which 50% and 95% of the TST was recovered. For example, in an oyster reef model of energy flux it required all pathways up to length 6 to account for 95% of TST, while it required pathways of length 158 in the average Neuse River Estuary model. The energy-matter decay rates in these network models also varied. It was slowest in the Neuse River Estuary models, with an average value of 0.98, and longest in two models of energy flux, with rates of 0.59. We conclude that indirect effects tend to develop rapidly in ecological network, bolstering the Holoecology hypothesis that indirect effects are dominant in ecological and evolutionary relationships.